VR spiders analyses
Stefan Wiens, Dani Cosme, Stephen Pierzchajlo
2021-12-02
load packages
packages <- c('tidyverse', # data handling
'lmerTest',
'modelr',
'sjPlot',
'kableExtra',
'broom.mixed',
'gridExtra',
'brms',
'bayesplot',
'rstanarm',
'performance',
'tidybayes',
'brant')
# Install packages not yet installed
installed_packages <- packages %in% rownames(installed.packages())
if (any(installed_packages == FALSE)) {
install.packages(packages[!installed_packages], repos = c(CRAN = "https://cran.rstudio.com"))
}
# Packages loading
invisible(lapply(packages, library, character.only = TRUE))
packv <- NULL
for (i in 1:length(packages)) {
packv = rbind(packv, c(packages[i], as.character(packageVersion(packages[i]))))
}
colnames(packv) <- c("Package", "Version")
packv %>%
as_tibble %>%
arrange(Package) %>%
kable(align = "l") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))| Package | Version |
|---|---|
| bayesplot | 1.8.1 |
| brant | 0.3.0 |
| brms | 2.16.1 |
| broom.mixed | 0.2.7 |
| gridExtra | 2.3 |
| kableExtra | 1.3.4 |
| lmerTest | 3.1.3 |
| modelr | 0.1.8 |
| performance | 0.8.0 |
| rstanarm | 2.21.1 |
| sjPlot | 2.8.9 |
| tidybayes | 3.0.1 |
| tidyverse | 1.3.1 |
define aesthetics
palette <- c("#ED5C4D", "#57B5ED", "#FBBE4B") # control vs each
palette2 <- c("#ED5C4D", "#5a4491") # control vs combined
plot_aes <- theme_minimal() +
theme(legend.position = "top",
text = element_text(size = 14), #, family = "Helvetica"), does not work in Win
axis.text = element_text(color = "black"),
axis.line = element_line(colour = "black"),
axis.ticks.y = element_blank())functions
source('src/LMM_functions.R')
source('src/myround.R')
# 95% confidence intervals
ci95LL <- function(data){return(t.test(data,
conf.level = 0.95,
alternative = "two.sided")$conf.int[1])}
ci95UL <- function(data){return(t.test(data,
conf.level = 0.95,
alternative = "two.sided")$conf.int[2])}set up directories
# directory with input EEG log files
dir_log <- 'data/log'
# directory with input EEG mean amp files
dir_meanamps <- 'data/mean_amps'check file integrity
The experimental groups were VRET (virtual reality exposure treatment) and IVET (in vivo exposure treatment). Subject numbering started from 1 for the experimental group (without any knowledge of treatment). Thus, in the experimental group, each subject (fp in Swedish) has their unique number. However, subject numbering in the control group also started from 1. Thus, the same ID number (e.g., 1) in the experimental and control group refers to different people. The script handles this by adding 100 to the ID number of the control group. Thus, there is a unique code for each subject.
Below, session 1 refers to pre-treatment and session 2 to post-treatment.
experimental group
# according to subject notes
# vret codes for treatment: 1= vret, 0 = ivet
file <- 'data/VR_spider_EEG-EG_final.tsv'
listEGnotes <- read.csv(file, sep = '\t', header = T)
listEGnotes$sess1 <- 1
listEGnotes$sess1[listEGnotes$pre=='nope'] <- 0
listEGnotes$sess2 <- 1
listEGnotes$sess2[listEGnotes$post=='nope'] <- 0
# EG according to EEG log files
fps <- list.files(file.path(dir_log,'experimental'), pattern = 'fp')
listEGlog <- data.frame()
for (f in fps){ # f = fps[6]
fp <- substring(f, first = 3)
sess <- as.integer(substring(fp, first = regexpr('_',fp)[1]+1))
fp <- as.integer(substring(fp, first = 1, last = regexpr('_',fp)[1]-1))
listEGlog <- rbind(listEGlog, cbind(fp,sess))
}
rm(f,fp,fps,sess,file)
# EG according to EEG mean amps
fps <- list.files(file.path(dir_meanamps), pattern = 'fp')
listamps <- data.frame()
for (f in fps){ # f = fps[6]
fp <- substring(f, first = 3, last = 11)
sess <- as.integer(substring(fp, first = regexpr('_ses', fp)[1]+4))
fp <- as.integer(substring(fp, first = 1, last = 3))
listamps <- rbind(listamps, cbind(fp,sess))
}
listEGamps <- listamps %>% filter(fp < 100)
rm(f,fp,fps,sess)
# check subject match between EEG amps and log
# session 1
if (setequal(listEGamps$fp[listEGamps$sess==1], listEGlog$fp[listEGlog$sess==1])!=T){
print('EG: Mismatch between EEG amps and log files: Session 1')
print('Unique in EEG amps')
print(setdiff(listEGamps$fp[listEGamps$sess==1], listEGlog$fp[listEGlog$sess==1]))
print('Unique in EEG log')
print(setdiff(listEGlog$fp[listEGlog$sess==1], listEGamps$fp[listEGamps$sess==1]))
stop('EG: mismatch between EEG amps and log files: Session 1')
}
# session 2
if (setequal(listEGamps$fp[listEGamps$sess==2], listEGlog$fp[listEGlog$sess==2])!=T){
print('EG: Mismatch between EEG amps and log files: Session 2')
print('Unique in EEG amps')
print(setdiff(listEGampsfp[listEGamps$sess==2], listEGlog$fp[listEGlog$sess==2]))
print('Unique in EEG log')
print(setdiff(listEGlog$fp[listEGlog$sess==2], listEGamps$fp[listEGamps$sess==2]))
stop('EG: Mismatch between EEG amps and log files: Session 2')
}
# check subject match between notes and EEG log
# session 1
if (setequal(listEGnotes$fp[listEGnotes$sess1==1], listEGlog$fp[listEGlog$sess==1])!=T){
print('EG: Mismatch between notes and EEG log files: Session 1')
print('Unique in notes')
print(setdiff(listEGnotes$fp[listEGnotes$sess1==1], listEGlog$fp[listEGlog$sess==1]))
print('Unique in EEG log')
print(setdiff(listEGlog$fp[listEGlog$sess==1], listEGnotes$fp[listEGnotes$sess1==1]))
stop('EG: Mismatch between notes and EEG log files: Session 1')
}
# session 2
if (setequal(listEGnotes$fp[listEGnotes$sess2==1], listEGlog$fp[listEGlog$sess==2])!=T){
print('EG: Mismatch between notes and EEG log files: Session 2')
print('Unique in notes')
print(setdiff(listEGnotes$fp[listEGnotes$sess2==1], listEGlog$fp[listEGlog$sess==2]))
print('Unique in EEG log')
print(setdiff(listEGlog$fp[listEGlog$sess==2], listEGnotes$fp[listEGnotes$sess2==1]))
stop('EG: Mismatch between notes and EEG log files: Session 2')
}
# make notes list the gold standard----
rm(listEGlog, listEGamps)control group
# The same ID number (e.g., 1) in the experimental and control group refers to different people. The script handles this by adding 100 to the ID number of the control group. Thus, there is a unique code for each subject.
# according to subject notes
file <- 'data/VR_spider_EEG-CG_final.tsv'
listCGnotes <- read.csv(file, sep = '\t', header = T)
listCGnotes$fp <- listCGnotes$fp + 100 # add 100 to create a unique code
# CG according to EEG log files
fps <- list.files(file.path(dir_log,'control'), pattern = 'fp')
listCGlog <- data.frame()
for (f in fps){ # f = fps[6]
fp <- as.integer(substring(f, first = 3))
listCGlog <- rbind(listCGlog, cbind(fp))
}
listCGlog$fp <- listCGlog$fp + 100 # add 100 to create a unique code
# CG according to EEG mean amps
# (data already read in for EG above)
listCGamps <- listamps %>%
filter(fp >= 100) %>%
select(-sess)
# check subject match between EEG amps and log
if (setequal(listCGamps$fp, listCGlog$fp)!=T){
print('CG: Mismatch between EEG amps and log files')
print('Unique in EEG amps')
print(setdiff(listCGamps$fp, listCGlog$fp))
print('Unique in EEG log')
print(setdiff(listCGlog$fp,listCGamps$fp))
stop('CG: Mismatch between EEG amps and log files')
}
# check subject match between notes and EEG log
if (setequal(listCGnotes$fp, listCGlog$fp)!=T){
print('CG: Mismatch between notes and EEG log files')
print('Unique in notes')
print(setdiff(listCGnotes$fp, listCGlog$fp))
print('Unique in EEG log')
print(setdiff(listCGlog$fp, listCGnotes$fp))
stop('Mismatch between notes and EEG log files: Control group')
}
# make notes list the gold standard----
rm(listCGlog, listCGamps)demographics
Demographics are in the data files only for the control group.
Mean (SD) of age = 25.9 (6.69).
listCGnotes %>%
count(gender) %>%
mutate(gender = case_when(gender == 'f' ~ 'female',
gender == 'm' ~ 'male')) %>%
kable(align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))| gender | n |
|---|---|
| female | 30 |
| male | 22 |
Handedness:
listCGnotes %>%
count(handedness) %>%
mutate(handedness = case_when(handedness == 'l' ~ 'left',
handedness == 'r' ~ 'right')) %>%
kable(align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))| handedness | n |
|---|---|
| left | 2 |
| right | 50 |
detection task: questionnaire
After the detection task (with EEG), subjects filled in a questionnaire.
Questions:
Q1) Task focus: ‘How much did you focus on the fixation cross? 1=never, 9=always
Q2) Flash visible: ’How easy to see the flash?’ 1=difficult, 9=easy
Q3) Spiders distract: ‘How distracted were you by spiders?’ 1=little, 9=lots
Q4) Nonspiders distract: ‘How distracted were you by nonspiders?’ 1=little, 9=lots
Q5) Task easy: ‘How easy was the task?’ 1=difficult, 9=easy
# experimental
file <- 'data/detection_que_experimental.tsv'
tmpque <- read.csv(file, skip = 0, sep = '\t', header = T)
# sess 1
tmp <- sort(intersect(listEGnotes$fp[listEGnotes$sess1==1],tmpque$fp[tmpque$sess==1]))
note1 <- paste0('EG Session 1: n = ', length(setdiff(listEGnotes$fp[listEGnotes$sess1==1], tmp)))
QueDetect <- tmpque[tmpque$fp %in% tmp & tmpque$sess == 1,]
# sess 2
tmp <- sort(intersect(listEGnotes$fp[listEGnotes$sess2==1],tmpque$fp[tmpque$sess==2]))
note2 <- paste0('EG Session 2: n = ', length(setdiff(listEGnotes$fp[listEGnotes$sess2==1], tmp)))
QueDetect <- rbind(QueDetect, tmpque[tmpque$fp %in% tmp & tmpque$sess == 2,])
QueDetect$treat <- 'IVET'
tmp <- listEGnotes$fp[listEGnotes$vret==1]
QueDetect$treat[QueDetect$fp %in% tmp] = 'VRET'
# control
file <- 'data/detection_que_control.tsv'
tmpque <- read.csv(file, skip = 0, sep = '\t', header = T)
tmpque$fp <- tmpque$fp + 100 # add 100 to get unique ID codes
tmp = sort(intersect(listCGnotes$fp, tmpque$fp))
note3 = paste0('CG: n = ', length(setdiff(listCGnotes$fp, tmp)))
tmpque = tmpque[tmpque$fp %in% tmp,]
tmpque$treat = 'Control'
QueDetect = rbind(QueDetect, tmpque)
rownames(QueDetect) = NULL
QueDetect$sess = QueDetect$sess - 1 # recode to session 0 and 1
QueDetect$treat = factor(QueDetect$treat, levels=c('Control', 'IVET', 'VRET'))
dataque <- QueDetect %>%
pivot_longer(cols = c(q1, q2, q3, q4, q5), names_to = 'que', values_to = 'dv') %>%
mutate(fp = as.character(fp))
# check that answers range between 1 and 9
dataque %>%
summarise(min_dv = min(dv),
max_dv = max(dv),
.groups = 'drop') %>%
as.numeric() %>%
identical(c(1,9)) %>%
isFALSE() %>%
{if(.)(stop("Error: Answers min and max are not 1 and 9, respectively!"))}write_tsv(dataque, file.path('results/dataque.tsv'))sample size
Data are almost complete except that four subjects (not from one particular group) have missing questionnaire data. These subjects are from these groups:
- EG Session 1: n = 1
- EG Session 2: n = 2
- CG: n = 1
The variable Both shows how many subjects participated in both sessions. So, these are not additional subjects.
tmptable <- dataque %>%
group_by(fp) %>%
slice(1) %>%
select(fp, treat) %>%
group_by(treat) %>%
summarise(N = n(), .groups = 'drop') %>%
rename("Treatment" = treat)
tmptable <- dataque %>%
select(fp, sess, treat) %>%
unique() %>%
group_by(sess, treat) %>%
mutate(sess = ifelse(sess==0, 'Pre', 'Post'),
sess = factor(sess, levels = c('Pre', 'Post'))) %>%
summarise(n = n(), .groups = 'drop') %>% # grouping is dropped
pivot_wider(names_from = sess, values_from = n) %>%
mutate_if(is.numeric, ~ ifelse(is.na(.), "--", .)) %>%
cbind(tmptable, .) %>%
select(-treat)
tmps1I <- dataque %>%
filter(treat == 'IVET',
sess == 0) %>%
distinct(., fp) %>%
pull()
tmps1V <- dataque %>%
filter(treat == 'VRET',
sess == 0) %>%
distinct(., fp) %>%
pull()
tmps2I <- dataque %>%
filter(treat == 'IVET',
sess == 1) %>%
distinct(., fp) %>%
pull()
tmps2V <- dataque %>%
filter(treat == 'VRET',
sess == 1) %>%
distinct(., fp) %>%
pull()
tmptable$'Both' = c('--', length(intersect(tmps1I, tmps2I)), length(intersect(tmps1V, tmps2V)))
tmptable %>%
kable(align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))| Treatment | N | Pre | Post | Both |
|---|---|---|---|---|
| Control | 51 | 51 | – | – |
| IVET | 33 | 16 | 30 | 13 |
| VRET | 37 | 20 | 34 | 17 |
rm(tmptable, tmps1I, tmps1V, tmps2I, tmps2V)descriptives
The table shows means (SD in parentheses).
dataque %>%
mutate(sess = ifelse(sess==0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post'))) %>%
group_by(sess, treat, que) %>%
summarise(m_sd = sprintf("%.2f (%.2f)", mean(dv, na.rm = TRUE),
sd(dv, na.rm = TRUE)), .groups = 'drop') %>%
# grouping is dropped
pivot_wider(names_from = que, values_from = m_sd) %>%
rename("Treatment" = treat,
"Session" = sess,
"Task focus" = q1,
"Flash visible" = q2,
"Spiders distract" = q3,
"Nonspiders distract" = q4,
"Task easy" = q5) %>%
arrange(Treatment, Session) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| Session | Treatment | Task focus | Flash visible | Spiders distract | Nonspiders distract | Task easy |
|---|---|---|---|---|---|---|
| pre | Control | 8.37 (0.63) | 4.24 (1.53) | 2.22 (1.47) | 3.02 (1.45) | 5.18 (1.74) |
| pre | IVET | 8.06 (0.85) | 4.31 (1.89) | 5.50 (2.07) | 3.25 (1.88) | 5.50 (2.48) |
| post | IVET | 8.37 (0.72) | 3.50 (1.46) | 3.77 (1.94) | 3.03 (1.52) | 5.83 (2.25) |
| pre | VRET | 8.05 (0.76) | 3.60 (1.57) | 5.55 (1.15) | 3.25 (1.29) | 5.00 (1.30) |
| post | VRET | 8.18 (0.90) | 3.97 (1.68) | 4.15 (2.00) | 3.09 (1.44) | 5.97 (1.80) |
session 1 across treatments
- standard regression model (no repeated measures)
- use session 1 from all three groups
- combine treatment groups
- no plots because the comparison involves two means (treatment vs. control). The B in the table shows the mean difference.
Q1
Task focus: ’How much did you focus on the fixation cross? 1=never, 9=always
Note that the intercept shows the mean score for Controls in Session 1.
Result: The (combined) treatment group tended to be less focused on the cross. Makes sense because in Q3, they rated to be more distracted by spiders.
mylabels = c('treatment (Control)',
'treatment (VRET/IVET)')
model_name = "quedetect_q1_acrosstreatment"
model_formula = formula("dv ~ 1 + treat")
# fp is not included because each subject contributes one data point
data <- dataque %>%
filter(sess == 0) %>%
filter(que == 'q1') %>%
mutate(treat = ifelse(treat == 'Control', 'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lm(model_formula, data = data))
table_model(get(model_name),
dv_labels = "Task focus",
pred_labels = mylabels)| Task focus | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) | 8.37 | 8.18 – 8.57 | 0.10 | 85.25 | <0.001 |
| treatment (VRET/IVET) | -0.32 | -0.62 – -0.01 | 0.15 | -2.08 | 0.041 |
| Observations | 87 | ||||
| R2 / R2 adjusted | 0.048 / 0.037 | ||||
Q2
Flash visible: ‘How easy to see the flash?’ 1=difficult, 9=easy
model_name = "quedetect_q2_acrosstreatment"
model_formula = formula("dv ~ 1 + treat")
data <- dataque %>%
filter(sess == 0) %>%
filter(que == 'q2') %>%
mutate(treat = ifelse(treat == 'Control', 'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lm(model_formula, data = data))
table_model(get(model_name),
dv_labels = "Flash visible",
pred_labels = mylabels)| Flash visible | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) | 4.24 | 3.79 – 4.69 | 0.23 | 18.72 | <0.001 |
| treatment (VRET/IVET) | -0.32 | -1.02 – 0.38 | 0.35 | -0.91 | 0.368 |
| Observations | 87 | ||||
| R2 / R2 adjusted | 0.010 / -0.002 | ||||
Q3
Spiders distract: ‘How distracted were you by spiders?’ 1=little, 9=lots
Result: The treatment group rated to be much more distracted by spiders.
model_name = "quedetect_q3_acrosstreatment"
model_formula = formula("dv ~ 1 + treat")
data <- dataque %>%
filter(sess == 0) %>%
filter(que == 'q3') %>%
mutate(treat = ifelse(treat == 'Control', 'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lm(model_formula, data = data))
table_model(get(model_name),
dv_labels = "Spiders distract",
pred_labels = mylabels)| Spiders distract | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) | 2.22 | 1.79 – 2.64 | 0.21 | 10.38 | <0.001 |
| treatment (VRET/IVET) | 3.31 | 2.65 – 3.97 | 0.33 | 9.98 | <0.001 |
| Observations | 87 | ||||
| R2 / R2 adjusted | 0.540 / 0.534 | ||||
Q4
Nonspiders distract: ‘How distracted were you by nonspiders?’ 1=little, 9=lots
model_name = "quedetect_q4_acrosstreatment"
model_formula = formula("dv ~ 1 + treat")
data <- dataque %>%
filter(sess == 0) %>%
filter(que == 'q4') %>%
mutate(treat = ifelse(treat == 'Control', 'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lm(model_formula, data = data))
table_model(get(model_name),
dv_labels = "Nonspiders distract",
pred_labels = mylabels)| Nonspiders distract | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) | 3.02 | 2.60 – 3.44 | 0.21 | 14.43 | <0.001 |
| treatment (VRET/IVET) | 0.23 | -0.42 – 0.88 | 0.33 | 0.71 | 0.481 |
| Observations | 87 | ||||
| R2 / R2 adjusted | 0.006 / -0.006 | ||||
Q3 vs Q4
Measure distraction by spiders versus nonspiders. That is, compute Q3 minus Q4 for each subject. Positive values mean that the subject reported being more distracted by spiders than nonspiders.
Result: Compared to controls, the treatment groups reported more distraction by spiders (vs. nonspiders) in session 1.
model_name = "quedetect_q34_acrosstreatment"
model_formula = formula("dv ~ 1 + treat")
data <- QueDetect %>%
filter(sess == 0) %>%
mutate(dv = q3 - q4) %>%
select(fp, sess, treat, dv) %>%
mutate(treat = ifelse(treat == 'Control', 'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lm(model_formula, data = data))
table_model(get(model_name),
dv_labels = "Distract spiders minus nonspiders",
pred_labels = mylabels)| Distract spiders minus nonspiders | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) | -0.80 | -1.31 – -0.30 | 0.26 | -3.14 | 0.002 |
| treatment (VRET/IVET) | 3.08 | 2.29 – 3.87 | 0.40 | 7.76 | <0.001 |
| Observations | 87 | ||||
| R2 / R2 adjusted | 0.414 / 0.407 | ||||
Q5
Task easy: ‘How easy was the task?’ 1=difficult, 9=easy
model_name = "quedetect_q5_acrosstreatment"
model_formula = formula("dv ~ 1 + treat")
data <- dataque %>%
filter(sess == 0) %>%
filter(que == 'q5') %>%
mutate(treat = ifelse(treat == 'Control', 'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lm(model_formula, data = data))
table_model(get(model_name),
dv_labels = "Task easy",
pred_labels = mylabels)| Task easy | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) | 5.18 | 4.67 – 5.68 | 0.25 | 20.45 | <0.001 |
| treatment (VRET/IVET) | 0.05 | -0.74 – 0.83 | 0.39 | 0.12 | 0.908 |
| Observations | 87 | ||||
| R2 / R2 adjusted | 0.000 / -0.012 | ||||
treatment comparison
- MLM model
- session 1 and session 2 (session 1 as reference)
- include only treatment groups
- IVET = -.5, VRET = .5
Q1
Task focus: ’How much did you focus on the fixation cross? 1=never, 9=always
model
mylabels = c('treatment (VRET/IVET) / session (1)',
'treatment (VRET vs IVET) / session (1)',
'treatment (VRET/IVET) / session (2)',
'treatment (VRET vs IVET) / session (2)')
model_name = "quedetect_q1_treatment"
model_formula = formula("dv ~ 1 + treat*sess + (1 | fp)")
data <- dataque %>%
filter(!treat == 'Control') %>%
filter(que == 'q1') %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5))
#recode treatment as -.5 and .5
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Task focus",
pred_labels = mylabels)| Task focus | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) | 8.14 | 7.88 – 8.39 | 0.13 | 63.47 | <0.001 |
| treatment (VRET vs IVET) / session (1) | 0.00 | -0.51 – 0.51 | 0.26 | 0.00 | 0.997 |
| treatment (VRET/IVET) / session (2) | 0.14 | -0.13 – 0.42 | 0.14 | 1.05 | 0.300 |
| treatment (VRET vs IVET) / session (2) | -0.19 | -0.74 – 0.36 | 0.27 | -0.70 | 0.484 |
| Random Effects | |||||
| σ2 | 0.35 | ||||
| τ00 fp | 0.29 | ||||
| ICC | 0.45 | ||||
| N fp | 70 | ||||
| Observations | 100 | ||||
| Marginal R2 / Conditional R2 | 0.016 / 0.463 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted rating\n", x = "\nsession") +
plot_aes
Q2
Flash visible: ‘How easy to see the flash?’ 1=difficult, 9=easy
Result: The interaction suggests that IVET rated the flash as more visible during session 1 than 2, whereas VRET rated the opposite. This effect does not seem meaningful.
model
model_name = "quedetect_q2_treatment"
model_formula = formula("dv ~ 1 + treat*sess + (1 | fp)")
data <- dataque %>%
filter(!treat == 'Control') %>%
filter(que == 'q2') %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5))
#recode treatment as -.5 and .5
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Flash visible",
pred_labels = mylabels)| Flash visible | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) | 3.93 | 3.43 – 4.42 | 0.25 | 15.75 | <0.001 |
| treatment (VRET vs IVET) / session (1) | -0.78 | -1.77 – 0.21 | 0.50 | -1.57 | 0.119 |
| treatment (VRET/IVET) / session (2) | -0.21 | -0.71 – 0.29 | 0.25 | -0.86 | 0.395 |
| treatment (VRET vs IVET) / session (2) | 1.28 | 0.28 – 2.28 | 0.50 | 2.58 | 0.013 |
| Random Effects | |||||
| σ2 | 1.11 | ||||
| τ00 fp | 1.49 | ||||
| ICC | 0.57 | ||||
| N fp | 70 | ||||
| Observations | 100 | ||||
| Marginal R2 / Conditional R2 | 0.037 / 0.589 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted rating\n", x = "\nsession") +
plot_aes
Q3
Spiders distract: ‘How distracted were you by spiders?’ 1=little, 9=lots
Result: The treatment groups rated less distraction by spiders in session 2 than 1.
See also the Q3 vs Q4 that uses the nonspiders as controls.
model
model_name = "quedetect_q3_treatment"
model_formula = formula("dv ~ 1 + treat*sess + (1 | fp)")
data <- dataque %>%
filter(!treat == 'Control') %>%
filter(que == 'q3') %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5))
#recode treatment as -.5 and .5
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Spider distract",
pred_labels = mylabels)| Spider distract | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) | 5.65 | 5.08 – 6.22 | 0.29 | 19.68 | <0.001 |
| treatment (VRET vs IVET) / session (1) | 0.05 | -1.09 – 1.19 | 0.57 | 0.09 | 0.932 |
| treatment (VRET/IVET) / session (2) | -1.65 | -2.20 – -1.09 | 0.27 | -6.06 | <0.001 |
| treatment (VRET vs IVET) / session (2) | 0.20 | -0.90 – 1.31 | 0.54 | 0.37 | 0.713 |
| Random Effects | |||||
| σ2 | 1.28 | ||||
| τ00 fp | 2.35 | ||||
| ICC | 0.65 | ||||
| N fp | 70 | ||||
| Observations | 100 | ||||
| Marginal R2 / Conditional R2 | 0.149 / 0.700 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted rating\n", x = "\nsession") +
plot_aes
Q4
Nonspiders distract: ‘How distracted were you by nonspiders?’ 1=little, 9=lots
model
model_name = "quedetect_q4_treatment"
model_formula = formula("dv ~ 1 + treat*sess + (1 | fp)")
data <- dataque %>%
filter(!treat == 'Control') %>%
filter(que == 'q4') %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5))
#recode treatment as -.5 and .5
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Nonspiders distract",
pred_labels = mylabels)| Nonspiders distract | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) | 3.18 | 2.72 – 3.64 | 0.23 | 13.73 | <0.001 |
| treatment (VRET vs IVET) / session (1) | 0.03 | -0.89 – 0.95 | 0.46 | 0.07 | 0.942 |
| treatment (VRET/IVET) / session (2) | -0.10 | -0.54 – 0.35 | 0.22 | -0.43 | 0.669 |
| treatment (VRET vs IVET) / session (2) | -0.12 | -1.02 – 0.77 | 0.44 | -0.28 | 0.782 |
| Random Effects | |||||
| σ2 | 0.85 | ||||
| τ00 fp | 1.49 | ||||
| ICC | 0.64 | ||||
| N fp | 70 | ||||
| Observations | 100 | ||||
| Marginal R2 / Conditional R2 | 0.002 / 0.637 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted rating\n", x = "\nsession") +
plot_aes
Q3 vs Q4
Measure distraction by spiders versus nonspiders. That is, compute Q3 minus Q4 for each subject.
Positive values mean that the subject reported being more distracted by spiders than nonspiders.
Result: The treatment groups rated less distraction by spiders (vs. nonspiders) in session 2 than 1.
model
model_name = "quedetect_q34_treatment"
model_formula = formula("dv ~ 1 + treat*sess + (1 | fp)")
data <- QueDetect %>%
filter(!treat == 'Control') %>%
mutate(dv = q3 - q4) %>%
select(fp, sess, treat, dv) %>%
mutate(treat = as.numeric(ifelse(as.character(treat) == "IVET", -.5, .5)))
#recode treatment as -.5 and .5
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Distract spiders minus nonspiders",
pred_labels = mylabels)| Distract spiders minus nonspiders | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) | 2.44 | 1.87 – 3.01 | 0.29 | 8.47 | <0.001 |
| treatment (VRET vs IVET) / session (1) | 0.02 | -1.12 – 1.16 | 0.58 | 0.04 | 0.972 |
| treatment (VRET/IVET) / session (2) | -1.52 | -2.12 – -0.93 | 0.29 | -5.20 | <0.001 |
| treatment (VRET vs IVET) / session (2) | 0.32 | -0.87 – 1.50 | 0.59 | 0.54 | 0.590 |
| Random Effects | |||||
| σ2 | 1.56 | ||||
| τ00 fp | 1.84 | ||||
| ICC | 0.54 | ||||
| N fp | 70 | ||||
| Observations | 100 | ||||
| Marginal R2 / Conditional R2 | 0.140 / 0.605 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted rating\n", x = "\nsession") +
plot_aes
Q5
Task easy: ‘How easy was the task?’ 1=difficult, 9=easy
Result: The treatment groups rated the task as easier during session 2 than 1.
model
model_name = "quedetect_q5_treatment"
model_formula = formula("dv ~ 1 + treat*sess + (1 | fp)")
data <- dataque %>%
filter(!treat == 'Control') %>%
filter(que == 'q5') %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5))
#recode treatment as -.5 and .5
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Task easy",
pred_labels = mylabels)| Task easy | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) | 5.20 | 4.67 – 5.73 | 0.27 | 19.34 | <0.001 |
| treatment (VRET vs IVET) / session (1) | -0.31 | -1.38 – 0.76 | 0.54 | -0.58 | 0.565 |
| treatment (VRET/IVET) / session (2) | 0.76 | 0.40 – 1.12 | 0.18 | 4.34 | <0.001 |
| treatment (VRET vs IVET) / session (2) | 0.27 | -0.44 – 0.99 | 0.35 | 0.78 | 0.443 |
| Random Effects | |||||
| σ2 | 0.48 | ||||
| τ00 fp | 3.63 | ||||
| ICC | 0.88 | ||||
| N fp | 70 | ||||
| Observations | 100 | ||||
| Marginal R2 / Conditional R2 | 0.035 / 0.887 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted rating\n", x = "\nsession") +
plot_aes
rm(list=ls(pattern='quedetect'))sample size
Nall = sum(c(nrow(listCGnotes),listEGnotes$sess1,listEGnotes$sess2))The total number of recordings is 155. A recording comprises data from two tasks of a single subject in a single session.
- Detection task (with EEG): Subjects detected flashing of the central fixation cross.
- Rating task: Subjects rated each picture on arousal and pleasantness. (Note that pleasantness is recoded below to unpleasantness.)
The table shows the number of subjects in the three groups.
The variable Both shows how many subjects participated in both sessions. So, these are not additional subjects.
tmptable <- listEGnotes %>%
select(vret, sess1, sess2) %>%
mutate(sess12 = ifelse(sess1==1 & sess2==1, 1, 0)) %>%
group_by(vret, sess1, sess2, sess12) %>%
summarise(n = n(), .groups = 'drop') # grouping is dropped
tmpd = data.frame(Treatment = c('Control','IVET','VRET'),
N = c(nrow(listCGnotes),
length(listEGnotes$fp[listEGnotes$vret==0]),
length(listEGnotes$fp[listEGnotes$vret==1])),
S1 = c(nrow(listCGnotes),
tmptable$n[2]+tmptable$n[3],
tmptable$n[5]+tmptable$n[6]),
S2 = c('--',
tmptable$n[1]+tmptable$n[3],
tmptable$n[4]+tmptable$n[6]),
Both = c('--', tmptable$n[3], tmptable$n[6]))
tmpd %>%
rename("Pre" = `S1`,
"Post" = `S2`) %>%
kable(align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))| Treatment | N | Pre | Post | Both |
|---|---|---|---|---|
| Control | 52 | 52 | – | – |
| IVET | 33 | 16 | 31 | 14 |
| VRET | 37 | 21 | 35 | 19 |
rm(tmptable, tmpd)read rating/EEG data
Read in the data from the detection task (with EEG) and the rating data from the rating task.
experimental group
# experimental group
fps <- c(listEGnotes$fp[listEGnotes$sess1==1],
listEGnotes$fp[listEGnotes$sess2==1])
ses <- as.integer(c(listEGnotes$sess1[listEGnotes$sess1==1],
listEGnotes$sess2[listEGnotes$sess2==1]*2))
vr <- as.integer(c(listEGnotes$vret[listEGnotes$sess1==1],
listEGnotes$vret[listEGnotes$sess2==1]))
RawDetect<- data.frame()
RawRate <- data.frame()
for (f in 1:length(fps)){ # f = 3
# read in detection behavioral data----
file <- file.path(dir_log,'experimental',sprintf('fp%s_%s/DATA_SpVR_%s_%s.txt',
fps[f],ses[f],fps[f], ses[f]))
if (file.exists(file)){
tmp <- read.csv(file, skip = 10, sep = '\t', header = F)[,1:13]
# header = T did not work because of an extra tab at the end of each row
colnames(tmp) <- c('Trial', 'Code', 'Targ', 'Gap', 'Emo', 'Pind', 'Pcode',
'PicOn', 'ProbeOn', 'NumResp', 'RespOn', 'Logcode', 'PPTcode')
if (nrow(tmp) != 200){
print(file)
stop('Not 200 trials per session!')
}
}
# read in detection EEG data----
# Trial fp ses cond EPN LPP bad
file <- file.path(dir_meanamps,sprintf('fp%03.0f_ses%02.0f.tsv',
fps[f],ses[f]))
if (file.exists(file)){
tmp2 <- read.csv(file, sep = '\t', header = T)
if (identical(rep(fps[f],length(tmp2$fp)), as.integer(tmp2$fp)) == F){
print(file)
stop('Subject id does not match!')
}
if (identical(rep(ses[f],length(tmp2$fp)), as.integer(tmp2$ses)) == F){
print(file)
stop('Session number does not match!')
}
# Some subjects had a trial missing in EEG
# apparently, no code was sent to the EEG
# fix these data
# Note: earlier file versions had trialonset as a variable
#tmp2$diff[2:length(tmp2$trialonset)] = diff(tmp2$trialonset, lag = 1)
# I used the timing difference to find which trial was missing
if (fps[f] == 13 & ses[f] == 1){
# trial 172 is missing; skip this trial
tmp2$Trial[172:199] <- 173:200
tmp2 <- rbind(tmp2, c(172,13,1,'pos/notarget',NA,NA,NA,NA,NA,NA,NA,NA,1))
tmp2 <- tmp2[order(as.numeric(tmp2$Trial)),]
}
if (fps[f] == 15 & ses[f] == 2){
# trial 140 is missing; skip this trial
tmp2$Trial[140:199] <- 141:200
tmp2 <- rbind(tmp2, c(140,15,1,'pos/notarget',NA,NA,NA,NA,NA,NA,NA,NA,1))
tmp2 <- tmp2[order(as.numeric(tmp2$Trial)),]
}
if (fps[f] == 71 & ses[f] == 1){
# trial 30 is missing; skip this trial
tmp2$Trial[30:199] <- 31:200
tmp2 <- rbind(tmp2, c(30,71,1,'neg/notarget',NA,NA,NA,NA,NA,NA,NA,NA,1))
tmp2 <- tmp2[order(as.numeric(tmp2$Trial)),]
}
# Emo: 1=spi, 2=unpleasant, 3=neutral, 4=pleasant
tmp2$Emo <- NA
tmp2$Emo[grepl('spi', tmp2$cond)] <- 1
tmp2$Emo[grepl('neg', tmp2$cond)] <- 2
tmp2$Emo[grepl('neu', tmp2$cond)] <- 3
tmp2$Emo[grepl('pos', tmp2$cond)] <- 4
tmp2$Targ <- 0
tmp2$Targ[grepl('/target', tmp2$cond)] <- 1
if (nrow(tmp2) != 200){
print(file)
stop('Not 200 trials per session!')
}
if (identical(tmp$Emo, as.integer(tmp2$Emo)) == F){
print(file)
stop('Emotion codes do not match!')
}
if (identical(tmp$Targ, as.integer(tmp2$Targ)) == F){
print(file)
stop('Target trials do not match!')
}
# copy mean amps
tmp$EPN <- as.numeric(tmp2$EPN_average)
tmp$LPP <- as.numeric(tmp2$LPP_average)
tmp$bad <- as.numeric(tmp2$bad)
tmp$fp <- fps[f]
tmp$sess <- ses[f]-1 # code session as 0 and 1
tmp$treat <- ifelse(vr[f] == 1, 'VRET', 'IVET')
RawDetect <- rbind(RawDetect, tmp)
rm(tmp, tmp2)
}
# read in rating data----
file <- file.path(dir_log,'experimental',sprintf('fp%s_%s/DATA_SpVRrate_%s_%s.txt',
fps[f],ses[f],fps[f],ses[f]))
if (file.exists(file)){
tmp <- read.csv(file, skip = 5, sep = '\t', header = T)[-c(1:4),]
# delete practice rows
if (nrow(tmp) != 40){
print(file)
stop('Not 40 trials per session!')
}
tmp$fp <- fps[f]
tmp$sess <- ses[f]-1
tmp$treat <- ifelse(vr[f] == 1, 'VRET', 'IVET')
RawRate <- rbind(RawRate, tmp)
}
}
rm(fps,tmp,file,f,ses,vr)control group
# control group
fps <- listCGnotes$fp
for (f in 1:length(fps)){ # f = 1
# read in detection data----
file <- file.path(dir_log,'control',sprintf('fp%s/DATA_SpVR_%s_1.txt',fps[f]-100,fps[f]-100))
# for log, fp number starts from 1
if (file.exists(file)){
tmp <- read.csv(file, skip = 10, sep = '\t', header = F)[,1:13]
# header = T did not work because of an extra tab at the end of each row
colnames(tmp) <- c('Trial', 'Code', 'Targ', 'Gap', 'Emo', 'Pind', 'Pcode',
'PicOn', 'ProbeOn', 'NumResp', 'RespOn', 'Logcode', 'PPTcode')
if (nrow(tmp) != 200){
print(file)
stop('Not 200 trials per session!')
}
}
# read in detection EEG data----
file <- file.path(dir_meanamps,sprintf('fp%03.0f_ses01.tsv',
fps[f])) # fp numbers already starts from 100
if (file.exists(file)){
tmp2 <- read.csv(file, sep = '\t', header = T, )
if (identical(as.integer(rep(fps[f],length(tmp2$fp))), tmp2$fp) == F){
print(file)
stop('Subject id does not match!')
}
# Emo: 1=spi, 2=unpleasant, 3=neutral, 4=pleasant
tmp2$Emo <- NA
tmp2$Emo[grepl('spi', tmp2$cond)] <- 1
tmp2$Emo[grepl('neg', tmp2$cond)] <- 2
tmp2$Emo[grepl('neu', tmp2$cond)] <- 3
tmp2$Emo[grepl('pos', tmp2$cond)] <- 4
tmp2$Targ <- 0
tmp2$Targ[grepl('/target', tmp2$cond)] <- 1
if (nrow(tmp2) != 200){
print(file)
stop('Not 200 trials per session!')
}
if (identical(tmp$Emo, as.integer(tmp2$Emo)) == F){
print(file)
stop('Emotion codes do not match!')
}
if (identical(tmp$Targ, as.integer(tmp2$Targ)) == F){
print(file)
stop('Target trials do not match!')
}
# copy mean amps
tmp$EPN <- as.numeric(tmp2$EPN_average)
tmp$LPP <- as.numeric(tmp2$LPP_average)
tmp$bad <- as.numeric(tmp2$bad)
tmp$fp <- fps[f]
tmp$sess <- 0 # code session as 0 and 1
tmp$treat <- 'Control'
RawDetect <- rbind(RawDetect, tmp)
rm(tmp, tmp2)
}
# read in rating data----
file <- file.path(dir_log,'control',sprintf('fp%s/DATA_SpVRrate_%s_1.txt',fps[f]-100,fps[f]-100))
# for rating, fp number starts from 1
if (file.exists(file)){
tmp <- read.csv(file, skip = 5, sep = '\t', header = T)[-c(1:4),]
# delete practice rows
if (nrow(tmp) != 40){
print(file)
stop('Not 40 trials per session!')
}
tmp$fp <- fps[f]
tmp$sess <- 0 # code session as 0 and 1
tmp$treat <- 'Control'
RawRate <- rbind(RawRate, tmp)
}
}
rm(fps,tmp,file,f)recode variables
- Subject ID (fp) as character (for an unknown reason, fp as factor messes up predicted())
- Control group as reference category
- Emotion categories: neutral, spider, negative, positive (in this order)
RawDetect <- RawDetect %>%
mutate(fp = as.character(fp),
treat = factor(treat, levels = c("Control", "IVET", "VRET")),
# relevel so control is the reference
Emo = recode(Emo, "1" = "spider", "2" = "negative", "3" = "neutral", "4" = "positive"),
# recode emotion categories
Emo = factor(Emo, levels = c("neutral", "spider", "negative", "positive")))
# relevel so that neutral is the reference
RawRate <- RawRate %>%
mutate(fp = as.character(fp),
treat = factor(treat, levels = c("Control", "IVET", "VRET")),
# relevel so control is the reference
Emo = recode(Emo, "1" = "spider", "2" = "negative", "3" = "neutral", "4" = "positive"),
# recode emotion categories
Emo = factor(Emo, levels = c("neutral", "spider", "negative", "positive")))write_tsv(RawDetect, file.path('results/datadetect.tsv'))
write_tsv(RawRate, file.path('results/datarate.tsv'))detection task performance
Process the performance data (false alarms, hit rate, reaction time to hits) from the detection task.
false alarms
In the plot, subject refers to the data from a subject in a single session (N = 155). Most subjects made very few false alarms with a couple of exceptions. However, these subjects were in the control group. So, ignore false alarms and focus on hits.
# false alarm
tmp <- RawDetect %>%
mutate(fals = ifelse(Targ==0 & NumResp>0, 1, 0)) %>%
group_by(fp, sess) %>%
summarise(sumfals = sum(fals), .groups = 'drop') %>%
pull(sumfals) %>%
mean()
RawDetect %>%
mutate(fals = ifelse(Targ==0 & NumResp>0, 1, 0)) %>%
group_by(fp, sess) %>%
summarise(sumfals = sum(fals), .groups = 'drop') %>%
ggplot(aes(sumfals)) +
geom_density() +
theme_bw() +
labs(title = paste0('Number of false alarms (mean = ', myround(tmp,1),')'),
x = 'Number of false alarms per subject (possible max = 160)') +
geom_vline(xintercept = tmp, linetype = 'longdash')
rm(tmp)hit rate
Hits are trials in which the flashing of the fixation cross was detected and reaction time (RT) > 200 ms.
plot
In the plot, subject refers to the data from a subject in a single session (N = 160).
Hit rate varied across subjects.
# hits
RawDetect <- RawDetect %>%
mutate(hit = ifelse(Targ == 1 & NumResp > 0 & RespOn - ProbeOn > 200, 1, 0))
tmp <- RawDetect %>%
filter(Targ == 1) %>%
group_by(fp, sess) %>%
summarise(mhit = mean(hit)*100, .groups = 'drop') %>%
pull(mhit) %>%
mean()
RawDetect %>%
filter(Targ == 1) %>%
group_by(fp, sess) %>%
summarise(mhit = mean(hit)*100, .groups = 'drop') %>%
ggplot(aes(mhit)) +
geom_density() +
theme_bw() +
labs(title = paste0('Hit rate (mean = ', myround(tmp,1),')'),
x = 'Hit rate (%) per subject') +
geom_vline(xintercept = tmp, linetype = 'longdash')
rm(tmp)session 1 across treatments
- use session 1 from all three groups
- combine treatment groups
- compute mean hit rate
- nonspiders (i.e., positive, neutral, negative) are combined
- compare spiders versus nonspiders
- intercept is control/nonspiders
Result: In Session 1, the combined treatment groups (vs controls) tended to have lower hit rates for spiders (vs nonspiders).
model
mylabels <- c('treatment (Control) / emotion (nonspiders)',
'treatment (VRET/IVET) / emotion (nonspiders)',
'treatment (Control) / emotion (spiders)',
'treatment (VRET/IVET) / emotion (spiders)')
model_name <- "perfdetect_acrosstreatment"
model_formula <- formula("mhit ~ 1 + treat*Emo + (1 | fp)")
data <- RawDetect %>%
filter(sess == 0 & Targ == 1) %>%
mutate(Emo = ifelse(Emo == 'spider', 'spider', 'nonspider'),
Emo = factor(Emo, levels = c("nonspider", "spider"))) %>%
group_by(fp, Emo) %>%
summarise(mhit = mean(hit)*100, .groups = 'drop') %>%
mutate(treat = ifelse(as.numeric(as.character(fp)) > 100,'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Mean Hit rate (%)",
pred_labels = mylabels)| Mean Hit rate (%) | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) / emotion (nonspiders) | 80.77 | 75.20 – 86.34 | 2.81 | 28.74 | <0.001 |
| treatment (VRET/IVET) / emotion (nonspiders) | -1.76 | -10.39 – 6.87 | 4.36 | -0.40 | 0.687 |
| treatment (Control) / emotion (spiders) | 0.38 | -3.90 – 4.67 | 2.16 | 0.18 | 0.859 |
| treatment (VRET/IVET) / emotion (spiders) | -6.42 | -13.06 – 0.22 | 3.34 | -1.92 | 0.058 |
| Random Effects | |||||
| σ2 | 120.75 | ||||
| τ00 fp | 289.99 | ||||
| ICC | 0.71 | ||||
| N fp | 89 | ||||
| Observations | 178 | ||||
| Marginal R2 / Conditional R2 | 0.023 / 0.713 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
mutate(group = factor(group, levels = c("nonspider", "spider"))) %>%
ggplot(aes(group, predicted, color = x)) +
#geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat, group = fp), alpha = .3, size = .2) +
# plotting individual lines is not meaningful because slopes are fixed in model
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette2, name = "treatment") +
labs(y = "predicted hit rate\n", x = "\nemotion") +
plot_aes
treatment comparison
- session 1 and session 2 (session 1 as reference)
- include only treatment groups
- IVET = -.5, VRET = .5
- compute mean hit rate
- nonspiders (i.e., positive, neutral, negative) are combined
- compare spiders versus nonspiders
- intercept is session 1/nonspiders
Results do not suggest that the treatment groups differed. However, across treatment groups, there were two effects:
- Performance was lower to spiders than nonspiders in Session 1.
- The performance difference between spiders vs nonspiders decreased from Session 1 to Session 2.
model
mylabels <- c('treatment (VRET/IVET) / session (1) / emotion (nonspider)',
'treatment (VRET vs IVET) / session (1) / emotion (nonspider)',
'treatment (VRET/IVET) / session (2) / emotion (nonspider)',
'treatment (VRET/IVET) / session (1) / emotion (spider)',
'treatment (VRET vs IVET) / session (2) / emotion (nonspider)',
'treatment (VRET vs IVET) / session (1) / emotion (spider)',
'treatment (VRET/IVET) / session (2) / emotion (spider)',
'treatment (VRET vs IVET) / session (2) / emotion (spider)')
model_name <- "perfdetect_treatment"
model_formula <- formula("mhit ~ 1 + treat*sess*Emo + (1 | fp)")
data <- RawDetect %>%
filter(!treat == 'Control' & Targ == 1) %>%
mutate(Emo = ifelse(Emo == 'spider', 'spider', 'nonspider'),
Emo = factor(Emo, levels = c("nonspider", "spider")),
treat = ifelse(as.character(treat) == "IVET", -.5, .5)) %>%
#recode treatment as -.5 and .5
group_by(treat, fp, sess, Emo) %>%
summarise(mhit = mean(hit)*100, .groups = 'drop')
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Mean Hit rate",
pred_labels = mylabels)| Mean Hit rate | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) / emotion (nonspider) | 79.26 | 73.57 – 84.94 | 2.88 | 27.54 | <0.001 |
| treatment (VRET vs IVET) / session (1) / emotion (nonspider) | -3.98 | -15.35 – 7.39 | 5.76 | -0.69 | 0.490 |
| treatment (VRET/IVET) / session (2) / emotion (nonspider) | -2.77 | -7.71 – 2.17 | 2.50 | -1.11 | 0.270 |
| treatment (VRET/IVET) / session (1) / emotion (spider) | -5.79 | -10.96 – -0.62 | 2.61 | -2.21 | 0.029 |
| treatment (VRET vs IVET) / session (2) / emotion (nonspider) | 4.38 | -5.51 – 14.26 | 5.00 | 0.88 | 0.383 |
| treatment (VRET vs IVET) / session (1) / emotion (spider) | -3.66 | -14.00 – 6.68 | 5.23 | -0.70 | 0.485 |
| treatment (VRET/IVET) / session (2) / emotion (spider) | 7.85 | 1.40 – 14.29 | 3.26 | 2.41 | 0.017 |
| treatment (VRET vs IVET) / session (2) / emotion (spider) | 4.12 | -8.77 – 17.01 | 6.52 | 0.63 | 0.528 |
| Random Effects | |||||
| σ2 | 124.16 | ||||
| τ00 fp | 287.89 | ||||
| ICC | 0.70 | ||||
| N fp | 70 | ||||
| Observations | 206 | ||||
| Marginal R2 / Conditional R2 | 0.019 / 0.704 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~facet) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted hit rate\n", x = "\nsession") +
plot_aes
hits RT (ms)
session 1 across treatments
- use session 1 from all three groups
- combine treatment groups
- compute mean hit RT (ms)
- nonspiders (i.e., positive, neutral, negative) are combined
- compare spiders versus nonspiders
- intercept is control/nonspiders
Results do not suggest differences in Session 1.
model
mylabels <- c('treatment (Control) / emotion (nonspiders)',
'treatment (VRET/IVET) / emotion (nonspiders)',
'treatment (Control) / emotion (spiders)',
'treatment (VRET/IVET) / emotion (spiders)')
model_name <- "perfdetectRT_acrosstreatment"
model_formula <- formula("mhitRT ~ 1 + treat*Emo + (1 | fp)")
data <- RawDetect %>%
filter(sess == 0,
hit == 1) %>%
mutate(hitRT = RespOn - ProbeOn,
Emo = ifelse(Emo == 'spider', 'spider', 'nonspider'),
Emo = factor(Emo, levels = c("nonspider", "spider"))) %>%
group_by(fp, Emo) %>%
summarise(mhitRT = mean(hitRT), .groups = 'drop') %>%
mutate(treat = ifelse(as.numeric(fp) < 100,'Control', 'VRET/IVET'),
treat = factor(treat, levels = c("Control", "VRET/IVET")))
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Mean Hit RT (ms)",
pred_labels = mylabels)| Mean Hit RT (ms) | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (Control) / emotion (nonspiders) | 521.59 | 494.68 – 548.50 | 13.57 | 38.43 | <0.001 |
| treatment (VRET/IVET) / emotion (nonspiders) | -24.56 | -59.77 – 10.65 | 17.75 | -1.38 | 0.170 |
| treatment (Control) / emotion (spiders) | 9.44 | -9.67 – 28.56 | 9.61 | 0.98 | 0.329 |
| treatment (VRET/IVET) / emotion (spiders) | -7.55 | -32.31 – 17.21 | 12.44 | -0.61 | 0.546 |
| Random Effects | |||||
| σ2 | 1625.32 | ||||
| τ00 fp | 5188.81 | ||||
| ICC | 0.76 | ||||
| N fp | 89 | ||||
| Observations | 176 | ||||
| Marginal R2 / Conditional R2 | 0.029 / 0.768 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
mutate(group = factor(group, levels = c("nonspider", "spider"))) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
scale_color_manual(values = palette2, name = "treatment") +
labs(y = "predicted hit RT (ms)\n", x = "\nemotion") +
plot_aes
treatment comparison
- session 1 and session 2 (session 1 as reference)
- include only treatment groups
- IVET = -.5, VRET = .5
- compute mean hit RT (ms)
- nonspiders (i.e., positive, neutral, negative) are combined
- compare spiders versus nonspiders
- intercept is session 1/nonspiders
Results suggest no differences.
model
mylabels <- c('treatment (VRET/IVET) / session (1) / emotion (nonspider)',
'treatment (VRET vs IVET) / session (1) / emotion (nonspider)',
'treatment (VRET/IVET) / session (2) / emotion (nonspider)',
'treatment (VRET/IVET) / session (1) / emotion (spider)',
'treatment (VRET vs IVET) / session (2) / emotion (nonspider)',
'treatment (VRET vs IVET) / session (1) / emotion (spider)',
'treatment (VRET/IVET) / session (2) / emotion (spider)',
'treatment (VRET vs IVET) / session (2) / emotion (spider)')
model_name <- "perfdetectRT_treatment"
model_formula <- formula("mhitRT ~ 1 + treat*sess*Emo + (1 | fp)")
data <- RawDetect %>%
filter(!treat == 'Control',
hit == 1) %>%
mutate(hitRT = RespOn - ProbeOn,
Emo = ifelse(Emo == 'spider', 'spider', 'nonspider'),
Emo = factor(Emo, levels = c("nonspider", "spider")),
treat = ifelse(as.character(treat) == "IVET", -.5, .5)) %>%
#recode treatment as -.5 and .5
group_by(treat, fp, sess, Emo) %>%
summarise(mhitRT = mean(hitRT), .groups = 'drop')
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
table_model(get(model_name),
dv_labels = "Mean Hit RT (ms)",
pred_labels = mylabels)| Mean Hit RT (ms) | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| treatment (VRET/IVET) / session (1) / emotion (nonspider) | 526.53 | 504.52 – 548.55 | 11.14 | 47.26 | <0.001 |
| treatment (VRET vs IVET) / session (1) / emotion (nonspider) | 13.04 | -30.98 – 57.07 | 22.28 | 0.59 | 0.559 |
| treatment (VRET/IVET) / session (2) / emotion (nonspider) | -7.88 | -27.75 – 12.00 | 10.05 | -0.78 | 0.435 |
| treatment (VRET/IVET) / session (1) / emotion (spider) | 5.67 | -15.38 – 26.73 | 10.63 | 0.53 | 0.595 |
| treatment (VRET vs IVET) / session (2) / emotion (nonspider) | -24.73 | -64.48 – 15.03 | 20.10 | -1.23 | 0.221 |
| treatment (VRET vs IVET) / session (1) / emotion (spider) | 26.94 | -15.17 – 69.04 | 21.27 | 1.27 | 0.208 |
| treatment (VRET/IVET) / session (2) / emotion (spider) | -12.13 | -38.24 – 13.98 | 13.19 | -0.92 | 0.359 |
| treatment (VRET vs IVET) / session (2) / emotion (spider) | -19.37 | -71.58 – 32.84 | 26.37 | -0.73 | 0.464 |
| Random Effects | |||||
| σ2 | 1964.18 | ||||
| τ00 fp | 4062.38 | ||||
| ICC | 0.67 | ||||
| N fp | 70 | ||||
| Observations | 202 | ||||
| Marginal R2 / Conditional R2 | 0.026 / 0.682 | ||||
plot
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET")) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~facet) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted hit RT (ms)\n", x = "\nsession") +
plot_aes
prepare rating/EEG subsets
emotion rating
Self-reported ratings of arousal and pleasantness during the rating task.
# check min=1 and max=9
RawRate %>%
summarise(min_aro = min(Aro),
max_aro = max(Aro),
min_uple = min(Ple),
max_uple = max(Ple), .groups = 'drop') %>%
as.numeric() %>%
identical(c(1,9,1,9)) %>%
isFALSE() %>%
{if(.)(stop("Error: Rating min and max are not 1 and 9, respectively!"))}
rate <- RawRate
# arousal and pleasantness separately
# ====================================
# subset baseline data
rate_baseline <- rate %>%
filter(sess == 0) %>%
pivot_longer(cols = c(Ple, Aro), names_to = 'rating_type', values_to = 'rating') %>%
mutate(rating_type = factor(rating_type, levels = c("Aro", "Ple")))
# combine treatments
# (IVET and VRET have different fp, ie subject ids)
rate_baseline_acrosstreatment <- rate_baseline %>%
mutate(treat = ifelse(treat == "Control", "Control", "IVET/VRET"),
treat = factor(treat, levels = c("Control", "IVET/VRET")))
# pivot_longer rating types and filter out control
rate_only_treat <- rate %>%
filter(!treat == "Control") %>%
pivot_longer(cols = c(Ple, Aro), names_to = 'rating_type', values_to = 'rating')
# recode treatment
rate_only_treat_recode <- rate_only_treat %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5))
#recode treatment as -.5 and .5
# subtract the average across neutral pictures from each trial
neutral_rate <- rate %>%
filter(Emo == "neutral") %>%
group_by(fp, sess) %>%
summarise(neutral_avg_Aro = mean(Aro, na.rm = TRUE),
neutral_avg_Ple = mean(Ple, na.rm = TRUE),
.groups = 'drop') # grouping is dropped
rate_diffneutral <- rate %>%
filter(!Emo == "neutral") %>%
left_join(., neutral_rate, by = c("fp", "sess")) %>%
mutate(Aro_diff = Aro - neutral_avg_Aro,
Ple_diff = Ple - neutral_avg_Ple,
Emo = factor(Emo, levels = c("spider", "negative", "positive")),
treat = factor(treat))detection task (EEG)
- remove bad trials from the EEG data
- remove outliers
- remove target trials from the EEG data (20% target trials)
- remove false alarms
all trials
Number of trials = 31000.
RawDetect %>%
pivot_longer(cols = c(EPN,LPP), names_to = 'ERP_type', values_to = 'amp' ) %>%
ggplot() +
geom_violin(aes(x = ERP_type, y = amp)) +
theme_bw() +
labs(title = paste0('Mean amplitude (µV) per trial (N = ', nrow(RawDetect),')'),
x = 'ERP interval')
remove bad trials
Below, the bad trials were removed. These were marked during the initial data preparation.
Number of trials = 30483. Percentage of remaining trials = 98.3.
The figure suggests that some outliers remained. The figure suggests that +/-25 µV is a reasonable cut off for these outliers.
RawDetect %>%
filter(bad == 0) %>% # remove bad EEG trials
pivot_longer(cols = c(EPN,LPP), names_to = 'ERP_type', values_to = 'amp' ) %>%
ggplot() +
geom_violin(aes(x = ERP_type, y = amp)) +
geom_hline(aes(yintercept = 25), linetype = 'longdash') +
geom_hline(aes(yintercept = -25), linetype = 'longdash') +
theme_bw() +
labs(title = paste0('Mean amplitude (µV) per trial (N = ', nrow(RawDetect %>% filter(bad == 0)),')'),
x = 'ERP interval')
# remove outliers
tmp <- nrow(RawDetect %>% filter(bad == 0))
RawDetect <- RawDetect %>%
mutate(bad = ifelse(abs(EPN) > 25 | abs(LPP) > 25 | is.na(EPN) | is.na(LPP), 1, bad))
tmp2 <- nrow(RawDetect %>% filter(bad == 0))remove outliers
The outliers were identified with the previous violin plot. Number of trials that were excluded: 66.
Number of remaining trials = 30417. Percentage of remaining trials = 98.1.
rm(tmp, tmp2)
RawDetect %>%
filter(bad == 0) %>% # remove bad trials and outliers
pivot_longer(cols = c(EPN,LPP), names_to = 'ERP_type', values_to = 'amp' ) %>%
ggplot() +
geom_violin(aes(x = ERP_type, y = amp)) +
geom_hline(aes(yintercept = 25), linetype = 'longdash') +
geom_hline(aes(yintercept = -25), linetype = 'longdash') +
theme_bw() +
labs(title = paste0('Mean amplitude (µV) per trial (N = ', nrow(RawDetect %>% filter(bad == 0)),')'),
x = 'ERP interval')
check distribution
Check how bad trials are distributed between spider and nonspiders. The expected percentages for bad spider trials is 25% (1 of 4 picture categories).
RawDetect %>%
mutate(Treatment = ifelse(treat == 'Control', 'Control', 'IVET/VRET'),
spider = ifelse(Emo == 'spider', 'spider', 'nonspider')) %>%
group_by(Treatment, spider) %>%
summarize(bad = sum(bad), .groups = 'drop') %>%
pivot_wider(names_from = 'spider', values_from = 'bad') %>%
mutate(bad_percent = spider/(spider+nonspider)*100) %>%
kable(align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))| Treatment | nonspider | spider | bad_percent |
|---|---|---|---|
| Control | 205 | 62 | 23.22097 |
| IVET/VRET | 241 | 75 | 23.73418 |
N trials
Percentage of good EEG trials per recording.
RawDetect %>%
group_by(treat, sess, fp) %>%
summarize(good = (1-sum(bad)/n())*100,.groups = 'drop') %>%
pull(good) %>%
summary()## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 73.50 98.00 99.50 98.12 100.00 100.00N trials by group
Percentage of good EEG trials per participant and group.
RawDetect %>%
group_by(treat, sess, fp) %>%
summarize(good = (1-sum(bad)/n())*100,.groups = 'drop') %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post')) %>%
unite(Condition, treat, sess, sep = " ") %>%
mutate(Condition = ifelse(Condition == 'Control pre', 'Control', Condition)) %>%
mutate(Condition = factor(Condition, levels=unique(as.character(Condition)))) %>%
group_by(Condition) %>%
summarize(N = n(),
Mean = myround(mean(good),2),
SD = myround(sd(good),2),
.groups = 'drop') %>%
kable(align = "c") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))| Condition | N | Mean | SD |
|---|---|---|---|
| Control | 52 | 97.43 | 4.81 |
| IVET pre | 16 | 97.06 | 6.60 |
| IVET post | 31 | 98.68 | 2.87 |
| VRET pre | 21 | 98.12 | 2.96 |
| VRET post | 35 | 99.13 | 1.75 |
N trials per block
RawDetect %>%
filter(bad == 0) %>% # remove bad trials and outliers
mutate(block = case_when(
Trial < 51 ~ 1,
Trial < 101 ~ 2,
Trial < 151 ~ 3,
Trial < 201 ~ 4)) %>%
group_by(treat, sess, fp, Emo, block) %>%
summarize(ntrial = n(), .groups = 'drop') %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post')) %>%
unite(Condition, treat, sess, sep = " ") %>%
mutate(Condition = ifelse(Condition == 'Control pre', 'Control', Condition)) %>%
group_by(Condition, Emo, block) %>%
summarise(N = paste0('(n=',n(),')'),
Mean = mean(ntrial),
.groups = 'drop') %>%
unite(Condition, Condition, N, sep = " ") %>%
ggplot(aes(x=block, y=Mean, by=Condition, color=Emo)) +
geom_line() +
theme_bw() + # get rid of background
facet_grid(~Condition) +
ylim(c(11, 13)) +
labs(title = "Mean N valid EEG trials",
y = "N trials")
write_tsv(RawDetect, file.path('results/datadetect_clean.tsv'))prepare files
detect <- RawDetect %>%
filter(bad == 0) #%>% # remove bad EEG trials and outliers
# # target trials
# filter(Targ == 0) %>%
# # false alarms
# mutate(fals = ifelse(Targ==0 & NumResp>0, 1, 0)) %>%
# filter(fals == 0) %>%
# select(-fals)
# subset baseline data
detect_baseline <- detect %>%
filter(sess == 0)
# combine treatments
# (IVET and VRET have different fp, ie subject ids)
detect_baseline_acrosstreatment <- detect_baseline %>%
mutate(treat = ifelse(treat == "Control", "Control", "IVET/VRET"),
treat = factor(treat, levels = c("Control", "IVET/VRET")))
# filter out control
detect_only_treat <- detect %>%
filter(!treat == "Control") %>%
mutate(treat = factor(treat))
# recode treatment as -.5 and .5
detect_only_treat_recode <- detect_only_treat %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5)) #recode rating_type as -.5 and .5
# subtract the average across neutral pictures from each trial and re-reference
neutral_ERP <- detect %>%
filter(Emo == "neutral") %>%
group_by(fp, sess) %>%
summarise(neutral_avg_LPP = mean(LPP, na.rm = TRUE),
neutral_avg_EPN = mean(EPN, na.rm = TRUE),
.groups = 'drop') # grouping is dropped
detect_diffneutral <- detect %>%
filter(!Emo == "neutral") %>%
left_join(., neutral_ERP, by = c("fp", "sess")) %>%
mutate(LPP_diff = LPP - neutral_avg_LPP,
EPN_diff = EPN - neutral_avg_EPN,
Emo = factor(Emo, levels = c("spider", "negative", "positive")),
treat = factor(treat))
detect_diffneutralEG <- detect_diffneutral %>%
filter(!treat == "Control") %>%
mutate(treat = ifelse(as.character(treat) == "IVET", -.5, .5))descriptives with figures
emotion ratings
means
The table shows means (SD in parentheses).
rate %>%
pivot_longer(cols = c(Ple, Aro), names_to = 'rating_type', values_to = 'rating') %>%
group_by(fp, sess, treat, Emo, rating_type) %>%
summarise(mean = mean(rating, na.rm = TRUE), .groups = 'drop') %>%
# grouping is dropped
mutate(rating_type = ifelse(rating_type == "Aro", "arousal", "pleasantness")) %>%
ungroup() %>%
mutate(sess = ifelse(sess == 0, "pre", "post"),
sess = factor(sess, levels = c('pre', 'post'))) %>%
unite(emo_rating, rating_type, Emo, sep = " ") %>%
group_by(sess, treat, emo_rating) %>%
summarise(N = n(),
m_sd = sprintf("%.2f (%.2f)", mean(mean, na.rm = TRUE),
sd(mean, na.rm = TRUE)), .groups = 'drop') %>%
# grouping is dropped
pivot_wider(names_from = emo_rating, values_from = m_sd) %>%
rename("Treatment" = treat,
"Session" = sess) %>%
arrange(Treatment) %>%
kable() %>%
kable_styling()| Session | Treatment | N | arousal negative | arousal neutral | arousal positive | arousal spider | pleasantness negative | pleasantness neutral | pleasantness positive | pleasantness spider |
|---|---|---|---|---|---|---|---|---|---|---|
| pre | Control | 52 | 5.45 (1.49) | 3.98 (1.26) | 4.74 (1.50) | 5.09 (1.69) | 3.30 (0.86) | 5.15 (0.38) | 6.80 (0.83) | 4.25 (1.23) |
| pre | IVET | 16 | 5.86 (0.83) | 4.50 (1.00) | 4.21 (1.13) | 7.16 (1.37) | 3.29 (0.97) | 5.22 (0.20) | 7.24 (0.84) | 2.24 (0.94) |
| post | IVET | 31 | 6.11 (1.02) | 4.54 (1.03) | 4.79 (1.26) | 6.30 (1.11) | 3.21 (0.99) | 5.11 (0.18) | 6.91 (0.80) | 3.24 (1.07) |
| pre | VRET | 21 | 5.45 (1.18) | 4.27 (1.03) | 4.13 (1.00) | 7.48 (0.70) | 3.47 (0.72) | 5.30 (0.35) | 6.84 (0.77) | 2.21 (0.97) |
| post | VRET | 35 | 5.51 (1.17) | 4.45 (1.12) | 4.12 (1.33) | 6.33 (1.38) | 3.61 (0.87) | 5.10 (0.27) | 6.44 (0.84) | 3.41 (1.32) |
change scores
Compute difference scores relative to neutral pictures. For example, spider = spider - neutral.
rate_diffneutral %>%
pivot_longer(cols = c(Aro_diff, Ple_diff), names_to = 'rating_type', values_to = 'rating') %>%
group_by(fp, sess, treat, Emo, rating_type) %>%
summarise(rating = mean(rating, na.rm = TRUE), .groups = 'drop') %>%
# grouping is dropped
mutate(sess = ifelse(sess == 0, "pre", "post"),
sess = factor(sess, levels = c('pre', 'post'))) %>%
group_by(sess, treat, Emo, rating_type) %>%
summarise(N = n(),
Mean = mean(rating),
LL = ci95LL(rating),
UL = ci95UL(rating),
.groups = 'drop') %>%
relocate(rating_type) %>%
arrange(rating_type, Emo, treat, sess) %>%
rename("Rating" = rating_type,
"Treatment" = treat,
"Session" = sess,
"Category" = Emo) %>%
kable() %>%
kable_styling()| Rating | Session | Treatment | Category | N | Mean | LL | UL |
|---|---|---|---|---|---|---|---|
| Aro_diff | pre | Control | spider | 52 | 1.1173077 | 0.7802942 | 1.4543212 |
| Aro_diff | pre | IVET | spider | 16 | 2.6562500 | 2.0754646 | 3.2370354 |
| Aro_diff | post | IVET | spider | 31 | 1.7580645 | 1.2091026 | 2.3070265 |
| Aro_diff | pre | VRET | spider | 21 | 3.2142857 | 2.5979574 | 3.8306140 |
| Aro_diff | post | VRET | spider | 35 | 1.8771429 | 1.3850908 | 2.3691949 |
| Aro_diff | pre | Control | negative | 52 | 1.4692308 | 1.1752932 | 1.7631683 |
| Aro_diff | pre | IVET | negative | 16 | 1.3625000 | 0.5818066 | 2.1431934 |
| Aro_diff | post | IVET | negative | 31 | 1.5677419 | 1.0868348 | 2.0486491 |
| Aro_diff | pre | VRET | negative | 21 | 1.1809524 | 0.8095797 | 1.5523250 |
| Aro_diff | post | VRET | negative | 35 | 1.0600000 | 0.7413093 | 1.3786907 |
| Aro_diff | pre | Control | positive | 52 | 0.7653846 | 0.4364422 | 1.0943270 |
| Aro_diff | pre | IVET | positive | 16 | -0.2937500 | -1.0663009 | 0.4788009 |
| Aro_diff | post | IVET | positive | 31 | 0.2516129 | -0.1549565 | 0.6581823 |
| Aro_diff | pre | VRET | positive | 21 | -0.1380952 | -0.5038055 | 0.2276150 |
| Aro_diff | post | VRET | positive | 35 | -0.3342857 | -0.6166870 | -0.0518844 |
| Ple_diff | pre | Control | spider | 52 | -0.8961538 | -1.2405823 | -0.5517254 |
| Ple_diff | pre | IVET | spider | 16 | -2.9812500 | -3.4347443 | -2.5277557 |
| Ple_diff | post | IVET | spider | 31 | -1.8741935 | -2.2920880 | -1.4562991 |
| Ple_diff | pre | VRET | spider | 21 | -3.0904762 | -3.6273173 | -2.5536351 |
| Ple_diff | post | VRET | spider | 35 | -1.6885714 | -2.1545913 | -1.2225516 |
| Ple_diff | pre | Control | negative | 52 | -1.8461538 | -2.1124729 | -1.5798348 |
| Ple_diff | pre | IVET | negative | 16 | -1.9312500 | -2.4561375 | -1.4063625 |
| Ple_diff | post | IVET | negative | 31 | -1.9032258 | -2.2905442 | -1.5159074 |
| Ple_diff | pre | VRET | negative | 21 | -1.8333333 | -2.1806958 | -1.4859709 |
| Ple_diff | post | VRET | negative | 35 | -1.4914286 | -1.8420773 | -1.1407798 |
| Ple_diff | pre | Control | positive | 52 | 1.6500000 | 1.4080789 | 1.8919211 |
| Ple_diff | pre | IVET | positive | 16 | 2.0250000 | 1.5485920 | 2.5014080 |
| Ple_diff | post | IVET | positive | 31 | 1.8000000 | 1.5065576 | 2.0934424 |
| Ple_diff | pre | VRET | positive | 21 | 1.5380952 | 1.2295431 | 1.8466474 |
| Ple_diff | post | VRET | positive | 35 | 1.3371429 | 1.0666502 | 1.6076355 |
plot
Plot change scores for spiders
fig_rating <- rate_diffneutral %>%
filter(Emo == "spider") %>%
pivot_longer(cols = c(Aro_diff, Ple_diff), names_to = 'rating_type', values_to = 'rating') %>%
group_by(fp, sess, treat, Emo, rating_type) %>%
summarise(rating = mean(rating, na.rm = TRUE), .groups = 'drop') %>%
# grouping is dropped
mutate(sess = ifelse(sess == 0, "pre", "post"),
sess = factor(sess, levels = c('pre', 'post')),
rating_type =
ifelse(rating_type == "Aro_diff", "Arousal", "Pleasantness")) %>%
group_by(sess, treat, rating_type) %>%
summarise(N = paste0('(n=',n(),')'),
Mean = mean(rating),
LL = ci95LL(rating),
UL = ci95UL(rating),
.groups = 'drop') %>%
relocate(rating_type) %>%
arrange(rating_type, treat, sess) %>%
unite(Condition, treat, sess, sep = "-") %>%
mutate(Condition = ifelse(Condition == 'Control-pre', 'Control', Condition)) %>%
unite(Condition, Condition, N, sep = "\n") %>%
mutate(Condition = factor(Condition, levels=unique(as.character(Condition)))) %>%
ggplot(aes(x=Condition, y=Mean)) +
geom_bar(stat="identity"
,fill="gray"
,color="black" # add black border to each bar
,position=position_dodge()) + # separate bars
theme_bw() + # get rid of background
geom_errorbar(position=position_dodge(.9), width=.25,
aes(ymin=LL, ymax=UL)) +
facet_wrap(~rating_type, nrow = 1) +
labs(title = "Picture ratings") +
# theme(axis.text.x = element_text(angle = 90, hjust = 1))+
labs(x = "Group by session") +
labs(y = "Rating difference (spiders-neutral)")
fig_rating
ggsave('results/figures/fig_rating.png')mean amplitudes (EEG)
means
The table shows means (SD in parentheses).
detect %>%
pivot_longer(cols = c(EPN, LPP), names_to = 'erp_type', values_to = 'value') %>%
group_by(fp, sess, treat, Emo, erp_type) %>%
summarise(mean = mean(value, na.rm = TRUE), .groups = 'drop') %>%
# grouping is dropped
mutate(sess = ifelse(sess == 0, "pre", "post"),
sess = factor(sess, levels = c('pre', 'post'))) %>%
unite(emo_rating, erp_type, Emo, sep = " ") %>%
group_by(sess, treat, emo_rating) %>%
summarise(N = n(),
m_sd = sprintf("%.2f (%.2f)",
mean(mean, na.rm = TRUE),
sd(mean, na.rm = TRUE)),
.groups = 'drop') %>%
# grouping is dropped
pivot_wider(names_from = emo_rating, values_from = m_sd) %>%
rename("Treatment" = treat,
"Session" = sess) %>%
arrange(Treatment) %>%
kable() %>%
kable_styling()| Session | Treatment | N | EPN negative | EPN neutral | EPN positive | EPN spider | LPP negative | LPP neutral | LPP positive | LPP spider |
|---|---|---|---|---|---|---|---|---|---|---|
| pre | Control | 52 | 3.42 (3.15) | 4.88 (2.99) | 4.69 (3.18) | 4.37 (2.90) | -0.09 (1.08) | -0.51 (1.11) | -0.33 (1.29) | 0.14 (1.40) |
| pre | IVET | 16 | 3.62 (2.41) | 5.31 (2.69) | 4.71 (2.48) | 2.24 (2.27) | 0.17 (1.00) | -0.12 (0.95) | -0.17 (1.39) | 1.33 (1.99) |
| post | IVET | 31 | 3.57 (2.50) | 5.42 (2.90) | 4.75 (2.79) | 2.76 (2.73) | -0.14 (1.00) | -0.72 (0.98) | -0.26 (1.01) | 0.99 (1.31) |
| pre | VRET | 21 | 3.53 (3.64) | 5.28 (3.75) | 4.74 (3.74) | 2.59 (3.83) | 0.16 (1.07) | -0.34 (0.93) | -0.01 (1.05) | 1.26 (1.32) |
| post | VRET | 35 | 2.53 (4.04) | 4.16 (3.91) | 3.59 (3.99) | 1.32 (3.52) | -0.06 (0.96) | -0.39 (0.87) | -0.16 (0.98) | 1.31 (1.35) |
change scores
Compute difference scores relative to neutral pictures. For example, spider = spider - neutral. Thus, the dependent variables capture EPN and LPP.
detect_diffneutral %>%
group_by(fp, sess, treat, Emo) %>%
summarise(EPN = mean(EPN_diff, na.rm = TRUE),
LPP = mean(LPP_diff, na.rm = TRUE), .groups = 'drop') %>% # grouping is dropped
mutate(sess = ifelse(sess == 0, "pre", "post"),
sess = factor(sess, levels = c('pre', 'post'))) %>%
group_by(sess, treat, Emo) %>%
summarise(N = n(),
EPN_Mean = mean(EPN),
EPN_LL = ci95LL(EPN),
EPN_UL = ci95UL(EPN),
LPP_Mean = mean(LPP),
LPP_LL = ci95LL(LPP),
LPP_UL = ci95UL(LPP),
.groups = 'drop') %>%
arrange(Emo, sess, treat) %>%
rename("Treatment" = treat,
"Session" = sess,
"Category" = Emo) %>%
kable() %>%
kable_styling()| Session | Treatment | Category | N | EPN_Mean | EPN_LL | EPN_UL | LPP_Mean | LPP_LL | LPP_UL |
|---|---|---|---|---|---|---|---|---|---|
| pre | Control | spider | 52 | -0.5105621 | -0.9121374 | -0.1089869 | 0.6452043 | 0.3010131 | 0.9893955 |
| pre | IVET | spider | 16 | -3.0702025 | -4.0378043 | -2.1026008 | 1.4504460 | 0.6518747 | 2.2490172 |
| pre | VRET | spider | 21 | -2.6944667 | -3.4631441 | -1.9257892 | 1.5945418 | 0.9555568 | 2.2335268 |
| post | IVET | spider | 31 | -2.6572096 | -3.2292855 | -2.0851336 | 1.7068249 | 1.1757293 | 2.2379205 |
| post | VRET | spider | 35 | -2.8390888 | -3.5471182 | -2.1310593 | 1.6979680 | 1.2859630 | 2.1099729 |
| pre | Control | negative | 52 | -1.4579606 | -1.8017130 | -1.1142082 | 0.4192847 | 0.1542869 | 0.6842825 |
| pre | IVET | negative | 16 | -1.6912858 | -2.5005630 | -0.8820087 | 0.2891053 | -0.1935955 | 0.7718061 |
| pre | VRET | negative | 21 | -1.7509105 | -2.3881818 | -1.1136391 | 0.4931391 | -0.1226002 | 1.1088784 |
| post | IVET | negative | 31 | -1.8442587 | -2.4537657 | -1.2347516 | 0.5818346 | 0.2558763 | 0.9077928 |
| post | VRET | negative | 35 | -1.6259855 | -2.0677187 | -1.1842523 | 0.3289925 | 0.0445736 | 0.6134114 |
| pre | Control | positive | 52 | -0.1871015 | -0.5504205 | 0.1762176 | 0.1824647 | -0.0569791 | 0.4219085 |
| pre | IVET | positive | 16 | -0.6044790 | -1.1840888 | -0.0248692 | -0.0453356 | -0.6917610 | 0.6010898 |
| pre | VRET | positive | 21 | -0.5358424 | -1.1293595 | 0.0576747 | 0.3219523 | -0.1526197 | 0.7965243 |
| post | IVET | positive | 31 | -0.6674684 | -1.1803651 | -0.1545717 | 0.4578520 | 0.1738761 | 0.7418280 |
| post | VRET | positive | 35 | -0.5713032 | -0.8877868 | -0.2548196 | 0.2290457 | 0.0106751 | 0.4474163 |
plot
Plot change scores for spiders
tmpdata <- detect_diffneutral %>%
filter(Emo == 'spider') %>%
pivot_longer(cols = c(EPN_diff, LPP_diff), names_to = 'erp_type',
values_to = 'value') %>%
mutate(erp_type = ifelse(erp_type == 'EPN_diff','EPN','LPP')) %>%
group_by(fp, sess, treat, erp_type) %>%
summarise(value = mean(value, na.rm = TRUE), .groups = 'drop') %>%
# grouping is dropped
mutate(sess = ifelse(sess == 0, "pre", "post"),
sess = factor(sess, levels = c('pre', 'post'))) %>%
group_by(sess, treat, erp_type) %>%
summarise(N = paste0('(n=',n(),')'),
Mean = mean(value),
LL = ci95LL(value),
UL = ci95UL(value),
.groups = 'drop') %>%
arrange(treat, sess) %>%
unite(Condition, treat, sess, sep = " ") %>%
mutate(Condition = ifelse(Condition == 'Control pre', 'Control', Condition)) %>%
unite(Condition, Condition, N, sep = " ") %>%
mutate(Condition = factor(Condition, levels=unique(as.character(Condition))))
fig_epn <- tmpdata %>%
filter(erp_type == 'EPN') %>%
ggplot(aes(x=Condition, y=Mean)) +
geom_bar(stat="identity"
,fill="gray"
,color="black" # add black border to each bar
,position=position_dodge()) + # separate bars
theme_bw() + # get rid of background
geom_errorbar(position=position_dodge(.9), width=.25,
aes(ymin=LL, ymax=UL)) +
labs(title = "EPN to spiders (vs neutral)") +
theme(plot.title = element_text(hjust = 0.5)) +
labs(x = "Group by session") +
labs(y = "Mean amplitude (µV)")
fig_epn
ggsave('results/figures/fig_meanamps_EPN.png', plot = fig_epn)
fig_lpp <- tmpdata %>%
filter(erp_type == 'LPP') %>%
ggplot(aes(x=Condition, y=Mean)) +
geom_bar(stat="identity"
,fill="gray"
,color="black" # add black border to each bar
,position=position_dodge()) + # separate bars
theme_bw() + # get rid of background
geom_errorbar(position=position_dodge(.9), width=.25,
aes(ymin=LL, ymax=UL)) +
labs(title = "LPP to spiders (vs neutral)") +
theme(plot.title = element_text(hjust = 0.5)) +
labs(x = "Group by session") +
labs(y = "Mean amplitude (µV)")
fig_lpp
ggsave('results/figures/fig_meanamps_LPP.png', plot = fig_lpp)
#fig_amp <- grid.arrange(fig_epn, fig_lpp, ncol = 2)save EPN and LPP
detect %>%
group_by(fp, sess, treat, Emo) %>%
summarise(EPN = mean(EPN, na.rm = TRUE),
LPP = mean(LPP, na.rm = TRUE), .groups = 'drop') %>% # grouping is dropped
write_tsv(file.path('results/datameanamps.tsv'))arousal ratings
Self-reported ratings of arousal during the rating task.
session 1 three groups
- use session 1 from all three groups
- examine if IVET and VRET differ from controls in spider (vs neutral) ratings in session 1
- compare IVET and VRET separately to the control group
- does not test whether the treatments differ from each other
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_all_groups_rating_arousal"
model_formula <- formula("rating ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- rate_baseline %>%
filter(rating_type == "Aro")
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plots
all categories
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .15), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .15), size = .5) +
scale_color_manual(values = palette, name = "treatment") +
labs(y = "predicted arousal\n", x = "\nemotion") +
plot_aes
ggsave('results/figures/fig_rating_arousal_pre.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 100000))
##
## REML criterion at convergence: 12243.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.0020 -0.4716 0.0277 0.4886 4.4734
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 1.2084 1.0993
## Emospider 1.2074 1.0988 -0.18
## Emonegative 0.8951 0.9461 -0.24 0.28
## Emopositive 1.0494 1.0244 -0.27 -0.06 0.13
## Residual 1.4759 1.2149
## Number of obs: 3560, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.9769 0.1615 85.9999 24.627 < 0.0000000000000002
## treatIVET 0.5231 0.3329 85.9999 1.571 0.11980
## treatVRET 0.2897 0.3011 85.9999 0.962 0.33858
## Emospider 1.1173 0.1700 85.9999 6.573 0.00000000363590090
## Emonegative 1.4692 0.1513 86.0000 9.711 0.00000000000000176
## Emopositive 0.7654 0.1608 86.0001 4.760 0.00000776364640558
## treatIVET:Emospider 1.5389 0.3504 85.9999 4.392 0.00003190160536559
## treatVRET:Emospider 2.0970 0.3169 85.9999 6.617 0.00000000299190059
## treatIVET:Emonegative -0.1067 0.3119 86.0000 -0.342 0.73304
## treatVRET:Emonegative -0.2883 0.2821 86.0000 -1.022 0.30965
## treatIVET:Emopositive -1.0591 0.3315 86.0001 -3.195 0.00196
## treatVRET:Emopositive -0.9035 0.2998 86.0001 -3.013 0.00339
##
## (Intercept) ***
## treatIVET
## treatVRET
## Emospider ***
## Emonegative ***
## Emopositive ***
## treatIVET:Emospider ***
## treatVRET:Emospider ***
## treatIVET:Emonegative
## treatVRET:Emonegative
## treatIVET:Emopositive **
## treatVRET:Emopositive **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET trVRET Emspdr Emngtv Empstv trtIVET:Ems trtVRET:Ems
## treatIVET -0.485
## treatVRET -0.536 0.260
## Emospider -0.253 0.123 0.136
## Emonegative -0.312 0.152 0.168 0.330
## Emopositive -0.335 0.162 0.179 0.055 0.217
## trtIVET:Ems 0.123 -0.253 -0.066 -0.485 -0.160 -0.027
## trtVRET:Ems 0.136 -0.066 -0.253 -0.536 -0.177 -0.030 0.260
## trtIVET:Emn 0.152 -0.312 -0.081 -0.160 -0.485 -0.105 0.330 0.086
## trtVRET:Emn 0.168 -0.081 -0.312 -0.177 -0.536 -0.116 0.086 0.330
## trtIVET:Emp 0.162 -0.335 -0.087 -0.027 -0.105 -0.485 0.055 0.014
## trtVRET:Emp 0.179 -0.087 -0.335 -0.030 -0.116 -0.536 0.014 0.055
## trtIVET:Emn trtVRET:Emn trtIVET:Emp
## treatIVET
## treatVRET
## Emospider
## Emonegative
## Emopositive
## trtIVET:Ems
## trtVRET:Ems
## trtIVET:Emn
## trtVRET:Emn 0.260
## trtIVET:Emp 0.217 0.056
## trtVRET:Emp 0.056 0.217 0.260tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:12)),
original = tidied_model$term[1:12],
standard = c("intercept (control, neutral)",
"treatment (IVET)",
"treatment (VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET) x emotion (spider)",
"treatment (VRET) x emotion (spider)",
"treatment (IVET) x emotion (negative)",
"treatment (VRET) x emotion (negative)",
"treatment (IVET) x emotion (positive)",
"treatment (VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET) / emotion (neutral)",
"treatment (VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET) / emotion (spider)",
"treatment (VRET) / emotion (spider)",
"treatment (IVET) / emotion (negative)",
"treatment (VRET) / emotion (negative)",
"treatment (IVET) / emotion (positive)",
"treatment (VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET | treatment (IVET) | treatment (IVET) / emotion (neutral) |
| 3 | treatVRET | treatment (VRET) | treatment (VRET) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 7 | treatIVET:Emospider | treatment (IVET) x emotion (spider) | treatment (IVET) / emotion (spider) |
| 8 | treatVRET:Emospider | treatment (VRET) x emotion (spider) | treatment (VRET) / emotion (spider) |
| 9 | treatIVET:Emonegative | treatment (IVET) x emotion (negative) | treatment (IVET) / emotion (negative) |
| 10 | treatVRET:Emonegative | treatment (VRET) x emotion (negative) | treatment (VRET) / emotion (negative) |
| 11 | treatIVET:Emopositive | treatment (IVET) x emotion (positive) | treatment (IVET) / emotion (positive) |
| 12 | treatVRET:Emopositive | treatment (VRET) x emotion (positive) | treatment (VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | 3.98 | 3.66 – 4.30 | 0.16 | 24.63 | <0.001 |
| 2 treatment (IVET) | 0.52 | -0.14 – 1.18 | 0.33 | 1.57 | 0.120 |
| 3 treatment (VRET) | 0.29 | -0.31 – 0.89 | 0.30 | 0.96 | 0.339 |
| 4 emotion (spider) | 1.12 | 0.78 – 1.46 | 0.17 | 6.57 | <0.001 |
| 5 emotion (negative) | 1.47 | 1.17 – 1.77 | 0.15 | 9.71 | <0.001 |
| 6 emotion (positive) | 0.77 | 0.45 – 1.09 | 0.16 | 4.76 | <0.001 |
| 7 treatment (IVET) x emotion (spider) | 1.54 | 0.84 – 2.24 | 0.35 | 4.39 | <0.001 |
| 8 treatment (VRET) x emotion (spider) | 2.10 | 1.47 – 2.73 | 0.32 | 6.62 | <0.001 |
| 9 treatment (IVET) x emotion (negative) | -0.11 | -0.73 – 0.51 | 0.31 | -0.34 | 0.733 |
| 10 treatment (VRET) x emotion (negative) | -0.29 | -0.85 – 0.27 | 0.28 | -1.02 | 0.310 |
| 11 treatment (IVET) x emotion (positive) | -1.06 | -1.72 – -0.40 | 0.33 | -3.19 | 0.002 |
| 12 treatment (VRET) x emotion (positive) | -0.90 | -1.50 – -0.31 | 0.30 | -3.01 | 0.003 |
| Random Effects | |||||
| σ2 | 1.48 | ||||
| τ00 fp | 1.21 | ||||
| τ11 fp.Emospider | 1.21 | ||||
| τ11 fp.Emonegative | 0.90 | ||||
| τ11 fp.Emopositive | 1.05 | ||||
| ρ01 | -0.18 | ||||
| -0.24 | |||||
| -0.27 | |||||
| ICC | 0.52 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.230 / 0.632 | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | 3.98 | 3.66 – 4.30 | 0.16 | 24.63 | <0.001 |
| 2 treatment (IVET) / emotion (neutral) | 0.52 | -0.14 – 1.18 | 0.33 | 1.57 | 0.120 |
| 3 treatment (VRET) / emotion (neutral) | 0.29 | -0.31 – 0.89 | 0.30 | 0.96 | 0.339 |
| 4 treatment (control) / emotion (spider) | 1.12 | 0.78 – 1.46 | 0.17 | 6.57 | <0.001 |
| 5 treatment (control) / emotion (negative) | 1.47 | 1.17 – 1.77 | 0.15 | 9.71 | <0.001 |
| 6 treatment (control) / emotion (positive) | 0.77 | 0.45 – 1.09 | 0.16 | 4.76 | <0.001 |
| 7 treatment (IVET) / emotion (spider) | 1.54 | 0.84 – 2.24 | 0.35 | 4.39 | <0.001 |
| 8 treatment (VRET) / emotion (spider) | 2.10 | 1.47 – 2.73 | 0.32 | 6.62 | <0.001 |
| 9 treatment (IVET) / emotion (negative) | -0.11 | -0.73 – 0.51 | 0.31 | -0.34 | 0.733 |
| 10 treatment (VRET) / emotion (negative) | -0.29 | -0.85 – 0.27 | 0.28 | -1.02 | 0.310 |
| 11 treatment (IVET) / emotion (positive) | -1.06 | -1.72 – -0.40 | 0.33 | -3.19 | 0.002 |
| 12 treatment (VRET) / emotion (positive) | -0.90 | -1.50 – -0.31 | 0.30 | -3.01 | 0.003 |
| Random Effects | |||||
| σ2 | 1.48 | ||||
| τ00 fp | 1.21 | ||||
| τ11 fp.Emospider | 1.21 | ||||
| τ11 fp.Emonegative | 0.90 | ||||
| τ11 fp.Emopositive | 1.05 | ||||
| ρ01 | -0.18 | ||||
| -0.24 | |||||
| -0.27 | |||||
| ICC | 0.52 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.230 / 0.632 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from controls in spider (vs neutral) ratings in the first session (but not in any other picture category). The analysis compares IVET and VRET separately to the control group and does not test whether the treatments differ from each other.
The formula was rating ~ 1 + treat * Emo + (1 + Emo | fp).
Up to Emo as random effects: This means that the emo effect can differ between subjects.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = 3.98. This is the mean rating for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t-test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether IVET and VRET differ from controls in their spider ratings. Because the intercept contains treatment(control) and emotion(neutral), we are interested in these tests:
For IVET:
treatIVET:Emospider
In the model table with condition labels, this is number 7.
treatment (IVET) / emotion (spider).
- estimate: 1.54
- p value: 3.1902e-05
This is the interaction of treatment(IVET vs control) x emotion (spider vs neutral) across ratings.
For VRET (same test as for IVET):
treatVRET:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET) / emotion (spider).
- estimate: 2.10
- p value: 2.9919e-09
This is the interaction of treatment(VRET vs control) x emotion (spider vs neutral) across ratings.
estimated means
mmeans1 <- data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA)) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean)
mmeans1 %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | 3.98 | 5.09 | 5.45 | 4.74 |
| IVET | 4.50 | 7.16 | 5.86 | 4.21 |
| VRET | 4.27 | 7.48 | 5.45 | 4.13 |
session 1 across treatments
- use session 1 from all three groups
- combine treatment groups
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_across_treat_rating_arousal"
model_formula <- formula("rating ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- rate_baseline_acrosstreatment %>%
filter(rating_type == "Aro")
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plots
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .15), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .15), size = .5) +
scale_color_manual(values = palette2, name = "treatment") +
labs(y = "predicted arousal\n", x = "\nemotion") +
plot_aes
### summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 100000))
##
## REML criterion at convergence: 12245.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9774 -0.4741 0.0258 0.4828 4.4714
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 1.1985 1.0948
## Emospider 1.2226 1.1057 -0.18
## Emonegative 0.8848 0.9407 -0.23 0.27
## Emopositive 1.0365 1.0181 -0.27 -0.05 0.13
## Residual 1.4759 1.2149
## Number of obs: 3560, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 3.9769 0.1609 87.0000 24.718
## treatIVET/VRET 0.3906 0.2495 87.0000 1.565
## Emospider 1.1173 0.1708 87.0000 6.540
## Emonegative 1.4692 0.1506 86.9999 9.753
## Emopositive 0.7654 0.1600 86.9999 4.783
## treatIVET/VRET:Emospider 1.8557 0.2650 87.0000 7.003
## treatIVET/VRET:Emonegative -0.2098 0.2336 86.9999 -0.898
## treatIVET/VRET:Emopositive -0.9708 0.2482 86.9999 -3.911
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## treatIVET/VRET 0.121102
## Emospider 0.00000000406015918 ***
## Emonegative 0.00000000000000129 ***
## Emopositive 0.00000699448394209 ***
## treatIVET/VRET:Emospider 0.00000000049883419 ***
## treatIVET/VRET:Emonegative 0.371734
## treatIVET/VRET:Emopositive 0.000181 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET/VRET Emspdr Emngtv Empstv trtIVET/VRET:Ems
## trIVET/VRET -0.645
## Emospider -0.259 0.167
## Emonegative -0.308 0.198 0.318
## Emopositive -0.336 0.217 0.061 0.214
## trtIVET/VRET:Ems 0.167 -0.259 -0.645 -0.205 -0.039
## trtIVET/VRET:Emn 0.198 -0.308 -0.205 -0.645 -0.138 0.318
## trtIVET/VRET:Emp 0.217 -0.336 -0.039 -0.138 -0.645 0.061
## trtIVET/VRET:Emn
## trIVET/VRET
## Emospider
## Emonegative
## Emopositive
## trtIVET/VRET:Ems
## trtIVET/VRET:Emn
## trtIVET/VRET:Emp 0.214tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:8)),
original = tidied_model$term[1:8],
standard = c("intercept (control, neutral)",
"treatment (IVET/VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET/VRET) x emotion (spider)",
"treatment (IVET/VRET) x emotion (negative)",
"treatment (IVET/VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET/VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET/VRET) / emotion (spider)",
"treatment (IVET/VRET) / emotion (negative)",
"treatment (IVET/VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET/VRET | treatment (IVET/VRET) | treatment (IVET/VRET) / emotion (neutral) |
| 3 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 4 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 5 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 6 | treatIVET/VRET:Emospider | treatment (IVET/VRET) x emotion (spider) | treatment (IVET/VRET) / emotion (spider) |
| 7 | treatIVET/VRET:Emonegative | treatment (IVET/VRET) x emotion (negative) | treatment (IVET/VRET) / emotion (negative) |
| 8 | treatIVET/VRET:Emopositive | treatment (IVET/VRET) x emotion (positive) | treatment (IVET/VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | 3.98 | 3.66 – 4.30 | 0.16 | 24.72 | <0.001 |
| 2 treatment (IVET/VRET) | 0.39 | -0.11 – 0.89 | 0.25 | 1.57 | 0.121 |
| 3 emotion (spider) | 1.12 | 0.78 – 1.46 | 0.17 | 6.54 | <0.001 |
| 4 emotion (negative) | 1.47 | 1.17 – 1.77 | 0.15 | 9.75 | <0.001 |
| 5 emotion (positive) | 0.77 | 0.45 – 1.08 | 0.16 | 4.78 | <0.001 |
| 6 treatment (IVET/VRET) x emotion (spider) | 1.86 | 1.33 – 2.38 | 0.26 | 7.00 | <0.001 |
| 7 treatment (IVET/VRET) x emotion (negative) | -0.21 | -0.67 – 0.25 | 0.23 | -0.90 | 0.372 |
| 8 treatment (IVET/VRET) x emotion (positive) | -0.97 | -1.46 – -0.48 | 0.25 | -3.91 | <0.001 |
| Random Effects | |||||
| σ2 | 1.48 | ||||
| τ00 fp | 1.20 | ||||
| τ11 fp.Emospider | 1.22 | ||||
| τ11 fp.Emonegative | 0.88 | ||||
| τ11 fp.Emopositive | 1.04 | ||||
| ρ01 | -0.18 | ||||
| -0.23 | |||||
| -0.27 | |||||
| ICC | 0.52 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.229 / 0.630 | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | 3.98 | 3.66 – 4.30 | 0.16 | 24.72 | <0.001 |
| 2 treatment (IVET/VRET) / emotion (neutral) | 0.39 | -0.11 – 0.89 | 0.25 | 1.57 | 0.121 |
| 3 treatment (control) / emotion (spider) | 1.12 | 0.78 – 1.46 | 0.17 | 6.54 | <0.001 |
| 4 treatment (control) / emotion (negative) | 1.47 | 1.17 – 1.77 | 0.15 | 9.75 | <0.001 |
| 5 treatment (control) / emotion (positive) | 0.77 | 0.45 – 1.08 | 0.16 | 4.78 | <0.001 |
| 6 treatment (IVET/VRET) / emotion (spider) | 1.86 | 1.33 – 2.38 | 0.26 | 7.00 | <0.001 |
| 7 treatment (IVET/VRET) / emotion (negative) | -0.21 | -0.67 – 0.25 | 0.23 | -0.90 | 0.372 |
| 8 treatment (IVET/VRET) / emotion (positive) | -0.97 | -1.46 – -0.48 | 0.25 | -3.91 | <0.001 |
| Random Effects | |||||
| σ2 | 1.48 | ||||
| τ00 fp | 1.20 | ||||
| τ11 fp.Emospider | 1.22 | ||||
| τ11 fp.Emonegative | 0.88 | ||||
| τ11 fp.Emopositive | 1.04 | ||||
| ρ01 | -0.18 | ||||
| -0.23 | |||||
| -0.27 | |||||
| ICC | 0.52 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.229 / 0.630 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether the combined treatment groups (IVET and VRET) differ from controls in spider (vs neutral) ratings in the first session (but not in any other picture category). The analysis compares the combined IVET and VRET to the control group and does not test whether the treatments differ from each other.
The formula was rating ~ 1 + treat * Emo + (1 + Emo | fp).
Up to Emo as random effects: This means that the emo effect can differ between subjects.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = 3.98. This is the mean rating for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t-test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether the combined treatment groups (IVET and VRET) differ from controls in their spider ratings. Because the intercept contains treatment(control) and emotion(neutral), we are interested in these tests:
treatIVET/VRET:Emospider
In the model table with condition labels, this is number 6.
treatment (IVET/VRET) / emotion (spider).
- estimate: 1.86
- p value: 4.9883e-10
This is the interaction of treatment(IVET/VRET vs control) x emotion (spider vs neutral) across ratings.
estimated means
data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA)) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | 3.98 | 5.09 | 5.45 | 4.74 |
| IVET/VRET | 4.37 | 7.34 | 5.63 | 4.16 |
Bayes
ordinal model
ratings_arousal_sess1 <- rate_baseline_acrosstreatment %>%
filter(rating_type == "Aro") %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp))
# Ordinal Regression Model.
ratings_arousal.sess1.model <- brm(rating ~ 1 + treat*Emo + (1 + Emo | fp),
family = cumulative("probit"),
data = na.omit(ratings_arousal_sess1),
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/ratings_arousal.sess1.model",
# file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(ratings_arousal.sess1.model)## Family: cumulative
## Links: mu = probit; disc = identity
## Formula: rating ~ 1 + treat * Emo + (1 + Emo | fp)
## Data: na.omit(ratings_arousal_sess1) (Number of observations: 1780)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 89)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.97 0.09 0.80 1.17 1.00 3028
## sd(Emospider) 1.24 0.12 1.04 1.48 1.00 2683
## cor(Intercept,Emospider) -0.10 0.12 -0.34 0.13 1.00 1851
## Tail_ESS
## sd(Intercept) 4867
## sd(Emospider) 4584
## cor(Intercept,Emospider) 3982
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept[1] -1.57 0.15 -1.88 -1.28 1.00 2294
## Intercept[2] -1.02 0.15 -1.31 -0.73 1.00 2308
## Intercept[3] -0.43 0.15 -0.71 -0.14 1.00 2289
## Intercept[4] -0.13 0.14 -0.41 0.16 1.00 2267
## Intercept[5] 1.72 0.15 1.43 2.02 1.00 2597
## Intercept[6] 2.54 0.16 2.23 2.85 1.00 2808
## Intercept[7] 3.93 0.17 3.60 4.27 1.00 3323
## Intercept[8] 4.90 0.19 4.53 5.27 1.00 3905
## treatIVETDVRET 0.28 0.22 -0.16 0.70 1.00 2043
## Emospider 1.23 0.18 0.88 1.59 1.00 2000
## treatIVETDVRET:Emospider 2.21 0.29 1.65 2.81 1.00 2061
## Tail_ESS
## Intercept[1] 4173
## Intercept[2] 4321
## Intercept[3] 4297
## Intercept[4] 3910
## Intercept[5] 4392
## Intercept[6] 4650
## Intercept[7] 4580
## Intercept[8] 5407
## treatIVETDVRET 3606
## Emospider 3927
## treatIVETDVRET:Emospider 3533
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null_arousal.sess1.model <- brm(rating ~ 1 + (1 + Emo | fp),
family = cumulative("probit"),
data = ratings_arousal_sess1,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/rating_arousal.sess1.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
emo_arousal.sess1.model <- brm(rating ~ 1 + Emo + (1 + Emo | fp),
family = cumulative("probit"),
data = ratings_arousal_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_arousal.sess1.emo",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
treat_arousal.sess1.model <- brm(rating ~ 1 + treat + (1 + Emo | fp),
family = cumulative("probit"),
data = ratings_arousal_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_arousal.sess1.treat",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
full_arousal.sess1.bayes <- bayes_factor(ratings_arousal.sess1.model, null_arousal.sess1.model)## Iteration: 1
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## Iteration: 11treat_arousal.sess1.bayes <- bayes_factor(treat_arousal.sess1.model, null_arousal.sess1.model)## Iteration: 1
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## Iteration: 9emo_arousal.sess1.bayes <- bayes_factor(emo_arousal.sess1.model, null_arousal.sess1.model)## Iteration: 1
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## Iteration: 7
## Iteration: 8
## Iteration: 9full_arousal.sess1.bayes## Estimated Bayes factor in favor of ratings_arousal.sess1.model over null_arousal.sess1.model: 50736408845223268900244688.00000treat_arousal.sess1.bayes## Estimated Bayes factor in favor of treat_arousal.sess1.model over null_arousal.sess1.model: 0.45199emo_arousal.sess1.bayes## Estimated Bayes factor in favor of emo_arousal.sess1.model over null_arousal.sess1.model: 80109640794898480.00000compare with null
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Null = format(c(full_arousal.sess1.bayes$bf,
treat_arousal.sess1.bayes$bf,
emo_arousal.sess1.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxEmo | 5.073641e+25 |
| Treat | 4.519939e-01 |
| Emo | 8.010964e+16 |
compare with Emo
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Emo =
format(c(full_arousal.sess1.bayes$bf/emo_arousal.sess1.bayes$bf,
treat_arousal.sess1.bayes$bf/emo_arousal.sess1.bayes$bf,
emo_arousal.sess1.bayes$bf/emo_arousal.sess1.bayes$bf),
scientific = TRUE),
BF01 =
format(c(emo_arousal.sess1.bayes$bf/full_arousal.sess1.bayes$bf,
emo_arousal.sess1.bayes$bf/treat_arousal.sess1.bayes$bf,
emo_arousal.sess1.bayes$bf/emo_arousal.sess1.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Emo | BF01 |
|---|---|---|
| TreatxEmo | 6.333371e+08 | 1.578938e-09 |
| Treat | 5.642191e-18 | 1.772361e+17 |
| Emo | 1.000000e+00 | 1.000000e+00 |
check assumptions
An ordinal regression has four assumptions:
- The dependent variables are ordered.
- One or more of the independent variables are either continuous, categorical, or ordinal.
- No multi-collinearity.
- Proportional odds.
Check vif and tolerance (multicollinearity)
check_collinearity(ratings_arousal.sess1.model)treatment comparison
- session 1 and session 2 (session 1 as reference)
- include only treatment groups
- IVET = -.5, VRET = .5
- use neutral pictures as reference emotion
model_name <- "only_treat_rating_arousal"
model_formula <- formula("rating ~ 1 + treat*sess*Emo + (1 + sess*Emo | fp)")
data <- rate_only_treat_recode %>%
filter(rating_type == "Aro")
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "nloptwrap",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plots
all categories
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted arousal\n", x = "\nsession") +
plot_aes
spider and neutral ratings
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
filter(Emo %in% c("neutral", "spider")) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
filter(facet %in% c("neutral", "spider")) %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted arousal\n", x = "\nsession") +
plot_aes
ggsave('results/figures/fig_rating_arousal_treat.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "nloptwrap", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 13882.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.4152 -0.4432 0.0625 0.4479 5.1629
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 0.9239 0.9612
## sess 2.1379 1.4622 -0.73
## Emospider 1.4393 1.1997 -0.58 0.38
## Emonegative 1.0299 1.0149 -0.49 0.26 0.07
## Emopositive 1.0415 1.0205 -0.51 0.77 -0.04 0.22
## sess:Emospider 3.2076 1.7910 0.62 -0.67 -0.66 -0.15 -0.38
## sess:Emonegative 2.0364 1.4270 0.26 -0.35 0.37 -0.73 -0.38
## sess:Emopositive 0.8907 0.9438 0.43 -0.81 -0.06 -0.25 -0.67
## Residual 1.4150 1.1895
##
##
##
##
##
##
##
## 0.09
## 0.30 0.49
##
## Number of obs: 4120, groups: fp, 70
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 4.38305 0.16541 36.77252 26.498
## treat -0.13144 0.33082 36.77252 -0.397
## sess 0.12285 0.21765 51.51200 0.564
## Emospider 2.97970 0.19591 39.06190 15.209
## Emonegative 1.25053 0.18832 35.32527 6.640
## Emopositive -0.19180 0.16642 45.45112 -1.153
## treat:sess 0.02591 0.43531 51.51200 0.060
## treat:Emospider 0.46925 0.39182 39.06190 1.198
## treat:Emonegative -0.17542 0.37664 35.32527 -0.466
## treat:Emopositive -0.10744 0.33284 45.45112 -0.323
## sess:Emospider -1.16133 0.26296 57.50945 -4.416
## sess:Emonegative 0.05705 0.23373 45.14238 0.244
## sess:Emopositive 0.15380 0.17481 54.83402 0.880
## treat:sess:Emospider -0.35006 0.52592 57.50945 -0.666
## treat:sess:Emonegative -0.34256 0.46746 45.14238 -0.733
## treat:sess:Emopositive -0.48085 0.34961 54.83402 -1.375
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## treat 0.693
## sess 0.575
## Emospider < 0.0000000000000002 ***
## Emonegative 0.000000107 ***
## Emopositive 0.255
## treat:sess 0.953
## treat:Emospider 0.238
## treat:Emonegative 0.644
## treat:Emopositive 0.748
## sess:Emospider 0.000044878 ***
## sess:Emonegative 0.808
## sess:Emopositive 0.383
## treat:sess:Emospider 0.508
## treat:sess:Emonegative 0.467
## treat:sess:Emopositive 0.175
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:16)),
original = tidied_model$term[1:16],
standard = c("intercept (avr_treat, session (1), neutral)",
"treatment (VRET vs IVET)",
"session (2)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (VRET vs IVET) x session",
"treatment (VRET vs IVET) x emotion (spider)",
"treatment (VRET vs IVET) x emotion (negative)",
"treatment (VRET vs IVET) x emotion (positive)",
"session x emotion (spider)",
"session x emotion (negative)",
"session x emotion (positive)",
"treatment (VRET vs IVET) x session x emotion (spider)",
"treatment (VRET vs IVET) x session x emotion (negative)",
"treatment (VRET vs IVET) x session x emotion (positive)"),
condition = c("treatment (avr_treat) / session (1) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (neutral)",
"treatment (avr_treat) / sess (2) / emotion (neutral)",
"treatment (avr_treat) / sess (1) / emotion (spider)",
"treatment (avr_treat) / sess (1) / emotion (negative)",
"treatment (avr_treat) / sess (1) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (spider)",
"treatment (VRET vs IVET) / sess (1) / emotion (negative)",
"treatment (VRET vs IVET) / sess (1) / emotion (positive)",
"treatment (avr_treat) / sess (2) / emotion (spider)",
"treatment (avr_treat) / sess (2) / emotion (negative)",
"treatment (avr_treat) / sess (2) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (spider)",
"treatment (VRET vs IVET) / sess (2) / emotion (negative)",
"treatment (VRET vs IVET) / sess (2) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (avr_treat, session (1), neutral) | treatment (avr_treat) / session (1) / emotion (neutral) |
| 2 | treat | treatment (VRET vs IVET) | treatment (VRET vs IVET) / sess (1) / emotion (neutral) |
| 3 | sess | session (2) | treatment (avr_treat) / sess (2) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (avr_treat) / sess (1) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (avr_treat) / sess (1) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (avr_treat) / sess (1) / emotion (positive) |
| 7 | treat:sess | treatment (VRET vs IVET) x session | treatment (VRET vs IVET) / sess (2) / emotion (neutral) |
| 8 | treat:Emospider | treatment (VRET vs IVET) x emotion (spider) | treatment (VRET vs IVET) / sess (1) / emotion (spider) |
| 9 | treat:Emonegative | treatment (VRET vs IVET) x emotion (negative) | treatment (VRET vs IVET) / sess (1) / emotion (negative) |
| 10 | treat:Emopositive | treatment (VRET vs IVET) x emotion (positive) | treatment (VRET vs IVET) / sess (1) / emotion (positive) |
| 11 | sess:Emospider | session x emotion (spider) | treatment (avr_treat) / sess (2) / emotion (spider) |
| 12 | sess:Emonegative | session x emotion (negative) | treatment (avr_treat) / sess (2) / emotion (negative) |
| 13 | sess:Emopositive | session x emotion (positive) | treatment (avr_treat) / sess (2) / emotion (positive) |
| 14 | treat:sess:Emospider | treatment (VRET vs IVET) x session x emotion (spider) | treatment (VRET vs IVET) / sess (2) / emotion (spider) |
| 15 | treat:sess:Emonegative | treatment (VRET vs IVET) x session x emotion (negative) | treatment (VRET vs IVET) / sess (2) / emotion (negative) |
| 16 | treat:sess:Emopositive | treatment (VRET vs IVET) x session x emotion (positive) | treatment (VRET vs IVET) / sess (2) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (avr_treat, session (1), neutral) | 4.38 | 4.05 – 4.72 | 0.17 | 26.50 | <0.001 |
| 2 treatment (VRET vs IVET) | -0.13 | -0.80 – 0.54 | 0.33 | -0.40 | 0.693 |
| 3 session (2) | 0.12 | -0.31 – 0.56 | 0.22 | 0.56 | 0.575 |
| 4 emotion (spider) | 2.98 | 2.58 – 3.38 | 0.20 | 15.21 | <0.001 |
| 5 emotion (negative) | 1.25 | 0.87 – 1.63 | 0.19 | 6.64 | <0.001 |
| 6 emotion (positive) | -0.19 | -0.53 – 0.14 | 0.17 | -1.15 | 0.255 |
| 7 treatment (VRET vs IVET) x session | 0.03 | -0.85 – 0.90 | 0.44 | 0.06 | 0.953 |
| 8 treatment (VRET vs IVET) x emotion (spider) | 0.47 | -0.32 – 1.26 | 0.39 | 1.20 | 0.238 |
| 9 treatment (VRET vs IVET) x emotion (negative) | -0.18 | -0.94 – 0.59 | 0.38 | -0.47 | 0.644 |
| 10 treatment (VRET vs IVET) x emotion (positive) | -0.11 | -0.78 – 0.56 | 0.33 | -0.32 | 0.748 |
| 11 session x emotion (spider) | -1.16 | -1.69 – -0.63 | 0.26 | -4.42 | <0.001 |
| 12 session x emotion (negative) | 0.06 | -0.41 – 0.53 | 0.23 | 0.24 | 0.808 |
| 13 session x emotion (positive) | 0.15 | -0.20 – 0.50 | 0.17 | 0.88 | 0.383 |
| 14 treatment (VRET vs IVET) x session x emotion (spider) | -0.35 | -1.40 – 0.70 | 0.53 | -0.67 | 0.508 |
| 15 treatment (VRET vs IVET) x session x emotion (negative) | -0.34 | -1.28 – 0.60 | 0.47 | -0.73 | 0.467 |
| 16 treatment (VRET vs IVET) x session x emotion (positive) | -0.48 | -1.18 – 0.22 | 0.35 | -1.38 | 0.175 |
| Random Effects | |||||
| σ2 | 1.42 | ||||
| τ00 fp | 0.92 | ||||
| τ11 fp.sess | 2.14 | ||||
| τ11 fp.Emospider | 1.44 | ||||
| τ11 fp.Emonegative | 1.03 | ||||
| τ11 fp.Emopositive | 1.04 | ||||
| τ11 fp.sess:Emospider | 3.21 | ||||
| τ11 fp.sess:Emonegative | 2.04 | ||||
| τ11 fp.sess:Emopositive | 0.89 | ||||
| ρ01 | -0.73 | ||||
| -0.58 | |||||
| -0.49 | |||||
| -0.51 | |||||
| 0.62 | |||||
| 0.26 | |||||
| 0.43 | |||||
| ICC | 0.45 | ||||
| N fp | 70 | ||||
| Observations | 4120 | ||||
| Marginal R2 / Conditional R2 | 0.292 / 0.609 | ||||
condition labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (avr_treat) / session (1) / emotion (neutral) | 4.38 | 4.05 – 4.72 | 0.17 | 26.50 | <0.001 |
| 2 treatment (VRET vs IVET) / sess (1) / emotion (neutral) | -0.13 | -0.80 – 0.54 | 0.33 | -0.40 | 0.693 |
| 3 treatment (avr_treat) / sess (2) / emotion (neutral) | 0.12 | -0.31 – 0.56 | 0.22 | 0.56 | 0.575 |
| 4 treatment (avr_treat) / sess (1) / emotion (spider) | 2.98 | 2.58 – 3.38 | 0.20 | 15.21 | <0.001 |
| 5 treatment (avr_treat) / sess (1) / emotion (negative) | 1.25 | 0.87 – 1.63 | 0.19 | 6.64 | <0.001 |
| 6 treatment (avr_treat) / sess (1) / emotion (positive) | -0.19 | -0.53 – 0.14 | 0.17 | -1.15 | 0.255 |
| 7 treatment (VRET vs IVET) / sess (2) / emotion (neutral) | 0.03 | -0.85 – 0.90 | 0.44 | 0.06 | 0.953 |
| 8 treatment (VRET vs IVET) / sess (1) / emotion (spider) | 0.47 | -0.32 – 1.26 | 0.39 | 1.20 | 0.238 |
| 9 treatment (VRET vs IVET) / sess (1) / emotion (negative) | -0.18 | -0.94 – 0.59 | 0.38 | -0.47 | 0.644 |
| 10 treatment (VRET vs IVET) / sess (1) / emotion (positive) | -0.11 | -0.78 – 0.56 | 0.33 | -0.32 | 0.748 |
| 11 treatment (avr_treat) / sess (2) / emotion (spider) | -1.16 | -1.69 – -0.63 | 0.26 | -4.42 | <0.001 |
| 12 treatment (avr_treat) / sess (2) / emotion (negative) | 0.06 | -0.41 – 0.53 | 0.23 | 0.24 | 0.808 |
| 13 treatment (avr_treat) / sess (2) / emotion (positive) | 0.15 | -0.20 – 0.50 | 0.17 | 0.88 | 0.383 |
| 14 treatment (VRET vs IVET) / sess (2) / emotion (spider) | -0.35 | -1.40 – 0.70 | 0.53 | -0.67 | 0.508 |
| 15 treatment (VRET vs IVET) / sess (2) / emotion (negative) | -0.34 | -1.28 – 0.60 | 0.47 | -0.73 | 0.467 |
| 16 treatment (VRET vs IVET) / sess (2) / emotion (positive) | -0.48 | -1.18 – 0.22 | 0.35 | -1.38 | 0.175 |
| Random Effects | |||||
| σ2 | 1.42 | ||||
| τ00 fp | 0.92 | ||||
| τ11 fp.sess | 2.14 | ||||
| τ11 fp.Emospider | 1.44 | ||||
| τ11 fp.Emonegative | 1.03 | ||||
| τ11 fp.Emopositive | 1.04 | ||||
| τ11 fp.sess:Emospider | 3.21 | ||||
| τ11 fp.sess:Emonegative | 2.04 | ||||
| τ11 fp.sess:Emopositive | 0.89 | ||||
| ρ01 | -0.73 | ||||
| -0.58 | |||||
| -0.49 | |||||
| -0.51 | |||||
| 0.62 | |||||
| 0.26 | |||||
| 0.43 | |||||
| ICC | 0.45 | ||||
| N fp | 70 | ||||
| Observations | 4120 | ||||
| Marginal R2 / Conditional R2 | 0.292 / 0.609 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from each other in spider (vs neutral) ratings in the first session and between the first and second session (but not in any other picture category).
The formula was rating ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp).
Emo by sess as random effects: This means that emo, session, and the emo by session can differ between subjects.
Intercept = treatment(avr_treat) / session (1) / emotion (neutral).
avr_treat is the mean of IVET and VRET.
The effect for the intercept = 4.38. This is the mean rating for the intercept that contains the average across treatments in session 1 to neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t-test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether the groups rated spiders differently from neutral pictures in session 1.
Emospider
In the model table with condition labels, this is number 4.
treatment (avr_treat) / sess (1) / emotion (spider).
- estimate: 2.98
- p value: 5.3068e-18
Indeed, spiders are rated more emotional.
(Note that the session 1 analysis with three groups tested each treatment compared to the control group.)
Did the groups differ in how they rated spiders from neutral pictures in session 1? The next analysis suggests: No.
treat:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET vs IVET) / sess (1) / emotion (spider).
- estimate: 0.47
- p value: 2.3829e-01
(Note that the session 1 analysis with three groups tested each treatment compared to the control group.)
Next, we examine whether the effect of spiders differed between sessions.
sess:Emospider
In the model table with condition labels, this is number 11.
treatment (avr_treat) / sess (2) / emotion (spider).
- estimate: -1.16
- p value: 4.4878e-05
Indeed, spiders (vs neutral) are rated less emotional in session 2 than session 1.
Critically, did this effect vary with treatment?
treat:sess:Emospider
In the model table with condition labels, this is number 14.
treatment (VRET vs IVET) / sess (2) / emotion (spider).
- estimate: -0.35
- p value: 5.0831e-01
No, it does not look like that the treatment groups differed.
All the other tests concern pictures other than spiders.
estimated means
data %>%
modelr::data_grid(treat, Emo, sess) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),
treat = ifelse(treat == -.5, "IVET", "VRET"),
sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post'))) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | sess | neutral | spider | negative | positive |
|---|---|---|---|---|---|
| IVET | pre | 4.45 | 7.19 | 5.79 | 4.31 |
| IVET | post | 4.56 | 6.32 | 6.13 | 4.81 |
| VRET | pre | 4.32 | 7.53 | 5.48 | 4.07 |
| VRET | post | 4.45 | 6.33 | 5.50 | 4.12 |
Bayes
ordinal model
ratings_arousal_treat <- rate_only_treat_recode %>%
filter(rating_type == "Aro") %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp))
# Ordinal Regression Model.
ratings_arousal.treat.model <- brm(rating ~ 1 + treat*sess*Emo + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = na.omit(ratings_arousal_treat),
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/ratings_arousal.treat.model",
# file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(ratings_arousal.treat.model)## Family: cumulative
## Links: mu = probit; disc = identity
## Formula: rating ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp)
## Data: na.omit(ratings_arousal_treat) (Number of observations: 2060)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 70)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.79 0.12 0.58 1.07 1.00
## sd(sess) 1.21 0.16 0.92 1.55 1.00
## sd(Emospider) 1.28 0.18 0.96 1.68 1.00
## sd(sess:Emospider) 1.74 0.24 1.33 2.25 1.00
## cor(Intercept,sess) -0.61 0.12 -0.80 -0.35 1.00
## cor(Intercept,Emospider) -0.29 0.17 -0.60 0.07 1.00
## cor(sess,Emospider) 0.02 0.18 -0.34 0.36 1.00
## cor(Intercept,sess:Emospider) 0.44 0.16 0.11 0.72 1.00
## cor(sess,sess:Emospider) -0.42 0.14 -0.67 -0.11 1.00
## cor(Emospider,sess:Emospider) -0.56 0.12 -0.77 -0.29 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 2959 4461
## sd(sess) 1408 2883
## sd(Emospider) 2604 3995
## sd(sess:Emospider) 1336 2586
## cor(Intercept,sess) 1341 2727
## cor(Intercept,Emospider) 2156 3793
## cor(sess,Emospider) 2222 3724
## cor(Intercept,sess:Emospider) 1548 2865
## cor(sess,sess:Emospider) 2139 3202
## cor(Emospider,sess:Emospider) 1357 2953
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept[1] -1.66 0.16 -1.98 -1.36 1.00 2954
## Intercept[2] -1.33 0.15 -1.63 -1.03 1.00 2790
## Intercept[3] -0.92 0.15 -1.21 -0.63 1.00 2567
## Intercept[4] -0.74 0.15 -1.02 -0.45 1.00 2533
## Intercept[5] 1.72 0.15 1.43 2.03 1.00 2626
## Intercept[6] 2.56 0.16 2.25 2.87 1.00 2784
## Intercept[7] 3.95 0.17 3.63 4.29 1.00 3171
## Intercept[8] 4.75 0.18 4.40 5.10 1.00 3429
## treat -0.18 0.29 -0.76 0.40 1.00 2514
## sess 0.07 0.19 -0.31 0.43 1.00 2650
## Emospider 3.66 0.24 3.18 4.14 1.00 2513
## treat:sess 0.08 0.38 -0.68 0.82 1.00 2563
## treat:Emospider 0.65 0.46 -0.24 1.55 1.00 2456
## sess:Emospider -1.27 0.28 -1.80 -0.71 1.00 2617
## treat:sess:Emospider -0.47 0.56 -1.54 0.65 1.00 2650
## Tail_ESS
## Intercept[1] 4680
## Intercept[2] 4811
## Intercept[3] 4480
## Intercept[4] 4313
## Intercept[5] 4676
## Intercept[6] 5116
## Intercept[7] 5311
## Intercept[8] 5382
## treat 3846
## sess 4128
## Emospider 3836
## treat:sess 4244
## treat:Emospider 3808
## sess:Emospider 3673
## treat:sess:Emospider 4452
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null_arousal.treat.model <- brm(rating ~ 1 + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = ratings_arousal_treat,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/rating_arousal.treat.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
sess_emo.treat_arousal.model <- brm(rating ~ 1 + sess*Emo + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = ratings_arousal_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_arousal.treat.sess_emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))
emo.treat_arousal.model <- brm(rating ~ 1 + Emo + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = ratings_arousal_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_arousal.treat.emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
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## Iteration: 1full.treat_arousal.bayes## Estimated Bayes factor in favor of ratings_arousal.treat.model over null_arousal.treat.model: 3270870518596406272.00000sess_emo.treat_arousal.bayes## Estimated Bayes factor in favor of sess_emo.treat_arousal.model over null_arousal.treat.model: 10402856073697644083200622.00000emo.treat_arousal.bayes## Estimated Bayes factor in favor of emo.treat_arousal.model over null_arousal.treat.model: 222024455502571757386002.00000compare with null
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Null = format(c(full.treat_arousal.bayes$bf,
sess_emo.treat_arousal.bayes$bf,
emo.treat_arousal.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxSessxEmo | 3.270871e+18 |
| SessxEmo | 1.040286e+25 |
| Emo | 2.220245e+23 |
compare with Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_SessxEmo =
format(c(full.treat_arousal.bayes$bf/sess_emo.treat_arousal.bayes$bf,
sess_emo.treat_arousal.bayes$bf/sess_emo.treat_arousal.bayes$bf,
emo.treat_arousal.bayes$bf/sess_emo.treat_arousal.bayes$bf),
scientific = TRUE),
BF01 = format(c(sess_emo.treat_arousal.bayes$bf/full.treat_arousal.bayes$bf,
sess_emo.treat_arousal.bayes$bf/sess_emo.treat_arousal.bayes$bf,
sess_emo.treat_arousal.bayes$bf/emo.treat_arousal.bayes$bf))) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_SessxEmo | BF01 |
|---|---|---|
| TreatxSessxEmo | 3.144204e-07 | 3180454.87113 |
| SessxEmo | 1.000000e+00 | 1.00000 |
| Emo | 2.134264e-02 | 46.85455 |
compare with Treat x Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_TreatxSessxEmo =
format(c(full.treat_arousal.bayes$bf/full.treat_arousal.bayes$bf,
sess_emo.treat_arousal.bayes$bf/full.treat_arousal.bayes$bf,
emo.treat_arousal.bayes$bf/full.treat_arousal.bayes$bf),
scientific = TRUE),
BF01 = format(c(full.treat_arousal.bayes$bf/full.treat_arousal.bayes$bf,
full.treat_arousal.bayes$bf/sess_emo.treat_arousal.bayes$bf,
full.treat_arousal.bayes$bf/emo.treat_arousal.bayes$bf))) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_TreatxSessxEmo | BF01 |
|---|---|---|
| TreatxSessxEmo | 1.000000e+00 | 1.0000000000000 |
| SessxEmo | 3.180455e+06 | 0.0000003144204 |
| Emo | 6.787932e+04 | 0.0000147320281 |
check assumptions
An ordinal regression has four assumptions:
- The dependent variables are ordered.
- One or more of the independent variables are either continuous, categorical, or ordinal.
- No multi-collinearity.
- Proportional odds.
Check vif and tolerance (multicollinearity)
check_collinearity(ratings_arousal.treat.model)valence ratings
Self-reported ratings of valence during the rating task.
session 1 three groups
- use session 1 from all three groups
- examine if IVET and VRET differ from controls in spider (vs neutral) ratings in session 1
- compare IVET and VRET separately to the control group
- does not test whether the treatments differ from each other
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_all_groups_rating_valence"
model_formula <- formula("rating ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- rate_baseline %>%
filter(rating_type == "Ple")
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa",
optCtrl = list(maxfun = 1e5)),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plots
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .15), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .15), size = .5) +
scale_color_manual(values = palette, name = "treatment") +
labs(y = "predicted valence\n", x = "\nemotion") +
plot_aes
ggsave('results/figures/fig_rating_valence_pre.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 100000))
##
## REML criterion at convergence: 11263.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5512 -0.4786 -0.0902 0.5630 4.9347
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 0.006459 0.08037
## Emospider 1.124151 1.06026 0.14
## Emonegative 0.614383 0.78383 -0.15 0.24
## Emopositive 0.462104 0.67978 0.79 -0.30 -0.66
## Residual 1.199022 1.09500
## Number of obs: 3560, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.14615 0.04930 563.07850 104.395
## treatIVET 0.07260 0.10162 563.07849 0.714
## treatVRET 0.15385 0.09191 563.07849 1.674
## Emospider -0.89615 0.16196 86.76765 -5.533
## Emonegative -1.84615 0.12817 88.21999 -14.404
## Emopositive 1.65000 0.11618 90.28325 14.202
## treatIVET:Emospider -2.08510 0.33388 86.76765 -6.245
## treatVRET:Emospider -2.19432 0.30196 86.76765 -7.267
## treatIVET:Emonegative -0.08510 0.26422 88.22000 -0.322
## treatVRET:Emonegative 0.01282 0.23896 88.21999 0.054
## treatIVET:Emopositive 0.37500 0.23952 90.28325 1.566
## treatVRET:Emopositive -0.11190 0.21662 90.28325 -0.517
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## treatIVET 0.4753
## treatVRET 0.0947 .
## Emospider 0.000000328147 ***
## Emonegative < 0.0000000000000002 ***
## Emopositive < 0.0000000000000002 ***
## treatIVET:Emospider 0.000000015188 ***
## treatVRET:Emospider 0.000000000151 ***
## treatIVET:Emonegative 0.7482
## treatVRET:Emonegative 0.9573
## treatIVET:Emopositive 0.1209
## treatVRET:Emopositive 0.6067
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET trVRET Emspdr Emngtv Empstv trtIVET:Ems trtVRET:Ems
## treatIVET -0.485
## treatVRET -0.536 0.260
## Emospider -0.259 0.126 0.139
## Emonegative -0.393 0.191 0.211 0.298
## Emopositive -0.258 0.125 0.138 -0.095 -0.299
## trtIVET:Ems 0.126 -0.259 -0.067 -0.485 -0.145 0.046
## trtVRET:Ems 0.139 -0.067 -0.259 -0.536 -0.160 0.051 0.260
## trtIVET:Emn 0.191 -0.393 -0.102 -0.145 -0.485 0.145 0.298 0.078
## trtVRET:Emn 0.211 -0.102 -0.393 -0.160 -0.536 0.160 0.078 0.298
## trtIVET:Emp 0.125 -0.258 -0.067 0.046 0.145 -0.485 -0.095 -0.025
## trtVRET:Emp 0.138 -0.067 -0.258 0.051 0.160 -0.536 -0.025 -0.095
## trtIVET:Emn trtVRET:Emn trtIVET:Emp
## treatIVET
## treatVRET
## Emospider
## Emonegative
## Emopositive
## trtIVET:Ems
## trtVRET:Ems
## trtIVET:Emn
## trtVRET:Emn 0.260
## trtIVET:Emp -0.299 -0.078
## trtVRET:Emp -0.078 -0.299 0.260
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingulartidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:12)),
original = tidied_model$term[1:12],
standard = c("intercept (control, neutral)",
"treatment (IVET)",
"treatment (VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET) x emotion (spider)",
"treatment (VRET) x emotion (spider)",
"treatment (IVET) x emotion (negative)",
"treatment (VRET) x emotion (negative)",
"treatment (IVET) x emotion (positive)",
"treatment (VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET) / emotion (neutral)",
"treatment (VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET) / emotion (spider)",
"treatment (VRET) / emotion (spider)",
"treatment (IVET) / emotion (negative)",
"treatment (VRET) / emotion (negative)",
"treatment (IVET) / emotion (positive)",
"treatment (VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET | treatment (IVET) | treatment (IVET) / emotion (neutral) |
| 3 | treatVRET | treatment (VRET) | treatment (VRET) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 7 | treatIVET:Emospider | treatment (IVET) x emotion (spider) | treatment (IVET) / emotion (spider) |
| 8 | treatVRET:Emospider | treatment (VRET) x emotion (spider) | treatment (VRET) / emotion (spider) |
| 9 | treatIVET:Emonegative | treatment (IVET) x emotion (negative) | treatment (IVET) / emotion (negative) |
| 10 | treatVRET:Emonegative | treatment (VRET) x emotion (negative) | treatment (VRET) / emotion (negative) |
| 11 | treatIVET:Emopositive | treatment (IVET) x emotion (positive) | treatment (IVET) / emotion (positive) |
| 12 | treatVRET:Emopositive | treatment (VRET) x emotion (positive) | treatment (VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | 5.15 | 5.05 – 5.24 | 0.05 | 104.39 | <0.001 |
| 2 treatment (IVET) | 0.07 | -0.13 – 0.27 | 0.10 | 0.71 | 0.475 |
| 3 treatment (VRET) | 0.15 | -0.03 – 0.33 | 0.09 | 1.67 | 0.095 |
| 4 emotion (spider) | -0.90 | -1.22 – -0.57 | 0.16 | -5.53 | <0.001 |
| 5 emotion (negative) | -1.85 | -2.10 – -1.59 | 0.13 | -14.40 | <0.001 |
| 6 emotion (positive) | 1.65 | 1.42 – 1.88 | 0.12 | 14.20 | <0.001 |
| 7 treatment (IVET) x emotion (spider) | -2.09 | -2.75 – -1.42 | 0.33 | -6.25 | <0.001 |
| 8 treatment (VRET) x emotion (spider) | -2.19 | -2.79 – -1.59 | 0.30 | -7.27 | <0.001 |
| 9 treatment (IVET) x emotion (negative) | -0.09 | -0.61 – 0.44 | 0.26 | -0.32 | 0.748 |
| 10 treatment (VRET) x emotion (negative) | 0.01 | -0.46 – 0.49 | 0.24 | 0.05 | 0.957 |
| 11 treatment (IVET) x emotion (positive) | 0.37 | -0.10 – 0.85 | 0.24 | 1.57 | 0.121 |
| 12 treatment (VRET) x emotion (positive) | -0.11 | -0.54 – 0.32 | 0.22 | -0.52 | 0.607 |
| Random Effects | |||||
| σ2 | 1.20 | ||||
| τ00 fp | 0.01 | ||||
| τ11 fp.Emospider | 1.12 | ||||
| τ11 fp.Emonegative | 0.61 | ||||
| τ11 fp.Emopositive | 0.46 | ||||
| ρ01 | 0.14 | ||||
| -0.15 | |||||
| 0.79 | |||||
| ICC | 0.33 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.574 / 0.713 | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | 5.15 | 5.05 – 5.24 | 0.05 | 104.39 | <0.001 |
| 2 treatment (IVET) / emotion (neutral) | 0.07 | -0.13 – 0.27 | 0.10 | 0.71 | 0.475 |
| 3 treatment (VRET) / emotion (neutral) | 0.15 | -0.03 – 0.33 | 0.09 | 1.67 | 0.095 |
| 4 treatment (control) / emotion (spider) | -0.90 | -1.22 – -0.57 | 0.16 | -5.53 | <0.001 |
| 5 treatment (control) / emotion (negative) | -1.85 | -2.10 – -1.59 | 0.13 | -14.40 | <0.001 |
| 6 treatment (control) / emotion (positive) | 1.65 | 1.42 – 1.88 | 0.12 | 14.20 | <0.001 |
| 7 treatment (IVET) / emotion (spider) | -2.09 | -2.75 – -1.42 | 0.33 | -6.25 | <0.001 |
| 8 treatment (VRET) / emotion (spider) | -2.19 | -2.79 – -1.59 | 0.30 | -7.27 | <0.001 |
| 9 treatment (IVET) / emotion (negative) | -0.09 | -0.61 – 0.44 | 0.26 | -0.32 | 0.748 |
| 10 treatment (VRET) / emotion (negative) | 0.01 | -0.46 – 0.49 | 0.24 | 0.05 | 0.957 |
| 11 treatment (IVET) / emotion (positive) | 0.37 | -0.10 – 0.85 | 0.24 | 1.57 | 0.121 |
| 12 treatment (VRET) / emotion (positive) | -0.11 | -0.54 – 0.32 | 0.22 | -0.52 | 0.607 |
| Random Effects | |||||
| σ2 | 1.20 | ||||
| τ00 fp | 0.01 | ||||
| τ11 fp.Emospider | 1.12 | ||||
| τ11 fp.Emonegative | 0.61 | ||||
| τ11 fp.Emopositive | 0.46 | ||||
| ρ01 | 0.14 | ||||
| -0.15 | |||||
| 0.79 | |||||
| ICC | 0.33 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.574 / 0.713 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from controls in spider (vs neutral) ratings in the first session (but not in any other picture category). The analysis compares IVET and VRET separately to the control group and does not test whether the treatments differ from each other.
The formula was rating ~ 1 + treat * Emo + (1 + Emo | fp).
Up to Emo as random effects: This means that the emo effect can differ between subjects.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = 5.15. This is the mean rating for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t-test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether IVET and VRET differ from controls in their spider ratings. Because the intercept contains treatment(control) and emotion(neutral), we are interested in these tests:
For IVET:
treatIVET:Emospider
In the model table with condition labels, this is number 7.
treatment (IVET) / emotion (spider).
- estimate: -2.09
- p value: 1.5188e-08
This is the interaction of treatment(IVET vs control) x emotion (spider vs neutral) across ratings.
For VRET (same test as for IVET):
treatVRET:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET) / emotion (spider).
- estimate: -2.19
- p value: 1.5072e-10
This is the interaction of treatment(VRET vs control) x emotion (spider vs neutral) across ratings.
estimated means
mmeans1 <- data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA)) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean)
mmeans1 %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | 5.15 | 4.25 | 3.30 | 6.80 |
| IVET | 5.22 | 2.24 | 3.29 | 7.24 |
| VRET | 5.30 | 2.21 | 3.47 | 6.84 |
session 1 across treatments
- use session 1 from all three groups
- combine treatment groups
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_across_treat_rating_valence"
model_formula <- formula("rating ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- rate_baseline_acrosstreatment %>%
filter(rating_type == "Ple")
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 1e5)),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plots
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .15), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .15), size = .5) +
scale_color_manual(values = palette2, name = "treatment") +
labs(y = "predicted valence\n", x = "\nemotion") +
plot_aes
### summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control: lmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 100000))
##
## REML criterion at convergence: 11262.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.5083 -0.4799 -0.0901 0.5618 4.9368
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 0.005582 0.07471
## Emospider 1.109578 1.05336 0.16
## Emonegative 0.605433 0.77810 -0.12 0.24
## Emopositive 0.478508 0.69174 0.77 -0.28 -0.66
## Residual 1.199056 1.09501
## Number of obs: 3560, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.14615 0.04912 633.02852 104.757
## treatIVET/VRET 0.11871 0.07619 633.02852 1.558
## Emospider -0.89615 0.16109 87.79048 -5.563
## Emonegative -1.84615 0.12749 89.29368 -14.480
## Emopositive 1.65000 0.11753 91.00494 14.039
## treatIVET/VRET:Emospider -2.14709 0.24984 87.79048 -8.594
## treatIVET/VRET:Emonegative -0.02952 0.19773 89.29368 -0.149
## treatIVET/VRET:Emopositive 0.09865 0.18229 91.00494 0.541
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## treatIVET/VRET 0.120
## Emospider 0.000000282864217 ***
## Emonegative < 0.0000000000000002 ***
## Emopositive < 0.0000000000000002 ***
## treatIVET/VRET:Emospider 0.000000000000286 ***
## treatIVET/VRET:Emonegative 0.882
## treatIVET/VRET:Emopositive 0.590
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET/VRET Emspdr Emngtv Empstv trtIVET/VRET:Ems
## trIVET/VRET -0.645
## Emospider -0.261 0.168
## Emonegative -0.389 0.251 0.297
## Emopositive -0.266 0.172 -0.088 -0.300
## trtIVET/VRET:Ems 0.168 -0.261 -0.645 -0.191 0.057
## trtIVET/VRET:Emn 0.251 -0.389 -0.191 -0.645 0.194 0.297
## trtIVET/VRET:Emp 0.172 -0.266 0.057 0.194 -0.645 -0.088
## trtIVET/VRET:Emn
## trIVET/VRET
## Emospider
## Emonegative
## Emopositive
## trtIVET/VRET:Ems
## trtIVET/VRET:Emn
## trtIVET/VRET:Emp -0.300
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingulartidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:8)),
original = tidied_model$term[1:8],
standard = c("intercept (control, neutral)",
"treatment (IVET/VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET/VRET) x emotion (spider)",
"treatment (IVET/VRET) x emotion (negative)",
"treatment (IVET/VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET/VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET/VRET) / emotion (spider)",
"treatment (IVET/VRET) / emotion (negative)",
"treatment (IVET/VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET/VRET | treatment (IVET/VRET) | treatment (IVET/VRET) / emotion (neutral) |
| 3 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 4 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 5 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 6 | treatIVET/VRET:Emospider | treatment (IVET/VRET) x emotion (spider) | treatment (IVET/VRET) / emotion (spider) |
| 7 | treatIVET/VRET:Emonegative | treatment (IVET/VRET) x emotion (negative) | treatment (IVET/VRET) / emotion (negative) |
| 8 | treatIVET/VRET:Emopositive | treatment (IVET/VRET) x emotion (positive) | treatment (IVET/VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | 5.15 | 5.05 – 5.24 | 0.05 | 104.76 | <0.001 |
| 2 treatment (IVET/VRET) | 0.12 | -0.03 – 0.27 | 0.08 | 1.56 | 0.120 |
| 3 emotion (spider) | -0.90 | -1.22 – -0.58 | 0.16 | -5.56 | <0.001 |
| 4 emotion (negative) | -1.85 | -2.10 – -1.59 | 0.13 | -14.48 | <0.001 |
| 5 emotion (positive) | 1.65 | 1.42 – 1.88 | 0.12 | 14.04 | <0.001 |
| 6 treatment (IVET/VRET) x emotion (spider) | -2.15 | -2.64 – -1.65 | 0.25 | -8.59 | <0.001 |
| 7 treatment (IVET/VRET) x emotion (negative) | -0.03 | -0.42 – 0.36 | 0.20 | -0.15 | 0.882 |
| 8 treatment (IVET/VRET) x emotion (positive) | 0.10 | -0.26 – 0.46 | 0.18 | 0.54 | 0.590 |
| Random Effects | |||||
| σ2 | 1.20 | ||||
| τ00 fp | 0.01 | ||||
| τ11 fp.Emospider | 1.11 | ||||
| τ11 fp.Emonegative | 0.61 | ||||
| τ11 fp.Emopositive | 0.48 | ||||
| ρ01 | 0.16 | ||||
| -0.12 | |||||
| 0.77 | |||||
| ICC | 0.32 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.574 / 0.712 | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | 5.15 | 5.05 – 5.24 | 0.05 | 104.76 | <0.001 |
| 2 treatment (IVET/VRET) / emotion (neutral) | 0.12 | -0.03 – 0.27 | 0.08 | 1.56 | 0.120 |
| 3 treatment (control) / emotion (spider) | -0.90 | -1.22 – -0.58 | 0.16 | -5.56 | <0.001 |
| 4 treatment (control) / emotion (negative) | -1.85 | -2.10 – -1.59 | 0.13 | -14.48 | <0.001 |
| 5 treatment (control) / emotion (positive) | 1.65 | 1.42 – 1.88 | 0.12 | 14.04 | <0.001 |
| 6 treatment (IVET/VRET) / emotion (spider) | -2.15 | -2.64 – -1.65 | 0.25 | -8.59 | <0.001 |
| 7 treatment (IVET/VRET) / emotion (negative) | -0.03 | -0.42 – 0.36 | 0.20 | -0.15 | 0.882 |
| 8 treatment (IVET/VRET) / emotion (positive) | 0.10 | -0.26 – 0.46 | 0.18 | 0.54 | 0.590 |
| Random Effects | |||||
| σ2 | 1.20 | ||||
| τ00 fp | 0.01 | ||||
| τ11 fp.Emospider | 1.11 | ||||
| τ11 fp.Emonegative | 0.61 | ||||
| τ11 fp.Emopositive | 0.48 | ||||
| ρ01 | 0.16 | ||||
| -0.12 | |||||
| 0.77 | |||||
| ICC | 0.32 | ||||
| N fp | 89 | ||||
| Observations | 3560 | ||||
| Marginal R2 / Conditional R2 | 0.574 / 0.712 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether the combined treatment groups (IVET and VRET) differ from controls in spider (vs neutral) ratings in the first session (but not in any other picture category). The analysis compares the combined IVET and VRET to the control group and does not test whether the treatments differ from each other.
The formula was rating ~ 1 + treat * Emo + (1 + Emo | fp).
Up to Emo as random effects: This means that the emo effect can differ between subjects.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = 5.15. This is the mean rating for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t-test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether the combined treatment groups (IVET and VRET) differ from controls in their spider ratings. Because the intercept contains treatment(control) and emotion(neutral), we are interested in these tests:
treatIVET/VRET:Emospider
In the model table with condition labels, this is number 6.
treatment (IVET/VRET) / emotion (spider).
- estimate: -2.15
- p value: 2.8589e-13
This is the interaction of treatment(IVET/VRET vs control) x emotion (spider vs neutral) across ratings.
estimated means
data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA)) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | 5.15 | 4.25 | 3.30 | 6.80 |
| IVET/VRET | 5.26 | 2.22 | 3.39 | 7.01 |
Bayes
ordinal model
ratings_valence_sess1 <- rate_baseline_acrosstreatment %>%
filter(rating_type == "Ple") %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp))
# Ordinal Regression Model.
ratings_valence.sess1.model <- brm(rating ~ 1 + treat*Emo + (1 + Emo | fp),
family = cumulative("probit"),
data = na.omit(ratings_valence_sess1),
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/ratings_valence.sess1.model",
# file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(ratings_valence.sess1.model)## Family: cumulative
## Links: mu = probit; disc = identity
## Formula: rating ~ 1 + treat * Emo + (1 + Emo | fp)
## Data: na.omit(ratings_valence_sess1) (Number of observations: 1780)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 89)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.19 0.09 0.02 0.34 1.01 640
## sd(Emospider) 1.43 0.13 1.20 1.72 1.00 1322
## cor(Intercept,Emospider) -0.00 0.30 -0.52 0.72 1.04 126
## Tail_ESS
## sd(Intercept) 1173
## sd(Emospider) 3117
## cor(Intercept,Emospider) 287
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept[1] -4.17 0.13 -4.43 -3.92 1.00 7076
## Intercept[2] -3.21 0.11 -3.43 -2.99 1.00 7800
## Intercept[3] -2.00 0.08 -2.16 -1.83 1.00 7364
## Intercept[4] -1.29 0.07 -1.44 -1.14 1.00 7997
## Intercept[5] 1.03 0.07 0.90 1.16 1.00 7331
## Intercept[6] 1.43 0.07 1.29 1.58 1.00 7921
## Intercept[7] 2.10 0.10 1.92 2.29 1.00 7942
## Intercept[8] 2.46 0.12 2.23 2.71 1.00 7436
## treatIVETDVRET 0.19 0.09 0.01 0.37 1.00 7553
## Emospider -1.17 0.21 -1.60 -0.77 1.00 1832
## treatIVETDVRET:Emospider -2.71 0.33 -3.38 -2.06 1.00 1995
## Tail_ESS
## Intercept[1] 5824
## Intercept[2] 5732
## Intercept[3] 6336
## Intercept[4] 5945
## Intercept[5] 6130
## Intercept[6] 6392
## Intercept[7] 5444
## Intercept[8] 6237
## treatIVETDVRET 5807
## Emospider 3338
## treatIVETDVRET:Emospider 3226
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null_valence.sess1.model <- brm(rating ~ 1 + (1 + Emo | fp),
family = cumulative("probit"),
data = ratings_valence_sess1,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/rating_valence.sess1.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
emo_valence.sess1.model <- brm(rating ~ 1 + Emo + (1 + Emo | fp),
family = cumulative("probit"),
data = ratings_valence_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_valence.sess1.emo",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
treat_valence.sess1.model <- brm(rating ~ 1 + treat + (1 + Emo | fp),
family = cumulative("probit"),
data = ratings_valence_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_valence.sess1.treat",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
full_valence.sess1.bayes <- bayes_factor(ratings_valence.sess1.model, null_valence.sess1.model)## Iteration: 1
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## Iteration: 1full_valence.sess1.bayes## Estimated Bayes factor in favor of ratings_valence.sess1.model over null_valence.sess1.model: 5955984675155534663288468.00000treat_valence.sess1.bayes## Estimated Bayes factor in favor of treat_valence.sess1.model over null_valence.sess1.model: 0.00015emo_valence.sess1.bayes## Estimated Bayes factor in favor of emo_valence.sess1.model over null_valence.sess1.model: 8323827854170430.00000compare with null
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Null = format(c(full_valence.sess1.bayes$bf,
treat_valence.sess1.bayes$bf,
emo_valence.sess1.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxEmo | 5.955985e+24 |
| Treat | 1.492199e-04 |
| Emo | 8.323828e+15 |
compare with Emo
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Emo =
format(c(full_valence.sess1.bayes$bf/emo_valence.sess1.bayes$bf,
treat_valence.sess1.bayes$bf/emo_valence.sess1.bayes$bf,
emo_valence.sess1.bayes$bf/emo_valence.sess1.bayes$bf),
scientific = TRUE),
BF01 =
format(c(emo_valence.sess1.bayes$bf/full_valence.sess1.bayes$bf,
emo_valence.sess1.bayes$bf/treat_valence.sess1.bayes$bf,
emo_valence.sess1.bayes$bf/emo_valence.sess1.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Emo | BF01 |
|---|---|---|
| TreatxEmo | 7.155343e+08 | 1.397557e-09 |
| Treat | 1.792684e-20 | 5.578228e+19 |
| Emo | 1.000000e+00 | 1.000000e+00 |
check assumptions
An ordinal regression has four assumptions:
- The dependent variables are ordered.
- One or more of the independent variables are either continuous, categorical, or ordinal.
- No multi-collinearity.
- Proportional odds.
Check vif and tolerance (multicollinearity)
check_collinearity(ratings_valence.sess1.model)treatment comparison
- session 1 and session 2 (session 1 as reference)
- include only treatment groups
- IVET = -.5, VRET = .5
- use neutral pictures as reference emotion
model_name <- "only_treat_rating_valence"
model_formula <- formula("rating ~ 1 + treat*sess*Emo + (1 + sess*Emo | fp)")
data <- rate_only_treat_recode %>%
filter(rating_type == "Ple")
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "nloptwrap",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plots
all categories
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted valence\n", x = "\nsession") +
plot_aes
spider and neutral ratings
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
filter(Emo %in% c("neutral", "spider")) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
filter(facet %in% c("neutral", "spider")) %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted valence\n", x = "\nsession") +
plot_aes
ggsave('results/figures/fig_rating_valence_treat.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "nloptwrap", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 12672.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.9989 -0.4449 -0.0886 0.5322 6.1583
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 0.000000 0.00000
## sess 0.007701 0.08776 NaN
## Emospider 0.945369 0.97230 NaN -0.67
## Emonegative 0.687228 0.82899 NaN -0.64 0.46
## Emopositive 0.648587 0.80535 NaN 0.70 -0.51 -0.49
## sess:Emospider 1.246364 1.11641 NaN 0.09 -0.35 0.09 0.33
## sess:Emonegative 0.495650 0.70402 NaN -0.59 0.41 -0.21 -0.34
## sess:Emopositive 0.110681 0.33269 NaN -0.19 0.12 -0.13 -0.49
## Residual 1.105887 1.05161
##
##
##
##
##
##
##
## -0.29
## -0.37 0.52
##
## Number of obs: 4120, groups: fp, 70
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 5.25938 0.05518 3805.17270 95.319
## treat 0.08125 0.11035 3805.17272 0.736
## sess -0.15341 0.06956 949.66103 -2.205
## Emospider -3.12865 0.16124 49.89962 -19.404
## Emonegative -1.96662 0.14225 54.31144 -13.825
## Emopositive 1.85772 0.13262 52.31807 14.008
## treat:sess -0.09901 0.13913 949.66103 -0.712
## treat:Emospider -0.34444 0.32248 49.89962 -1.068
## treat:Emonegative -0.10529 0.28449 54.31144 -0.370
## treat:Emopositive -0.33251 0.26524 52.31807 -1.254
## sess:Emospider 1.36332 0.18698 51.88640 7.291
## sess:Emonegative 0.26072 0.14625 52.22535 1.783
## sess:Emopositive -0.27034 0.11662 79.82985 -2.318
## treat:sess:Emospider 0.59326 0.37397 51.88640 1.586
## treat:sess:Emonegative 0.60865 0.29250 52.22535 2.081
## treat:sess:Emopositive -0.19312 0.23324 79.82985 -0.828
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## treat 0.4616
## sess 0.0277 *
## Emospider < 0.0000000000000002 ***
## Emonegative < 0.0000000000000002 ***
## Emopositive < 0.0000000000000002 ***
## treat:sess 0.4769
## treat:Emospider 0.2906
## treat:Emonegative 0.7128
## treat:Emopositive 0.2156
## sess:Emospider 0.00000000172 ***
## sess:Emonegative 0.0804 .
## sess:Emopositive 0.0230 *
## treat:sess:Emospider 0.1187
## treat:sess:Emonegative 0.0424 *
## treat:sess:Emopositive 0.4101
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:16)),
original = tidied_model$term[1:16],
standard = c("intercept (avr_treat, session (1), neutral)",
"treatment (VRET vs IVET)",
"session (2)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (VRET vs IVET) x session",
"treatment (VRET vs IVET) x emotion (spider)",
"treatment (VRET vs IVET) x emotion (negative)",
"treatment (VRET vs IVET) x emotion (positive)",
"session x emotion (spider)",
"session x emotion (negative)",
"session x emotion (positive)",
"treatment (VRET vs IVET) x session x emotion (spider)",
"treatment (VRET vs IVET) x session x emotion (negative)",
"treatment (VRET vs IVET) x session x emotion (positive)"),
condition = c("treatment (avr_treat) / session (1) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (neutral)",
"treatment (avr_treat) / sess (2) / emotion (neutral)",
"treatment (avr_treat) / sess (1) / emotion (spider)",
"treatment (avr_treat) / sess (1) / emotion (negative)",
"treatment (avr_treat) / sess (1) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (spider)",
"treatment (VRET vs IVET) / sess (1) / emotion (negative)",
"treatment (VRET vs IVET) / sess (1) / emotion (positive)",
"treatment (avr_treat) / sess (2) / emotion (spider)",
"treatment (avr_treat) / sess (2) / emotion (negative)",
"treatment (avr_treat) / sess (2) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (spider)",
"treatment (VRET vs IVET) / sess (2) / emotion (negative)",
"treatment (VRET vs IVET) / sess (2) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (avr_treat, session (1), neutral) | treatment (avr_treat) / session (1) / emotion (neutral) |
| 2 | treat | treatment (VRET vs IVET) | treatment (VRET vs IVET) / sess (1) / emotion (neutral) |
| 3 | sess | session (2) | treatment (avr_treat) / sess (2) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (avr_treat) / sess (1) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (avr_treat) / sess (1) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (avr_treat) / sess (1) / emotion (positive) |
| 7 | treat:sess | treatment (VRET vs IVET) x session | treatment (VRET vs IVET) / sess (2) / emotion (neutral) |
| 8 | treat:Emospider | treatment (VRET vs IVET) x emotion (spider) | treatment (VRET vs IVET) / sess (1) / emotion (spider) |
| 9 | treat:Emonegative | treatment (VRET vs IVET) x emotion (negative) | treatment (VRET vs IVET) / sess (1) / emotion (negative) |
| 10 | treat:Emopositive | treatment (VRET vs IVET) x emotion (positive) | treatment (VRET vs IVET) / sess (1) / emotion (positive) |
| 11 | sess:Emospider | session x emotion (spider) | treatment (avr_treat) / sess (2) / emotion (spider) |
| 12 | sess:Emonegative | session x emotion (negative) | treatment (avr_treat) / sess (2) / emotion (negative) |
| 13 | sess:Emopositive | session x emotion (positive) | treatment (avr_treat) / sess (2) / emotion (positive) |
| 14 | treat:sess:Emospider | treatment (VRET vs IVET) x session x emotion (spider) | treatment (VRET vs IVET) / sess (2) / emotion (spider) |
| 15 | treat:sess:Emonegative | treatment (VRET vs IVET) x session x emotion (negative) | treatment (VRET vs IVET) / sess (2) / emotion (negative) |
| 16 | treat:sess:Emopositive | treatment (VRET vs IVET) x session x emotion (positive) | treatment (VRET vs IVET) / sess (2) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (avr_treat, session (1), neutral) | 5.26 | 5.15 – 5.37 | 0.06 | 95.32 | <0.001 |
| 2 treatment (VRET vs IVET) | 0.08 | -0.14 – 0.30 | 0.11 | 0.74 | 0.462 |
| 3 session (2) | -0.15 | -0.29 – -0.02 | 0.07 | -2.21 | 0.028 |
| 4 emotion (spider) | -3.13 | -3.45 – -2.80 | 0.16 | -19.40 | <0.001 |
| 5 emotion (negative) | -1.97 | -2.25 – -1.68 | 0.14 | -13.83 | <0.001 |
| 6 emotion (positive) | 1.86 | 1.59 – 2.12 | 0.13 | 14.01 | <0.001 |
| 7 treatment (VRET vs IVET) x session | -0.10 | -0.37 – 0.17 | 0.14 | -0.71 | 0.477 |
| 8 treatment (VRET vs IVET) x emotion (spider) | -0.34 | -0.99 – 0.30 | 0.32 | -1.07 | 0.291 |
| 9 treatment (VRET vs IVET) x emotion (negative) | -0.11 | -0.68 – 0.47 | 0.28 | -0.37 | 0.713 |
| 10 treatment (VRET vs IVET) x emotion (positive) | -0.33 | -0.86 – 0.20 | 0.27 | -1.25 | 0.216 |
| 11 session x emotion (spider) | 1.36 | 0.99 – 1.74 | 0.19 | 7.29 | <0.001 |
| 12 session x emotion (negative) | 0.26 | -0.03 – 0.55 | 0.15 | 1.78 | 0.080 |
| 13 session x emotion (positive) | -0.27 | -0.50 – -0.04 | 0.12 | -2.32 | 0.023 |
| 14 treatment (VRET vs IVET) x session x emotion (spider) | 0.59 | -0.16 – 1.34 | 0.37 | 1.59 | 0.119 |
| 15 treatment (VRET vs IVET) x session x emotion (negative) | 0.61 | 0.02 – 1.20 | 0.29 | 2.08 | 0.042 |
| 16 treatment (VRET vs IVET) x session x emotion (positive) | -0.19 | -0.66 – 0.27 | 0.23 | -0.83 | 0.410 |
| Random Effects | |||||
| σ2 | 1.11 | ||||
| τ00 fp | 0.00 | ||||
| τ11 fp.sess | 0.01 | ||||
| τ11 fp.Emospider | 0.95 | ||||
| τ11 fp.Emonegative | 0.69 | ||||
| τ11 fp.Emopositive | 0.65 | ||||
| τ11 fp.sess:Emospider | 1.25 | ||||
| τ11 fp.sess:Emonegative | 0.50 | ||||
| τ11 fp.sess:Emopositive | 0.11 | ||||
| ρ01 | |||||
| N fp | 70 | ||||
| Observations | 4120 | ||||
| Marginal R2 / Conditional R2 | 0.697 / NA | ||||
condition labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (avr_treat) / session (1) / emotion (neutral) | 5.26 | 5.15 – 5.37 | 0.06 | 95.32 | <0.001 |
| 2 treatment (VRET vs IVET) / sess (1) / emotion (neutral) | 0.08 | -0.14 – 0.30 | 0.11 | 0.74 | 0.462 |
| 3 treatment (avr_treat) / sess (2) / emotion (neutral) | -0.15 | -0.29 – -0.02 | 0.07 | -2.21 | 0.028 |
| 4 treatment (avr_treat) / sess (1) / emotion (spider) | -3.13 | -3.45 – -2.80 | 0.16 | -19.40 | <0.001 |
| 5 treatment (avr_treat) / sess (1) / emotion (negative) | -1.97 | -2.25 – -1.68 | 0.14 | -13.83 | <0.001 |
| 6 treatment (avr_treat) / sess (1) / emotion (positive) | 1.86 | 1.59 – 2.12 | 0.13 | 14.01 | <0.001 |
| 7 treatment (VRET vs IVET) / sess (2) / emotion (neutral) | -0.10 | -0.37 – 0.17 | 0.14 | -0.71 | 0.477 |
| 8 treatment (VRET vs IVET) / sess (1) / emotion (spider) | -0.34 | -0.99 – 0.30 | 0.32 | -1.07 | 0.291 |
| 9 treatment (VRET vs IVET) / sess (1) / emotion (negative) | -0.11 | -0.68 – 0.47 | 0.28 | -0.37 | 0.713 |
| 10 treatment (VRET vs IVET) / sess (1) / emotion (positive) | -0.33 | -0.86 – 0.20 | 0.27 | -1.25 | 0.216 |
| 11 treatment (avr_treat) / sess (2) / emotion (spider) | 1.36 | 0.99 – 1.74 | 0.19 | 7.29 | <0.001 |
| 12 treatment (avr_treat) / sess (2) / emotion (negative) | 0.26 | -0.03 – 0.55 | 0.15 | 1.78 | 0.080 |
| 13 treatment (avr_treat) / sess (2) / emotion (positive) | -0.27 | -0.50 – -0.04 | 0.12 | -2.32 | 0.023 |
| 14 treatment (VRET vs IVET) / sess (2) / emotion (spider) | 0.59 | -0.16 – 1.34 | 0.37 | 1.59 | 0.119 |
| 15 treatment (VRET vs IVET) / sess (2) / emotion (negative) | 0.61 | 0.02 – 1.20 | 0.29 | 2.08 | 0.042 |
| 16 treatment (VRET vs IVET) / sess (2) / emotion (positive) | -0.19 | -0.66 – 0.27 | 0.23 | -0.83 | 0.410 |
| Random Effects | |||||
| σ2 | 1.11 | ||||
| τ00 fp | 0.00 | ||||
| τ11 fp.sess | 0.01 | ||||
| τ11 fp.Emospider | 0.95 | ||||
| τ11 fp.Emonegative | 0.69 | ||||
| τ11 fp.Emopositive | 0.65 | ||||
| τ11 fp.sess:Emospider | 1.25 | ||||
| τ11 fp.sess:Emonegative | 0.50 | ||||
| τ11 fp.sess:Emopositive | 0.11 | ||||
| ρ01 | |||||
| N fp | 70 | ||||
| Observations | 4120 | ||||
| Marginal R2 / Conditional R2 | 0.697 / NA | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from each other in spider (vs neutral) ratings in the first session and between the first and second session (but not in any other picture category).
The formula was rating ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp).
Emo by sess as random effects: This means that emo, session, and the emo by session can differ between subjects.
Intercept = treatment(avr_treat) / session (1) / emotion (neutral).
avr_treat is the mean of IVET and VRET.
The effect for the intercept = 5.26. This is the mean rating for the intercept that contains the average across treatments in session 1 to neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t-test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether the groups rated spiders differently from neutral pictures in session 1.
Emospider
In the model table with condition labels, this is number 4.
treatment (avr_treat) / sess (1) / emotion (spider).
- estimate: -3.13
- p value: 6.7617e-25
Indeed, spiders are rated more emotional.
(Note that the session 1 analysis with three groups tested each treatment compared to the control group.)
Did the groups differ in how they rated spiders from neutral pictures in session 1? The next analysis suggests: No.
treat:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET vs IVET) / sess (1) / emotion (spider).
- estimate: -0.34
- p value: 2.9061e-01
(Note that the session 1 analysis with three groups tested each treatment compared to the control group.)
Next, we examine whether the effect of spiders differed between sessions.
sess:Emospider
In the model table with condition labels, this is number 11.
treatment (avr_treat) / sess (2) / emotion (spider).
- estimate: 1.36
- p value: 1.7200e-09
Indeed, spiders (vs neutral) are rated less emotional in session 2 than session 1.
Critically, did this effect vary with treatment?
treat:sess:Emospider
In the model table with condition labels, this is number 14.
treatment (VRET vs IVET) / sess (2) / emotion (spider).
- estimate: 0.59
- p value: 1.1873e-01
No, it does not look like that the treatment groups differed.
All the other tests concern pictures other than spiders.
estimated means
data %>%
modelr::data_grid(treat, Emo, sess) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),
treat = ifelse(treat == -.5, "IVET", "VRET"),
sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post'))) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | sess | neutral | spider | negative | positive |
|---|---|---|---|---|---|
| IVET | pre | 5.22 | 2.26 | 3.30 | 7.24 |
| IVET | post | 5.11 | 3.23 | 3.16 | 6.97 |
| VRET | pre | 5.30 | 2.00 | 3.28 | 6.99 |
| VRET | post | 5.10 | 3.46 | 3.64 | 6.42 |
Bayes
ordinal model
ratings_valence_treat <- rate_only_treat_recode %>%
filter(rating_type == "Ple") %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp))
# Ordinal Regression Model.
ratings_valence.treat.model <- brm(rating ~ 1 + treat*sess*Emo + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = na.omit(ratings_valence_treat),
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/ratings_valence.treat.model",
# file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(ratings_valence.treat.model)## Family: cumulative
## Links: mu = probit; disc = identity
## Formula: rating ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp)
## Data: na.omit(ratings_valence_treat) (Number of observations: 2060)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 70)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.08 0.06 0.00 0.22 1.00
## sd(sess) 0.08 0.06 0.00 0.23 1.00
## sd(Emospider) 1.40 0.21 1.05 1.87 1.00
## sd(sess:Emospider) 1.59 0.23 1.18 2.10 1.00
## cor(Intercept,sess) -0.14 0.45 -0.89 0.77 1.00
## cor(Intercept,Emospider) -0.05 0.40 -0.78 0.76 1.01
## cor(sess,Emospider) -0.02 0.43 -0.79 0.77 1.01
## cor(Intercept,sess:Emospider) 0.16 0.41 -0.70 0.84 1.01
## cor(sess,sess:Emospider) -0.18 0.42 -0.87 0.69 1.01
## cor(Emospider,sess:Emospider) -0.40 0.14 -0.66 -0.10 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 2019 3905
## sd(sess) 2160 3296
## sd(Emospider) 3548 5125
## sd(sess:Emospider) 2477 4752
## cor(Intercept,sess) 4845 5068
## cor(Intercept,Emospider) 393 999
## cor(sess,Emospider) 303 904
## cor(Intercept,sess:Emospider) 385 494
## cor(sess,sess:Emospider) 410 1394
## cor(Emospider,sess:Emospider) 3360 4605
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept[1] -4.72 0.13 -4.97 -4.48 1.00 7904
## Intercept[2] -3.82 0.11 -4.04 -3.60 1.00 9498
## Intercept[3] -2.41 0.09 -2.59 -2.23 1.00 10258
## Intercept[4] -1.66 0.08 -1.83 -1.50 1.00 10560
## Intercept[5] 0.97 0.07 0.83 1.11 1.00 10446
## Intercept[6] 1.27 0.08 1.12 1.43 1.00 11353
## Intercept[7] 1.80 0.10 1.62 2.00 1.00 12595
## Intercept[8] 2.13 0.12 1.91 2.37 1.00 13727
## treat 0.04 0.13 -0.22 0.30 1.00 5931
## sess -0.23 0.08 -0.40 -0.07 1.00 12733
## Emospider -4.25 0.25 -4.76 -3.76 1.00 4060
## treat:sess -0.03 0.17 -0.36 0.29 1.00 6545
## treat:Emospider -0.20 0.49 -1.17 0.76 1.00 3615
## sess:Emospider 1.73 0.27 1.21 2.27 1.00 4068
## treat:sess:Emospider 0.50 0.56 -0.60 1.58 1.00 3558
## Tail_ESS
## Intercept[1] 5756
## Intercept[2] 6184
## Intercept[3] 6712
## Intercept[4] 6575
## Intercept[5] 6584
## Intercept[6] 7093
## Intercept[7] 6035
## Intercept[8] 6122
## treat 5880
## sess 5972
## Emospider 5333
## treat:sess 6174
## treat:Emospider 4921
## sess:Emospider 5547
## treat:sess:Emospider 4295
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## disc 1.00 0.00 1.00 1.00 NA NA NA
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null_valence.treat.model <- brm(rating ~ 1 + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = ratings_valence_treat,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/rating_valence.treat.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
sess_emo.treat_valence.model <- brm(rating ~ 1 + sess*Emo + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = ratings_valence_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_valence.treat.sess_emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))
emo.treat_valence.model <- brm(rating ~ 1 + Emo + (1 + sess*Emo | fp),
family = cumulative("probit"),
data = ratings_valence_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/rating_valence.treat.emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
full.treat_valence.bayes <- bayes_factor(ratings_valence.treat.model, null_valence.treat.model)## Iteration: 1
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## Iteration: 1full.treat_valence.bayes## Estimated Bayes factor in favor of ratings_valence.treat.model over null_valence.treat.model: 340797569866239771220824860464082048864200060242866422404684488666848846088060284620620808422822044466464062222.00000sess_emo.treat_valence.bayes## Estimated Bayes factor in favor of sess_emo.treat_valence.model over null_valence.treat.model: 1497734727796046631080424020620602666860080026282064042886664088886840660248264088262442600648008266040404842284262.00000emo.treat_valence.bayes## Estimated Bayes factor in favor of emo.treat_valence.model over null_valence.treat.model: 91035955249920028720224822202402626042802028880860646446626468828064808822442028408668646660.00000compare with null
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Null = format(c(full.treat_valence.bayes$bf,
sess_emo.treat_valence.bayes$bf,
emo.treat_valence.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxSessxEmo | 3.407976e+110 |
| SessxEmo | 1.497735e+114 |
| Emo | 9.103596e+91 |
compare with Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_SessxEmo =
format(c(full.treat_valence.bayes$bf/sess_emo.treat_valence.bayes$bf,
sess_emo.treat_valence.bayes$bf/sess_emo.treat_valence.bayes$bf,
emo.treat_valence.bayes$bf/sess_emo.treat_valence.bayes$bf),
scientific = TRUE),
BF01 = format(c(sess_emo.treat_valence.bayes$bf/full.treat_valence.bayes$bf,
sess_emo.treat_valence.bayes$bf/sess_emo.treat_valence.bayes$bf,
sess_emo.treat_valence.bayes$bf/emo.treat_valence.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_SessxEmo | BF01 |
|---|---|---|
| TreatxSessxEmo | 2.275420e-04 | 4.394793e+03 |
| SessxEmo | 1.000000e+00 | 1.000000e+00 |
| Emo | 6.078243e-23 | 1.645212e+22 |
compare with Treat x Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_TreatxSessxEmo =
format(c(full.treat_valence.bayes$bf/full.treat_valence.bayes$bf,
sess_emo.treat_valence.bayes$bf/full.treat_valence.bayes$bf,
emo.treat_valence.bayes$bf/full.treat_valence.bayes$bf),
scientific = TRUE),
BF01 = format(c(full.treat_valence.bayes$bf/full.treat_valence.bayes$bf,
full.treat_valence.bayes$bf/sess_emo.treat_valence.bayes$bf,
full.treat_valence.bayes$bf/emo.treat_valence.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_TreatxSessxEmo | BF01 |
|---|---|---|
| TreatxSessxEmo | 1.000000e+00 | 1.000000e+00 |
| SessxEmo | 4.394793e+03 | 2.275420e-04 |
| Emo | 2.671262e-19 | 3.743549e+18 |
check assumptions
An ordinal regression has four assumptions:
- The dependent variables are ordered.
- One or more of the independent variables are either continuous, categorical, or ordinal.
- No multi-collinearity.
- Proportional odds.
Check vif and tolerance (multicollinearity)
check_collinearity(ratings_valence.treat.model)EEG: EPN-relevant amplitude
EEG data during the detection task
session 1 three groups
- use session 1 from all three groups
- examine whether IVET and VRET differ from controls to spiders (vs neutral) in session 1
- compare IVET and VRET separately to the control group
- do not test whether the treatments differ from each other
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_all_groups_EPN"
model_formula <- formula("EPN ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- detect_baseline
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "nloptwrap",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}
# with nloptwrap: Model failed to converge with 1 negative eigenvalue: -1.5e+03
# Nelder_Mead: Model failed to converge with 1 negative eigenvalue: -2.3e+02
# results looked similarplot
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .15), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .15), size = .5) +
scale_color_manual(values = palette, name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nemotion") +
plot_aes
ggsave('results/figures/fig_meanamps_EPN_pre.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "nloptwrap", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 109165.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.5941 -0.5970 0.0034 0.6177 4.0229
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 9.0953 3.0158
## Emospider 0.0255 0.1597 -1.00
## Emonegative 0.7771 0.8815 -0.10 0.10
## Emopositive 0.8176 0.9042 -0.05 0.05 0.64
## Residual 30.7074 5.5414
## Number of obs: 17360, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 4.8798 0.4325 86.1517 11.282
## treatIVET 0.4419 0.8917 86.1771 0.496
## treatVRET 0.3926 0.8062 86.0656 0.487
## Emospider -0.5201 0.1573 1858.2153 -3.307
## Emonegative -1.4642 0.1981 115.9796 -7.392
## Emopositive -0.1879 0.2000 117.4984 -0.939
## treatIVET:Emospider -2.5674 0.3251 1876.8873 -7.897
## treatVRET:Emospider -2.1420 0.2924 1840.7098 -7.325
## treatIVET:Emonegative -0.2335 0.4082 115.7678 -0.572
## treatVRET:Emonegative -0.2796 0.3685 115.1414 -0.759
## treatIVET:Emopositive -0.4361 0.4129 117.9486 -1.056
## treatVRET:Emopositive -0.3384 0.3724 116.8471 -0.909
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## treatIVET 0.621482
## treatVRET 0.627536
## Emospider 0.000962 ***
## Emonegative 0.00000000002441116 ***
## Emopositive 0.349437
## treatIVET:Emospider 0.00000000000000481 ***
## treatVRET:Emospider 0.00000000000035467 ***
## treatIVET:Emonegative 0.568438
## treatVRET:Emonegative 0.449606
## treatIVET:Emopositive 0.293050
## treatVRET:Emopositive 0.365349
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET trVRET Emspdr Emngtv Empstv trtIVET:Ems trtVRET:Ems
## treatIVET -0.485
## treatVRET -0.536 0.260
## Emospider -0.315 0.153 0.169
## Emonegative -0.199 0.097 0.107 0.398
## Emopositive -0.169 0.082 0.090 0.390 0.554
## trtIVET:Ems 0.152 -0.314 -0.082 -0.484 -0.193 -0.189
## trtVRET:Ems 0.169 -0.082 -0.314 -0.538 -0.214 -0.210 0.260
## trtIVET:Emn 0.097 -0.200 -0.052 -0.193 -0.485 -0.269 0.398 0.104
## trtVRET:Emn 0.107 -0.052 -0.199 -0.214 -0.537 -0.298 0.104 0.398
## trtIVET:Emp 0.082 -0.169 -0.044 -0.189 -0.268 -0.484 0.389 0.102
## trtVRET:Emp 0.091 -0.044 -0.168 -0.210 -0.298 -0.537 0.101 0.389
## trtIVET:Emn trtVRET:Emn trtIVET:Emp
## treatIVET
## treatVRET
## Emospider
## Emonegative
## Emopositive
## trtIVET:Ems
## trtVRET:Ems
## trtIVET:Emn
## trtVRET:Emn 0.261
## trtIVET:Emp 0.554 0.144
## trtVRET:Emp 0.144 0.554 0.260tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:12)),
original = tidied_model$term[1:12],
standard = c("intercept (control, neutral)",
"treatment (IVET)",
"treatment (VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET) x emotion (spider)",
"treatment (VRET) x emotion (spider)",
"treatment (IVET) x emotion (negative)",
"treatment (VRET) x emotion (negative)",
"treatment (IVET) x emotion (positive)",
"treatment (VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET) / emotion (neutral)",
"treatment (VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET) / emotion (spider)",
"treatment (VRET) / emotion (spider)",
"treatment (IVET) / emotion (negative)",
"treatment (VRET) / emotion (negative)",
"treatment (IVET) / emotion (positive)",
"treatment (VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET | treatment (IVET) | treatment (IVET) / emotion (neutral) |
| 3 | treatVRET | treatment (VRET) | treatment (VRET) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 7 | treatIVET:Emospider | treatment (IVET) x emotion (spider) | treatment (IVET) / emotion (spider) |
| 8 | treatVRET:Emospider | treatment (VRET) x emotion (spider) | treatment (VRET) / emotion (spider) |
| 9 | treatIVET:Emonegative | treatment (IVET) x emotion (negative) | treatment (IVET) / emotion (negative) |
| 10 | treatVRET:Emonegative | treatment (VRET) x emotion (negative) | treatment (VRET) / emotion (negative) |
| 11 | treatIVET:Emopositive | treatment (IVET) x emotion (positive) | treatment (IVET) / emotion (positive) |
| 12 | treatVRET:Emopositive | treatment (VRET) x emotion (positive) | treatment (VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | 4.88 | 4.02 – 5.74 | 0.43 | 11.28 | <0.001 |
| 2 treatment (IVET) | 0.44 | -1.33 – 2.21 | 0.89 | 0.50 | 0.621 |
| 3 treatment (VRET) | 0.39 | -1.21 – 2.00 | 0.81 | 0.49 | 0.628 |
| 4 emotion (spider) | -0.52 | -0.83 – -0.21 | 0.16 | -3.31 | 0.001 |
| 5 emotion (negative) | -1.46 | -1.86 – -1.07 | 0.20 | -7.39 | <0.001 |
| 6 emotion (positive) | -0.19 | -0.58 – 0.21 | 0.20 | -0.94 | 0.349 |
| 7 treatment (IVET) x emotion (spider) | -2.57 | -3.21 – -1.93 | 0.33 | -7.90 | <0.001 |
| 8 treatment (VRET) x emotion (spider) | -2.14 | -2.72 – -1.57 | 0.29 | -7.33 | <0.001 |
| 9 treatment (IVET) x emotion (negative) | -0.23 | -1.04 – 0.58 | 0.41 | -0.57 | 0.568 |
| 10 treatment (VRET) x emotion (negative) | -0.28 | -1.01 – 0.45 | 0.37 | -0.76 | 0.450 |
| 11 treatment (IVET) x emotion (positive) | -0.44 | -1.25 – 0.38 | 0.41 | -1.06 | 0.293 |
| 12 treatment (VRET) x emotion (positive) | -0.34 | -1.08 – 0.40 | 0.37 | -0.91 | 0.365 |
| Random Effects | |||||
| σ2 | 30.71 | ||||
| τ00 fp | 9.10 | ||||
| τ11 fp.Emospider | 0.03 | ||||
| τ11 fp.Emonegative | 0.78 | ||||
| τ11 fp.Emopositive | 0.82 | ||||
| ρ01 | -1.00 | ||||
| -0.10 | |||||
| -0.05 | |||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.023 / NA | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | 4.88 | 4.02 – 5.74 | 0.43 | 11.28 | <0.001 |
| 2 treatment (IVET) / emotion (neutral) | 0.44 | -1.33 – 2.21 | 0.89 | 0.50 | 0.621 |
| 3 treatment (VRET) / emotion (neutral) | 0.39 | -1.21 – 2.00 | 0.81 | 0.49 | 0.628 |
| 4 treatment (control) / emotion (spider) | -0.52 | -0.83 – -0.21 | 0.16 | -3.31 | 0.001 |
| 5 treatment (control) / emotion (negative) | -1.46 | -1.86 – -1.07 | 0.20 | -7.39 | <0.001 |
| 6 treatment (control) / emotion (positive) | -0.19 | -0.58 – 0.21 | 0.20 | -0.94 | 0.349 |
| 7 treatment (IVET) / emotion (spider) | -2.57 | -3.21 – -1.93 | 0.33 | -7.90 | <0.001 |
| 8 treatment (VRET) / emotion (spider) | -2.14 | -2.72 – -1.57 | 0.29 | -7.33 | <0.001 |
| 9 treatment (IVET) / emotion (negative) | -0.23 | -1.04 – 0.58 | 0.41 | -0.57 | 0.568 |
| 10 treatment (VRET) / emotion (negative) | -0.28 | -1.01 – 0.45 | 0.37 | -0.76 | 0.450 |
| 11 treatment (IVET) / emotion (positive) | -0.44 | -1.25 – 0.38 | 0.41 | -1.06 | 0.293 |
| 12 treatment (VRET) / emotion (positive) | -0.34 | -1.08 – 0.40 | 0.37 | -0.91 | 0.365 |
| Random Effects | |||||
| σ2 | 30.71 | ||||
| τ00 fp | 9.10 | ||||
| τ11 fp.Emospider | 0.03 | ||||
| τ11 fp.Emonegative | 0.78 | ||||
| τ11 fp.Emopositive | 0.82 | ||||
| ρ01 | -1.00 | ||||
| -0.10 | |||||
| -0.05 | |||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.023 / NA | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from controls in spider (vs neutral) mean amplitude in the first session (but not in any other picture category). The analysis compares IVET and VRET separately to the control group and does not test whether the treatments differ from each other.
The formula was EPN ~ 1 + treat * Emo + (1 + Emo | fp).
Emo as random effect.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = 4.88. This is the mean amplitude for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The first effect shows that there is an effect of spider (vs neutral). It shows that for the control group, spiders have lower amps than neutral pictures. This relative negativity supports an EPN. But, this effect is not of particular interest because it is only for the control group.
Emospider
In the model table with condition labels, this is number 4.
treatment (control) / emotion (spider).
- estimate: -0.52
- p value: 9.6189e-04
The main interest is to see whether IVET and VRET differ from controls in their amps to spiders. Particularly, the difference between spiders and neutral pictures should be more negative for each treatment group compared to controls. Because the intercept contains treatment(control) and emotion(neutral), we are interested in these tests:
For IVET:
treatIVET:Emospider
In the model table with condition labels, this is number 7.
treatment (IVET) / emotion (spider).
- estimate: -2.57
- p value: 4.8116e-15
This is the interaction of treatment(IVET vs control) x emotion (spider vs neutral).
For VRET (same test as for IVET):
treatVRET:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET) / emotion (spider).
- estimate: -2.14
- p value: 3.5467e-13
This is the interaction of treatment(VRET vs control) x emotion (spider vs neutral).
estimated means
data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | 4.88 | 4.36 | 3.42 | 4.69 |
| IVET | 5.32 | 2.23 | 3.62 | 4.70 |
| VRET | 5.27 | 2.61 | 3.53 | 4.75 |
session 1 across treatments
- use session 1 from all three groups
- combine treatment groups
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_across_treat_EPN"
model_formula <- formula("EPN ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- detect_baseline_acrosstreatment
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "nloptwrap",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plot
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1), size = .5) +
scale_color_manual(values = palette2, name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nemotion") +
plot_aes
summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "nloptwrap", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 109131
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.6152 -0.5945 0.0013 0.6173 4.0387
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 9.1029 3.0171
## Emospider 1.1830 1.0876 -0.26
## Emonegative 0.5147 0.7174 -0.08 0.04
## Emopositive 0.3305 0.5749 0.03 -0.32 0.34
## Residual 30.5617 5.5283
## Number of obs: 17360, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value
## (Intercept) 4.8784 0.4326 87.0637 11.276
## treatIVET/VRET 0.4162 0.6709 87.0317 0.620
## Emospider -0.5154 0.2166 86.5825 -2.380
## Emonegative -1.4629 0.1846 88.4801 -7.925
## Emopositive -0.1861 0.1747 86.8951 -1.065
## treatIVET/VRET:Emospider -2.3363 0.3358 86.4976 -6.957
## treatIVET/VRET:Emonegative -0.2619 0.2859 88.0938 -0.916
## treatIVET/VRET:Emopositive -0.3826 0.2708 86.7534 -1.413
## Pr(>|t|)
## (Intercept) < 0.0000000000000002 ***
## treatIVET/VRET 0.5366
## Emospider 0.0195 *
## Emonegative 0.0000000000064 ***
## Emopositive 0.2897
## treatIVET/VRET:Emospider 0.0000000006301 ***
## treatIVET/VRET:Emonegative 0.3621
## treatIVET/VRET:Emopositive 0.1613
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET/VRET Emspdr Emngtv Empstv trtIVET/VRET:Ems
## trIVET/VRET -0.645
## Emospider -0.306 0.198
## Emonegative -0.195 0.126 0.316
## Emopositive -0.146 0.094 0.218 0.460
## trtIVET/VRET:Ems 0.198 -0.306 -0.645 -0.204 -0.141
## trtIVET/VRET:Emn 0.126 -0.195 -0.204 -0.646 -0.297 0.315
## trtIVET/VRET:Emp 0.094 -0.146 -0.141 -0.296 -0.645 0.218
## trtIVET/VRET:Emn
## trIVET/VRET
## Emospider
## Emonegative
## Emopositive
## trtIVET/VRET:Ems
## trtIVET/VRET:Emn
## trtIVET/VRET:Emp 0.459tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:8)),
original = tidied_model$term[1:8],
standard = c("intercept (control, neutral)",
"treatment (IVET/VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET/VRET) x emotion (spider)",
"treatment (IVET/VRET) x emotion (negative)",
"treatment (IVET/VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET/VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET/VRET) / emotion (spider)",
"treatment (IVET/VRET) / emotion (negative)",
"treatment (IVET/VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET/VRET | treatment (IVET/VRET) | treatment (IVET/VRET) / emotion (neutral) |
| 3 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 4 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 5 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 6 | treatIVET/VRET:Emospider | treatment (IVET/VRET) x emotion (spider) | treatment (IVET/VRET) / emotion (spider) |
| 7 | treatIVET/VRET:Emonegative | treatment (IVET/VRET) x emotion (negative) | treatment (IVET/VRET) / emotion (negative) |
| 8 | treatIVET/VRET:Emopositive | treatment (IVET/VRET) x emotion (positive) | treatment (IVET/VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | 4.88 | 4.02 – 5.74 | 0.43 | 11.28 | <0.001 |
| 2 treatment (IVET/VRET) | 0.42 | -0.92 – 1.75 | 0.67 | 0.62 | 0.537 |
| 3 emotion (spider) | -0.52 | -0.95 – -0.08 | 0.22 | -2.38 | 0.020 |
| 4 emotion (negative) | -1.46 | -1.83 – -1.10 | 0.18 | -7.92 | <0.001 |
| 5 emotion (positive) | -0.19 | -0.53 – 0.16 | 0.17 | -1.07 | 0.290 |
| 6 treatment (IVET/VRET) x emotion (spider) | -2.34 | -3.00 – -1.67 | 0.34 | -6.96 | <0.001 |
| 7 treatment (IVET/VRET) x emotion (negative) | -0.26 | -0.83 – 0.31 | 0.29 | -0.92 | 0.362 |
| 8 treatment (IVET/VRET) x emotion (positive) | -0.38 | -0.92 – 0.16 | 0.27 | -1.41 | 0.161 |
| Random Effects | |||||
| σ2 | 30.56 | ||||
| τ00 fp | 9.10 | ||||
| τ11 fp.Emospider | 1.18 | ||||
| τ11 fp.Emonegative | 0.51 | ||||
| τ11 fp.Emopositive | 0.33 | ||||
| ρ01 | -0.26 | ||||
| -0.08 | |||||
| 0.03 | |||||
| ICC | 0.23 | ||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.018 / 0.243 | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | 4.88 | 4.02 – 5.74 | 0.43 | 11.28 | <0.001 |
| 2 treatment (IVET/VRET) / emotion (neutral) | 0.42 | -0.92 – 1.75 | 0.67 | 0.62 | 0.537 |
| 3 treatment (control) / emotion (spider) | -0.52 | -0.95 – -0.08 | 0.22 | -2.38 | 0.020 |
| 4 treatment (control) / emotion (negative) | -1.46 | -1.83 – -1.10 | 0.18 | -7.92 | <0.001 |
| 5 treatment (control) / emotion (positive) | -0.19 | -0.53 – 0.16 | 0.17 | -1.07 | 0.290 |
| 6 treatment (IVET/VRET) / emotion (spider) | -2.34 | -3.00 – -1.67 | 0.34 | -6.96 | <0.001 |
| 7 treatment (IVET/VRET) / emotion (negative) | -0.26 | -0.83 – 0.31 | 0.29 | -0.92 | 0.362 |
| 8 treatment (IVET/VRET) / emotion (positive) | -0.38 | -0.92 – 0.16 | 0.27 | -1.41 | 0.161 |
| Random Effects | |||||
| σ2 | 30.56 | ||||
| τ00 fp | 9.10 | ||||
| τ11 fp.Emospider | 1.18 | ||||
| τ11 fp.Emonegative | 0.51 | ||||
| τ11 fp.Emopositive | 0.33 | ||||
| ρ01 | -0.26 | ||||
| -0.08 | |||||
| 0.03 | |||||
| ICC | 0.23 | ||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.018 / 0.243 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether the combined treatment groups (IVET and VRET) differ from controls in spider (vs neutral) mean amplitude in the first session (but not in any other picture category). The analysis compares the combined IVET and VRET to the control group and does not test whether the treatments differ from each other.
The formula was EPN ~ 1 + treat * Emo + (1 + Emo | fp).
Emo as random effect.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = 4.88. This is the mean amplitude for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The first effect shows that there is an effect of spider (vs neutral). It shows that for the control group, spiders have lower amps than neutral pictures. This relative negativity supports an EPN. But, this effect is not of particular interest because it is only for the control group.
Emospider
In the model table with condition labels, this is number 3.
treatment (control) / emotion (spider).
- estimate: -0.52
- p value: 1.9525e-02
The main interest is to see whether the combined treatment groups (IVET and VRET) differ from controls in their amps to spiders. Particularly, the difference between spiders and neutral pictures should be more negative across treatment groups compared to controls. Because the intercept contains treatment(control) and emotion(neutral), we are interested in this test:
treatIVET/VRET:Emospider
In the model table with condition labels, this is number 6.
treatment (IVET/VRET) / emotion (spider).
- estimate: -2.34
- p value: 6.3010e-10
This is the interaction of treatment(IVET/VRET vs control) x emotion (spider vs neutral).
estimated means
data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | 4.88 | 4.36 | 3.42 | 4.69 |
| IVET/VRET | 5.29 | 2.44 | 3.57 | 4.73 |
Bayes
only spider and neutral
gaussian model
# Prepare dataframe.
detect_sess1 <- detect_baseline_acrosstreatment %>%
select(Emo, EPN, LPP, fp, sess, treat) %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp),
Emo = factor(Emo, levels = c('neutral','spider'))) %>%
na.omit()
# Regression Model.
EPN.sess1.model <- brm(EPN ~ 1 + treat*Emo + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/EPN.sess1.model", # file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(EPN.sess1.model)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: EPN ~ 1 + treat * Emo + (1 + Emo | fp)
## Data: detect_sess1 (Number of observations: 8677)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 89)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 3.06 0.25 2.62 3.60 1.00 1918
## sd(Emospider) 1.12 0.18 0.78 1.47 1.00 3472
## cor(Intercept,Emospider) -0.25 0.14 -0.51 0.05 1.00 6980
## Tail_ESS
## sd(Intercept) 3637
## sd(Emospider) 4526
## cor(Intercept,Emospider) 6513
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 4.85 0.43 4.02 5.71 1.00 1124
## treatIVETDVRET 0.41 0.67 -0.86 1.73 1.00 1092
## Emospider -0.52 0.22 -0.96 -0.09 1.00 5798
## treatIVETDVRET:Emospider -2.32 0.34 -2.99 -1.65 1.00 5267
## Tail_ESS
## Intercept 1980
## treatIVETDVRET 2026
## Emospider 5791
## treatIVETDVRET:Emospider 5899
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 5.41 0.04 5.33 5.50 1.00 18330 5344
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null.sess1.model <- brm(EPN ~ 1 + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/EPN.sess1.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
emo.sess1.model <- brm(EPN ~ 1 + Emo + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/EPN.sess1.emo",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
treat.sess1.model <- brm(EPN ~ 1 + treat + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/EPN.sess1.treat",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
full.sess1.bayes <- bayes_factor(EPN.sess1.model, null.sess1.model)## Iteration: 1
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## Iteration: 7treat.sess1.bayes <- bayes_factor(treat.sess1.model, null.sess1.model)## Iteration: 1
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## Iteration: 7emo.sess1.bayes <- bayes_factor(emo.sess1.model, null.sess1.model)## Iteration: 1
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## Iteration: 6full.sess1.bayes## Estimated Bayes factor in favor of EPN.sess1.model over null.sess1.model: 348247035184728.56250treat.sess1.bayes## Estimated Bayes factor in favor of treat.sess1.model over null.sess1.model: 0.40278emo.sess1.bayes## Estimated Bayes factor in favor of emo.sess1.model over null.sess1.model: 33859255.67491compare with null
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Null = format(c(full.sess1.bayes$bf,
treat.sess1.bayes$bf,
emo.sess1.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxEmo | 3.482470e+14 |
| Treat | 4.027773e-01 |
| Emo | 3.385926e+07 |
compare with Emo
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Emo = format(c(full.sess1.bayes$bf/emo.sess1.bayes$bf,
treat.sess1.bayes$bf/emo.sess1.bayes$bf,
emo.sess1.bayes$bf/emo.sess1.bayes$bf),
scientific = TRUE),
BF01 = format(c(emo.sess1.bayes$bf/full.sess1.bayes$bf,
emo.sess1.bayes$bf/treat.sess1.bayes$bf,
emo.sess1.bayes$bf/emo.sess1.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Emo | BF01 |
|---|---|---|
| TreatxEmo | 1.028514e+07 | 9.722769e-08 |
| Treat | 1.189563e-08 | 8.406446e+07 |
| Emo | 1.000000e+00 | 1.000000e+00 |
check assumptions
Linear regression has these assumptions:
- Linear association
- Normality of residuals
- No heteroskedasticity
- No multicollinearity
linearity
# Check linearity
na.omit(detect_sess1) %>%
#add_residual_draws(EPN.sess1.model) %>%
add_residual_draws(EPN.sess1.model, ndraws = 1) %>%
ggplot(aes(x = .row, y = .residual)) +
stat_pointinterval()
normality
# Check normality
na.omit(detect_sess1) %>%
add_residual_draws(EPN.sess1.model, ndraws = 1) %>%
median_qi() %>%
ggplot(aes(sample = .residual)) +
geom_qq() +
geom_qq_line()
multicollinearity
# Check vif and tolerance
check_collinearity(EPN.sess1.model)treatment comparison
- session 1 and session 2 (session 1 as reference)
- include only treatment groups
- IVET = -.5, VRET = .5
- use neutral pictures as reference emotion
model_name <- "only_treat_EPN"
model_formula <- formula("EPN ~ 1 + treat*sess*Emo + (1 + sess * Emo | fp)")
data <- detect_only_treat_recode
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "nloptwrap",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plot
all categories
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nsession") +
plot_aes
spider and neutral
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
filter(Emo %in% c("neutral", "spider")) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
filter(facet %in% c("neutral", "spider")) %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nsession") +
plot_aes
ggsave('results/figures/fig_estimated_EPN_treat.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "nloptwrap", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 123655.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.3128 -0.6168 0.0083 0.6223 4.2434
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 12.6616 3.5583
## sess 0.8901 0.9435 -0.31
## Emospider 2.0838 1.4435 -0.32 0.37
## Emonegative 1.1931 1.0923 -0.34 0.08 0.38
## Emopositive 0.5011 0.7079 -0.13 0.18 0.04 0.32
## sess:Emospider 1.3879 1.1781 -0.24 0.05 -0.34 0.16 -0.59
## sess:Emonegative 0.9383 0.9687 0.12 -0.10 0.02 -0.45 0.34
## sess:Emopositive 0.8358 0.9142 0.08 -0.24 -0.14 -0.55 -0.74
## Residual 25.2321 5.0232
##
##
##
##
##
##
##
## -0.62
## 0.28 0.31
##
## Number of obs: 20284, groups: fp, 70
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 4.61116 0.45963 59.80823 10.032 0.0000000000000196
## treat -1.46091 0.91925 59.80823 -1.589 0.1173
## sess 0.17971 0.23022 32.93086 0.781 0.4406
## Emospider -2.93909 0.27427 39.60494 -10.716 0.0000000000002868
## Emonegative -1.77110 0.23150 43.06249 -7.650 0.0000000014768418
## Emopositive -0.58988 0.19816 46.88578 -2.977 0.0046
## treat:sess 0.48778 0.46044 32.93086 1.059 0.2971
## treat:Emospider 0.65797 0.54853 39.60494 1.200 0.2375
## treat:Emonegative 0.30534 0.46301 43.06249 0.659 0.5131
## treat:Emopositive 0.25546 0.39633 46.88578 0.645 0.5223
## sess:Emospider 0.19675 0.28780 38.74402 0.684 0.4983
## sess:Emonegative 0.03905 0.25898 54.28829 0.151 0.8807
## sess:Emopositive -0.03538 0.24476 53.64553 -0.145 0.8856
## treat:sess:Emospider -0.83686 0.57559 38.74402 -1.454 0.1540
## treat:sess:Emonegative -0.16927 0.51796 54.28829 -0.327 0.7451
## treat:sess:Emopositive -0.14777 0.48952 53.64553 -0.302 0.7639
##
## (Intercept) ***
## treat
## sess
## Emospider ***
## Emonegative ***
## Emopositive **
## treat:sess
## treat:Emospider
## treat:Emonegative
## treat:Emopositive
## sess:Emospider
## sess:Emonegative
## sess:Emopositive
## treat:sess:Emospider
## treat:sess:Emonegative
## treat:sess:Emopositive
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:16)),
original = tidied_model$term[1:16],
standard = c("intercept (avr_treat, session (1), neutral)",
"treatment (VRET vs IVET)",
"session (2)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (VRET vs IVET) x session",
"treatment (VRET vs IVET) x emotion (spider)",
"treatment (VRET vs IVET) x emotion (negative)",
"treatment (VRET vs IVET) x emotion (positive)",
"session x emotion (spider)",
"session x emotion (negative)",
"session x emotion (positive)",
"treatment (VRET vs IVET) x session x emotion (spider)",
"treatment (VRET vs IVET) x session x emotion (negative)",
"treatment (VRET vs IVET) x session x emotion (positive)"),
condition = c("treatment (avr_treat) / session (1) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (neutral)",
"treatment (avr_treat) / sess (2) / emotion (neutral)",
"treatment (avr_treat) / sess (1) / emotion (spider)",
"treatment (avr_treat) / sess (1) / emotion (negative)",
"treatment (avr_treat) / sess (1) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (spider)",
"treatment (VRET vs IVET) / sess (1) / emotion (negative)",
"treatment (VRET vs IVET) / sess (1) / emotion (positive)",
"treatment (avr_treat) / sess (2) / emotion (spider)",
"treatment (avr_treat) / sess (2) / emotion (negative)",
"treatment (avr_treat) / sess (2) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (spider)",
"treatment (VRET vs IVET) / sess (2) / emotion (negative)",
"treatment (VRET vs IVET) / sess (2) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (avr_treat, session (1), neutral) | treatment (avr_treat) / session (1) / emotion (neutral) |
| 2 | treat | treatment (VRET vs IVET) | treatment (VRET vs IVET) / sess (1) / emotion (neutral) |
| 3 | sess | session (2) | treatment (avr_treat) / sess (2) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (avr_treat) / sess (1) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (avr_treat) / sess (1) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (avr_treat) / sess (1) / emotion (positive) |
| 7 | treat:sess | treatment (VRET vs IVET) x session | treatment (VRET vs IVET) / sess (2) / emotion (neutral) |
| 8 | treat:Emospider | treatment (VRET vs IVET) x emotion (spider) | treatment (VRET vs IVET) / sess (1) / emotion (spider) |
| 9 | treat:Emonegative | treatment (VRET vs IVET) x emotion (negative) | treatment (VRET vs IVET) / sess (1) / emotion (negative) |
| 10 | treat:Emopositive | treatment (VRET vs IVET) x emotion (positive) | treatment (VRET vs IVET) / sess (1) / emotion (positive) |
| 11 | sess:Emospider | session x emotion (spider) | treatment (avr_treat) / sess (2) / emotion (spider) |
| 12 | sess:Emonegative | session x emotion (negative) | treatment (avr_treat) / sess (2) / emotion (negative) |
| 13 | sess:Emopositive | session x emotion (positive) | treatment (avr_treat) / sess (2) / emotion (positive) |
| 14 | treat:sess:Emospider | treatment (VRET vs IVET) x session x emotion (spider) | treatment (VRET vs IVET) / sess (2) / emotion (spider) |
| 15 | treat:sess:Emonegative | treatment (VRET vs IVET) x session x emotion (negative) | treatment (VRET vs IVET) / sess (2) / emotion (negative) |
| 16 | treat:sess:Emopositive | treatment (VRET vs IVET) x session x emotion (positive) | treatment (VRET vs IVET) / sess (2) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (avr_treat, session (1), neutral) | 4.61 | 3.69 – 5.53 | 0.46 | 10.03 | <0.001 |
| 2 treatment (VRET vs IVET) | -1.46 | -3.30 – 0.38 | 0.92 | -1.59 | 0.117 |
| 3 session (2) | 0.18 | -0.29 – 0.65 | 0.23 | 0.78 | 0.441 |
| 4 emotion (spider) | -2.94 | -3.49 – -2.38 | 0.27 | -10.72 | <0.001 |
| 5 emotion (negative) | -1.77 | -2.24 – -1.30 | 0.23 | -7.65 | <0.001 |
| 6 emotion (positive) | -0.59 | -0.99 – -0.19 | 0.20 | -2.98 | 0.005 |
| 7 treatment (VRET vs IVET) x session | 0.49 | -0.45 – 1.42 | 0.46 | 1.06 | 0.297 |
| 8 treatment (VRET vs IVET) x emotion (spider) | 0.66 | -0.45 – 1.77 | 0.55 | 1.20 | 0.237 |
| 9 treatment (VRET vs IVET) x emotion (negative) | 0.31 | -0.63 – 1.24 | 0.46 | 0.66 | 0.513 |
| 10 treatment (VRET vs IVET) x emotion (positive) | 0.26 | -0.54 – 1.05 | 0.40 | 0.64 | 0.522 |
| 11 session x emotion (spider) | 0.20 | -0.39 – 0.78 | 0.29 | 0.68 | 0.498 |
| 12 session x emotion (negative) | 0.04 | -0.48 – 0.56 | 0.26 | 0.15 | 0.881 |
| 13 session x emotion (positive) | -0.04 | -0.53 – 0.46 | 0.24 | -0.14 | 0.886 |
| 14 treatment (VRET vs IVET) x session x emotion (spider) | -0.84 | -2.00 – 0.33 | 0.58 | -1.45 | 0.154 |
| 15 treatment (VRET vs IVET) x session x emotion (negative) | -0.17 | -1.21 – 0.87 | 0.52 | -0.33 | 0.745 |
| 16 treatment (VRET vs IVET) x session x emotion (positive) | -0.15 | -1.13 – 0.83 | 0.49 | -0.30 | 0.764 |
| Random Effects | |||||
| σ2 | 25.23 | ||||
| τ00 fp | 12.66 | ||||
| τ11 fp.sess | 0.89 | ||||
| τ11 fp.Emospider | 2.08 | ||||
| τ11 fp.Emonegative | 1.19 | ||||
| τ11 fp.Emopositive | 0.50 | ||||
| τ11 fp.sess:Emospider | 1.39 | ||||
| τ11 fp.sess:Emonegative | 0.94 | ||||
| τ11 fp.sess:Emopositive | 0.84 | ||||
| ρ01 | -0.31 | ||||
| -0.32 | |||||
| -0.34 | |||||
| -0.13 | |||||
| -0.24 | |||||
| 0.12 | |||||
| 0.08 | |||||
| ICC | 0.31 | ||||
| N fp | 70 | ||||
| Observations | 20284 | ||||
| Marginal R2 / Conditional R2 | 0.038 / 0.335 | ||||
condition labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (avr_treat) / session (1) / emotion (neutral) | 4.61 | 3.69 – 5.53 | 0.46 | 10.03 | <0.001 |
| 2 treatment (VRET vs IVET) / sess (1) / emotion (neutral) | -1.46 | -3.30 – 0.38 | 0.92 | -1.59 | 0.117 |
| 3 treatment (avr_treat) / sess (2) / emotion (neutral) | 0.18 | -0.29 – 0.65 | 0.23 | 0.78 | 0.441 |
| 4 treatment (avr_treat) / sess (1) / emotion (spider) | -2.94 | -3.49 – -2.38 | 0.27 | -10.72 | <0.001 |
| 5 treatment (avr_treat) / sess (1) / emotion (negative) | -1.77 | -2.24 – -1.30 | 0.23 | -7.65 | <0.001 |
| 6 treatment (avr_treat) / sess (1) / emotion (positive) | -0.59 | -0.99 – -0.19 | 0.20 | -2.98 | 0.005 |
| 7 treatment (VRET vs IVET) / sess (2) / emotion (neutral) | 0.49 | -0.45 – 1.42 | 0.46 | 1.06 | 0.297 |
| 8 treatment (VRET vs IVET) / sess (1) / emotion (spider) | 0.66 | -0.45 – 1.77 | 0.55 | 1.20 | 0.237 |
| 9 treatment (VRET vs IVET) / sess (1) / emotion (negative) | 0.31 | -0.63 – 1.24 | 0.46 | 0.66 | 0.513 |
| 10 treatment (VRET vs IVET) / sess (1) / emotion (positive) | 0.26 | -0.54 – 1.05 | 0.40 | 0.64 | 0.522 |
| 11 treatment (avr_treat) / sess (2) / emotion (spider) | 0.20 | -0.39 – 0.78 | 0.29 | 0.68 | 0.498 |
| 12 treatment (avr_treat) / sess (2) / emotion (negative) | 0.04 | -0.48 – 0.56 | 0.26 | 0.15 | 0.881 |
| 13 treatment (avr_treat) / sess (2) / emotion (positive) | -0.04 | -0.53 – 0.46 | 0.24 | -0.14 | 0.886 |
| 14 treatment (VRET vs IVET) / sess (2) / emotion (spider) | -0.84 | -2.00 – 0.33 | 0.58 | -1.45 | 0.154 |
| 15 treatment (VRET vs IVET) / sess (2) / emotion (negative) | -0.17 | -1.21 – 0.87 | 0.52 | -0.33 | 0.745 |
| 16 treatment (VRET vs IVET) / sess (2) / emotion (positive) | -0.15 | -1.13 – 0.83 | 0.49 | -0.30 | 0.764 |
| Random Effects | |||||
| σ2 | 25.23 | ||||
| τ00 fp | 12.66 | ||||
| τ11 fp.sess | 0.89 | ||||
| τ11 fp.Emospider | 2.08 | ||||
| τ11 fp.Emonegative | 1.19 | ||||
| τ11 fp.Emopositive | 0.50 | ||||
| τ11 fp.sess:Emospider | 1.39 | ||||
| τ11 fp.sess:Emonegative | 0.94 | ||||
| τ11 fp.sess:Emopositive | 0.84 | ||||
| ρ01 | -0.31 | ||||
| -0.32 | |||||
| -0.34 | |||||
| -0.13 | |||||
| -0.24 | |||||
| 0.12 | |||||
| 0.08 | |||||
| ICC | 0.31 | ||||
| N fp | 70 | ||||
| Observations | 20284 | ||||
| Marginal R2 / Conditional R2 | 0.038 / 0.335 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from each other in spider (vs neutral) mean amps in the first session and between the first and second session (but not in any other picture category).
The formula was EPN ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp).
Sess * Emo as random effects: This means that emo, session, and the 2-way interaction can differ between subjects.
Intercept = treatment(avr_treat) / session (1) / emotion (neutral).
avr_treat is the mean of IVET and VRET.
The effect for the intercept = 4.61. This is the mean amp for the intercept that contains the average across treatments in session 1 to neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t-test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether the groups showed lower amps to spiders than neutral pictures in session 1.
Emospider
In the model table with condition labels, this is number 4.
treatment (avr_treat) / sess (1) / emotion (spider).
- estimate: -2.94
- p value: 2.8677e-13
Indeed, mean amps are relatively negative to spiders.
Did the groups differ in how they responded to spiders versus neutral pictures in session 1? No.
treat:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET vs IVET) / sess (1) / emotion (spider).
- estimate: 0.66
- p value: 2.3745e-01
Did the effect of spiders differ between sessions: No difference!
sess:Emospider
In the model table with condition labels, this is number 11.
treatment (avr_treat) / sess (2) / emotion (spider).
- estimate: 0.20
- p value: 4.9826e-01
Critically, did this effect vary with treatment? No difference!
treat:sess:Emospider
In the model table with condition labels, this is number 14.
treatment (VRET vs IVET) / sess (2) / emotion (spider).
- estimate: -0.84
- p value: 1.5403e-01
estimated means
data %>%
modelr::data_grid(treat, Emo, sess) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),
treat = ifelse(treat == -.5, "IVET", "VRET"),
sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post'))) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | sess | neutral | spider | negative | positive |
|---|---|---|---|---|---|
| IVET | pre | 5.34 | 2.07 | 3.42 | 4.62 |
| IVET | post | 5.28 | 2.62 | 3.48 | 4.60 |
| VRET | pre | 3.88 | 1.27 | 2.26 | 3.42 |
| VRET | post | 4.30 | 1.47 | 2.64 | 3.73 |
Bayes
only spider and neutral
gaussian model
detect_treat <- detect_only_treat_recode %>%
select(Emo, EPN, LPP, fp, sess, treat) %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp),
Emo = factor(Emo, levels = c('neutral','spider'))) %>%
na.omit()
# Regression Model.
EPN.treat.model <- brm(EPN ~ 1 + treat*sess*Emo + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/EPN.treat.model", # file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(EPN.treat.model)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: EPN ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp)
## Data: detect_treat (Number of observations: 10145)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 70)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 3.57 0.37 2.91 4.37 1.00
## sd(sess) 0.97 0.28 0.44 1.53 1.00
## sd(Emospider) 1.45 0.25 1.00 1.97 1.00
## sd(sess:Emospider) 0.95 0.39 0.14 1.70 1.00
## cor(Intercept,sess) -0.17 0.23 -0.60 0.31 1.00
## cor(Intercept,Emospider) -0.31 0.17 -0.61 0.04 1.00
## cor(sess,Emospider) 0.18 0.26 -0.37 0.64 1.00
## cor(Intercept,sess:Emospider) -0.31 0.27 -0.79 0.25 1.00
## cor(sess,sess:Emospider) 0.20 0.35 -0.49 0.83 1.00
## cor(Emospider,sess:Emospider) -0.11 0.31 -0.62 0.60 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 2292 3752
## sd(sess) 1172 787
## sd(Emospider) 3315 5043
## sd(sess:Emospider) 979 1566
## cor(Intercept,sess) 4972 4938
## cor(Intercept,Emospider) 4181 5417
## cor(sess,Emospider) 1267 2631
## cor(Intercept,sess:Emospider) 4648 4034
## cor(sess,sess:Emospider) 1700 2824
## cor(Emospider,sess:Emospider) 2535 3629
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept 4.57 0.46 3.63 5.47 1.00 1204
## treat -1.37 0.90 -3.16 0.42 1.00 1358
## sess 0.17 0.25 -0.33 0.65 1.00 4647
## Emospider -2.86 0.28 -3.40 -2.30 1.00 4597
## treat:sess 0.50 0.49 -0.47 1.46 1.00 4733
## treat:Emospider 0.53 0.53 -0.53 1.59 1.00 4886
## sess:Emospider 0.12 0.28 -0.43 0.67 1.00 6636
## treat:sess:Emospider -0.79 0.56 -1.89 0.33 1.00 7282
## Tail_ESS
## Intercept 2453
## treat 2410
## sess 5863
## Emospider 5757
## treat:sess 5030
## treat:Emospider 5932
## sess:Emospider 5591
## treat:sess:Emospider 6578
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 4.94 0.03 4.87 5.01 1.00 16291 5261
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null.treat.model <- brm(EPN ~ 1 + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/EPN.treat.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
sess_emo.treat.model <- brm(EPN ~ 1 + sess*Emo + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/EPN.treat.sess_emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))
emo.treat.model <- brm(EPN ~ 1 + Emo + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/EPN.treat.emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
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## Iteration: 176sess_emo.treat.bayes <- bayes_factor(sess_emo.treat.model, null.treat.model)## Iteration: 1
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## Iteration: 13emo.treat.bayes <- bayes_factor(emo.treat.model, null.treat.model)## Iteration: 1
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## Iteration: 32full.treat.bayes## Estimated Bayes factor in favor of EPN.treat.model over null.treat.model: 15919855820418.37109sess_emo.treat.bayes## Estimated Bayes factor in favor of sess_emo.treat.model over null.treat.model: 11831242103522704.00000emo.treat.bayes## Estimated Bayes factor in favor of emo.treat.model over null.treat.model: 2097671964500722176.00000compare with null
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Null = format(c(full.treat.bayes$bf,
sess_emo.treat.bayes$bf,
emo.treat.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxSessxEmo | 1.591986e+13 |
| SessxEmo | 1.183124e+16 |
| Emo | 2.097672e+18 |
compare with Treat x Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Treat.Sess.Emo =
format(c(full.treat.bayes$bf/full.treat.bayes$bf,
sess_emo.treat.bayes$bf/full.treat.bayes$bf,
emo.treat.bayes$bf/full.treat.bayes$bf),
scientific = TRUE),
BF01 =
format(c(full.treat.bayes$bf/full.treat.bayes$bf,
full.treat.bayes$bf/sess_emo.treat.bayes$bf,
full.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Treat.Sess.Emo | BF01 |
|---|---|---|
| TreatxSessxEmo | 1.000000e+00 | 1.000000e+00 |
| SessxEmo | 7.431752e+02 | 1.345578e-03 |
| Emo | 1.317645e+05 | 7.589297e-06 |
compare with Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Sess.Emo = format(c(full.treat.bayes$bf/sess_emo.treat.bayes$bf,
sess_emo.treat.bayes$bf/sess_emo.treat.bayes$bf,
emo.treat.bayes$bf/sess_emo.treat.bayes$bf),
scientific = TRUE),
BF01 = format(c(sess_emo.treat.bayes$bf/full.treat.bayes$bf,
sess_emo.treat.bayes$bf/sess_emo.treat.bayes$bf,
sess_emo.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Sess.Emo | BF01 |
|---|---|---|
| TreatxSessxEmo | 1.345578e-03 | 7.431752e+02 |
| SessxEmo | 1.000000e+00 | 1.000000e+00 |
| Emo | 1.772994e+02 | 5.640177e-03 |
compare with Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Emo = format(c(full.treat.bayes$bf/emo.treat.bayes$bf,
sess_emo.treat.bayes$bf/emo.treat.bayes$bf,
emo.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE),
BF01 = format(c(emo.treat.bayes$bf/full.treat.bayes$bf,
emo.treat.bayes$bf/sess_emo.treat.bayes$bf,
emo.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Emo | BF01 |
|---|---|---|
| TreatxSessxEmo | 7.589297e-06 | 1.317645e+05 |
| SessxEmo | 5.640177e-03 | 1.772994e+02 |
| Emo | 1.000000e+00 | 1.000000e+00 |
check assumptions
Linear regression has these assumptions:
- Linear association
- Normality of residuals
- No heteroskedasticity
- No multicollinearity
linearity
# Check linearity
na.omit(detect_treat) %>%
add_residual_draws(EPN.treat.model, ndraws = 1) %>%
ggplot(aes(x = .row, y = .residual)) +
stat_pointinterval()
normality
# Check normality
na.omit(detect_treat) %>%
add_residual_draws(EPN.treat.model, ndraws = 1) %>%
median_qi() %>%
ggplot(aes(sample = .residual)) +
geom_qq() +
geom_qq_line()
multicollinearity
# Check vif and tolerance
check_collinearity(EPN.treat.model)EEG: LPP-relevant amplitude
EEG data during the detection task
session 1 three groups
- use session 1 from all three groups
- examine whether IVET and VRET differ from controls to spiders (vs neutral) in session 1
- compare IVET and VRET separately to the control group
- do not test whether the treatments differ from each other
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_all_groups_LPP"
model_formula <- formula("LPP ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- detect_baseline
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "Nelder_Mead",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}
# nloptwrap: Model failed to converge with 1 negative eigenvalue: -8.0e+02plot
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .15), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .15), size = .5) +
scale_color_manual(values = palette, name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nemotion") +
plot_aes
ggsave('results/figures/fig_meanamps_LPP_pre.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "Nelder_Mead", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 103073.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.4655 -0.5470 -0.0018 0.5473 5.3080
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 1.275 1.129
## Emospider 5.874 2.424 -0.64
## Emonegative 2.578 1.606 -0.69 0.94
## Emopositive 1.191 1.091 -0.49 0.89 0.94
## Residual 21.657 4.654
## Number of obs: 17360, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.5088 0.1820 56.0223 -2.796 0.00707 **
## treatIVET 0.3663 0.3753 56.0868 0.976 0.33326
## treatVRET 0.1735 0.3389 55.7998 0.512 0.61064
## Emospider 0.6451 0.3607 164.5251 1.789 0.07552 .
## Emonegative 0.4224 0.2583 68.6949 1.635 0.10654
## Emopositive 0.1809 0.2001 49.6938 0.904 0.37042
## treatIVET:Emospider 0.8040 0.7440 164.7964 1.081 0.28142
## treatVRET:Emospider 0.9524 0.6722 164.2231 1.417 0.15841
## treatIVET:Emonegative -0.1017 0.5324 68.6512 -0.191 0.84907
## treatVRET:Emonegative 0.0612 0.4812 68.4786 0.127 0.89915
## treatIVET:Emopositive -0.1706 0.4129 49.8336 -0.413 0.68120
## treatVRET:Emopositive 0.1363 0.3726 49.4989 0.366 0.71620
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET trVRET Emspdr Emngtv Empstv trtIVET:Ems trtVRET:Ems
## treatIVET -0.485
## treatVRET -0.537 0.260
## Emospider -0.646 0.313 0.347
## Emonegative -0.695 0.337 0.373 0.848
## Emopositive -0.553 0.268 0.297 0.748 0.777
## trtIVET:Ems 0.313 -0.645 -0.168 -0.485 -0.411 -0.362
## trtVRET:Ems 0.346 -0.168 -0.645 -0.537 -0.455 -0.401 0.260
## trtIVET:Emn 0.337 -0.695 -0.181 -0.411 -0.485 -0.377 0.848 0.221
## trtVRET:Emn 0.373 -0.181 -0.694 -0.455 -0.537 -0.417 0.221 0.848
## trtIVET:Emp 0.268 -0.552 -0.144 -0.362 -0.377 -0.485 0.747 0.194
## trtVRET:Emp 0.297 -0.144 -0.552 -0.401 -0.417 -0.537 0.195 0.748
## trtIVET:Emn trtVRET:Emn trtIVET:Emp
## treatIVET
## treatVRET
## Emospider
## Emonegative
## Emopositive
## trtIVET:Ems
## trtVRET:Ems
## trtIVET:Emn
## trtVRET:Emn 0.260
## trtIVET:Emp 0.777 0.202
## trtVRET:Emp 0.202 0.778 0.260tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:12)),
original = tidied_model$term[1:12],
standard = c("intercept (control, neutral)",
"treatment (IVET)",
"treatment (VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET) x emotion (spider)",
"treatment (VRET) x emotion (spider)",
"treatment (IVET) x emotion (negative)",
"treatment (VRET) x emotion (negative)",
"treatment (IVET) x emotion (positive)",
"treatment (VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET) / emotion (neutral)",
"treatment (VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET) / emotion (spider)",
"treatment (VRET) / emotion (spider)",
"treatment (IVET) / emotion (negative)",
"treatment (VRET) / emotion (negative)",
"treatment (IVET) / emotion (positive)",
"treatment (VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET | treatment (IVET) | treatment (IVET) / emotion (neutral) |
| 3 | treatVRET | treatment (VRET) | treatment (VRET) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 7 | treatIVET:Emospider | treatment (IVET) x emotion (spider) | treatment (IVET) / emotion (spider) |
| 8 | treatVRET:Emospider | treatment (VRET) x emotion (spider) | treatment (VRET) / emotion (spider) |
| 9 | treatIVET:Emonegative | treatment (IVET) x emotion (negative) | treatment (IVET) / emotion (negative) |
| 10 | treatVRET:Emonegative | treatment (VRET) x emotion (negative) | treatment (VRET) / emotion (negative) |
| 11 | treatIVET:Emopositive | treatment (IVET) x emotion (positive) | treatment (IVET) / emotion (positive) |
| 12 | treatVRET:Emopositive | treatment (VRET) x emotion (positive) | treatment (VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | -0.51 | -0.87 – -0.14 | 0.18 | -2.80 | 0.007 |
| 2 treatment (IVET) | 0.37 | -0.39 – 1.12 | 0.38 | 0.98 | 0.333 |
| 3 treatment (VRET) | 0.17 | -0.51 – 0.85 | 0.34 | 0.51 | 0.611 |
| 4 emotion (spider) | 0.65 | -0.07 – 1.36 | 0.36 | 1.79 | 0.076 |
| 5 emotion (negative) | 0.42 | -0.09 – 0.94 | 0.26 | 1.64 | 0.107 |
| 6 emotion (positive) | 0.18 | -0.22 – 0.58 | 0.20 | 0.90 | 0.370 |
| 7 treatment (IVET) x emotion (spider) | 0.80 | -0.66 – 2.27 | 0.74 | 1.08 | 0.281 |
| 8 treatment (VRET) x emotion (spider) | 0.95 | -0.37 – 2.28 | 0.67 | 1.42 | 0.158 |
| 9 treatment (IVET) x emotion (negative) | -0.10 | -1.16 – 0.96 | 0.53 | -0.19 | 0.849 |
| 10 treatment (VRET) x emotion (negative) | 0.06 | -0.90 – 1.02 | 0.48 | 0.13 | 0.899 |
| 11 treatment (IVET) x emotion (positive) | -0.17 | -1.00 – 0.66 | 0.41 | -0.41 | 0.681 |
| 12 treatment (VRET) x emotion (positive) | 0.14 | -0.61 – 0.88 | 0.37 | 0.37 | 0.716 |
| Random Effects | |||||
| σ2 | 21.66 | ||||
| τ00 fp | 1.28 | ||||
| τ11 fp.Emospider | 5.87 | ||||
| τ11 fp.Emonegative | 2.58 | ||||
| τ11 fp.Emopositive | 1.19 | ||||
| ρ01 | -0.64 | ||||
| -0.69 | |||||
| -0.49 | |||||
| ICC | 0.08 | ||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.010 / 0.089 | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | -0.51 | -0.87 – -0.14 | 0.18 | -2.80 | 0.007 |
| 2 treatment (IVET) / emotion (neutral) | 0.37 | -0.39 – 1.12 | 0.38 | 0.98 | 0.333 |
| 3 treatment (VRET) / emotion (neutral) | 0.17 | -0.51 – 0.85 | 0.34 | 0.51 | 0.611 |
| 4 treatment (control) / emotion (spider) | 0.65 | -0.07 – 1.36 | 0.36 | 1.79 | 0.076 |
| 5 treatment (control) / emotion (negative) | 0.42 | -0.09 – 0.94 | 0.26 | 1.64 | 0.107 |
| 6 treatment (control) / emotion (positive) | 0.18 | -0.22 – 0.58 | 0.20 | 0.90 | 0.370 |
| 7 treatment (IVET) / emotion (spider) | 0.80 | -0.66 – 2.27 | 0.74 | 1.08 | 0.281 |
| 8 treatment (VRET) / emotion (spider) | 0.95 | -0.37 – 2.28 | 0.67 | 1.42 | 0.158 |
| 9 treatment (IVET) / emotion (negative) | -0.10 | -1.16 – 0.96 | 0.53 | -0.19 | 0.849 |
| 10 treatment (VRET) / emotion (negative) | 0.06 | -0.90 – 1.02 | 0.48 | 0.13 | 0.899 |
| 11 treatment (IVET) / emotion (positive) | -0.17 | -1.00 – 0.66 | 0.41 | -0.41 | 0.681 |
| 12 treatment (VRET) / emotion (positive) | 0.14 | -0.61 – 0.88 | 0.37 | 0.37 | 0.716 |
| Random Effects | |||||
| σ2 | 21.66 | ||||
| τ00 fp | 1.28 | ||||
| τ11 fp.Emospider | 5.87 | ||||
| τ11 fp.Emonegative | 2.58 | ||||
| τ11 fp.Emopositive | 1.19 | ||||
| ρ01 | -0.64 | ||||
| -0.69 | |||||
| -0.49 | |||||
| ICC | 0.08 | ||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.010 / 0.089 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from controls in spider (vs neutral) mean amplitude in the first session (but not in any other picture category). The analysis compares IVET and VRET separately to the control group and does not test whether the treatments differ from each other.
The formula was LPP ~ 1 + treat * Emo + (1 + Emo | fp).
Emo as random effect.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = -0.51. This is the mean amplitude for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The first effect shows that there is an effect of spider (vs neutral). It shows that for the control group, spiders have higher amps than neutral pictures. This relative positivity supports an LPP. But, this effect is not of particular interest because it is only for the control group.
Emospider
In the model table with condition labels, this is number 4.
treatment (control) / emotion (spider).
- estimate: 0.65
- p value: 7.5522e-02
The main interest is to see whether IVET and VRET differ from controls in their amps to spiders. Particularly, the difference between spiders and neutral pictures should be more positive for each treatment group compared to controls. Because the intercept contains treatment(control) and emotion(neutral), we are interested in these tests:
For IVET:
treatIVET:Emospider
In the model table with condition labels, this is number 7.
treatment (IVET) / emotion (spider).
- estimate: 0.80
- p value: 2.8142e-01
This is the interaction of treatment(IVET vs control) x emotion (spider vs neutral).
For VRET (same test as for IVET):
treatVRET:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET) / emotion (spider).
- estimate: 0.95
- p value: 1.5841e-01
This is the interaction of treatment(VRET vs control) x emotion (spider vs neutral).
estimated means
data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | -0.51 | 0.14 | -0.09 | -0.33 |
| IVET | -0.14 | 1.31 | 0.18 | -0.13 |
| VRET | -0.34 | 1.26 | 0.15 | -0.02 |
session 1 across treatments
- use session 1 from all three groups
- combine treatment groups
- use neutral pictures as reference emotion
- save the model to save time
model_name <- "session_pre_across_treat_LPP"
model_formula <- formula("LPP ~ 1 + treat*Emo + (1 + Emo | fp)")
data <- detect_baseline_acrosstreatment
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "nloptwrap",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}plot
fits <- data %>%
modelr::data_grid(treat, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat))
ggeffects::ggpredict(get(model_name), c("treat", "Emo")) %>%
data.frame() %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = Emo, y = predicted_re, color = treat,
group = interaction(fp, treat)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1), size = 1) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1), size = .5) +
scale_color_manual(values = palette2, name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nemotion") +
plot_aes
summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "nloptwrap", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 103003.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -5.4308 -0.5421 0.0009 0.5444 5.3091
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 0.6396 0.7998
## Emospider 0.8690 0.9322 0.17
## Emonegative 0.1431 0.3783 -0.16 0.23
## Emopositive 0.1090 0.3302 0.74 0.25 0.54
## Residual 21.7360 4.6622
## Number of obs: 17360, groups: fp, 89
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.515606 0.144588 91.462137 -3.566 0.000579
## treatIVET/VRET 0.264373 0.224117 91.265705 1.180 0.241219
## Emospider 0.654496 0.184094 89.431828 3.555 0.000606
## Emonegative 0.432262 0.141208 83.697640 3.061 0.002963
## Emopositive 0.187415 0.138838 248.440820 1.350 0.178280
## treatIVET/VRET:Emospider 0.875490 0.285461 89.347173 3.067 0.002862
## treatIVET/VRET:Emonegative -0.022285 0.218676 83.280734 -0.102 0.919073
## treatIVET/VRET:Emopositive -0.002446 0.215233 247.998807 -0.011 0.990943
##
## (Intercept) ***
## treatIVET/VRET
## Emospider ***
## Emonegative **
## Emopositive
## treatIVET/VRET:Emospider **
## treatIVET/VRET:Emonegative
## treatIVET/VRET:Emopositive
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trIVET/VRET Emspdr Emngtv Empstv trtIVET/VRET:Ems
## trIVET/VRET -0.645
## Emospider -0.230 0.149
## Emonegative -0.466 0.301 0.392
## Emopositive -0.241 0.155 0.394 0.505
## trtIVET/VRET:Ems 0.149 -0.230 -0.645 -0.253 -0.254
## trtIVET/VRET:Emn 0.301 -0.466 -0.253 -0.646 -0.326 0.392
## trtIVET/VRET:Emp 0.155 -0.240 -0.254 -0.326 -0.645 0.393
## trtIVET/VRET:Emn
## trIVET/VRET
## Emospider
## Emonegative
## Emopositive
## trtIVET/VRET:Ems
## trtIVET/VRET:Emn
## trtIVET/VRET:Emp 0.505tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:8)),
original = tidied_model$term[1:8],
standard = c("intercept (control, neutral)",
"treatment (IVET/VRET)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (IVET/VRET) x emotion (spider)",
"treatment (IVET/VRET) x emotion (negative)",
"treatment (IVET/VRET) x emotion (positive)"),
condition = c("treatment (control) / emotion (neutral)",
"treatment (IVET/VRET) / emotion (neutral)",
"treatment (control) / emotion (spider)",
"treatment (control) / emotion (negative)",
"treatment (control) / emotion (positive)",
"treatment (IVET/VRET) / emotion (spider)",
"treatment (IVET/VRET) / emotion (negative)",
"treatment (IVET/VRET) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (control, neutral) | treatment (control) / emotion (neutral) |
| 2 | treatIVET/VRET | treatment (IVET/VRET) | treatment (IVET/VRET) / emotion (neutral) |
| 3 | Emospider | emotion (spider) | treatment (control) / emotion (spider) |
| 4 | Emonegative | emotion (negative) | treatment (control) / emotion (negative) |
| 5 | Emopositive | emotion (positive) | treatment (control) / emotion (positive) |
| 6 | treatIVET/VRET:Emospider | treatment (IVET/VRET) x emotion (spider) | treatment (IVET/VRET) / emotion (spider) |
| 7 | treatIVET/VRET:Emonegative | treatment (IVET/VRET) x emotion (negative) | treatment (IVET/VRET) / emotion (negative) |
| 8 | treatIVET/VRET:Emopositive | treatment (IVET/VRET) x emotion (positive) | treatment (IVET/VRET) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (control, neutral) | -0.52 | -0.80 – -0.23 | 0.14 | -3.57 | 0.001 |
| 2 treatment (IVET/VRET) | 0.26 | -0.18 – 0.71 | 0.22 | 1.18 | 0.241 |
| 3 emotion (spider) | 0.65 | 0.29 – 1.02 | 0.18 | 3.56 | 0.001 |
| 4 emotion (negative) | 0.43 | 0.15 – 0.71 | 0.14 | 3.06 | 0.003 |
| 5 emotion (positive) | 0.19 | -0.09 – 0.46 | 0.14 | 1.35 | 0.178 |
| 6 treatment (IVET/VRET) x emotion (spider) | 0.88 | 0.31 – 1.44 | 0.29 | 3.07 | 0.003 |
| 7 treatment (IVET/VRET) x emotion (negative) | -0.02 | -0.46 – 0.41 | 0.22 | -0.10 | 0.919 |
| 8 treatment (IVET/VRET) x emotion (positive) | -0.00 | -0.43 – 0.42 | 0.22 | -0.01 | 0.991 |
| Random Effects | |||||
| σ2 | 21.74 | ||||
| τ00 fp | 0.64 | ||||
| τ11 fp.Emospider | 0.87 | ||||
| τ11 fp.Emonegative | 0.14 | ||||
| τ11 fp.Emopositive | 0.11 | ||||
| ρ01 | 0.17 | ||||
| -0.16 | |||||
| 0.74 | |||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.011 / NA | ||||
condition labels
table_model(get(model_name),
dv_labels = "session 1",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| session 1 | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (control) / emotion (neutral) | -0.52 | -0.80 – -0.23 | 0.14 | -3.57 | 0.001 |
| 2 treatment (IVET/VRET) / emotion (neutral) | 0.26 | -0.18 – 0.71 | 0.22 | 1.18 | 0.241 |
| 3 treatment (control) / emotion (spider) | 0.65 | 0.29 – 1.02 | 0.18 | 3.56 | 0.001 |
| 4 treatment (control) / emotion (negative) | 0.43 | 0.15 – 0.71 | 0.14 | 3.06 | 0.003 |
| 5 treatment (control) / emotion (positive) | 0.19 | -0.09 – 0.46 | 0.14 | 1.35 | 0.178 |
| 6 treatment (IVET/VRET) / emotion (spider) | 0.88 | 0.31 – 1.44 | 0.29 | 3.07 | 0.003 |
| 7 treatment (IVET/VRET) / emotion (negative) | -0.02 | -0.46 – 0.41 | 0.22 | -0.10 | 0.919 |
| 8 treatment (IVET/VRET) / emotion (positive) | -0.00 | -0.43 – 0.42 | 0.22 | -0.01 | 0.991 |
| Random Effects | |||||
| σ2 | 21.74 | ||||
| τ00 fp | 0.64 | ||||
| τ11 fp.Emospider | 0.87 | ||||
| τ11 fp.Emonegative | 0.14 | ||||
| τ11 fp.Emopositive | 0.11 | ||||
| ρ01 | 0.17 | ||||
| -0.16 | |||||
| 0.74 | |||||
| N fp | 89 | ||||
| Observations | 17360 | ||||
| Marginal R2 / Conditional R2 | 0.011 / NA | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether the combined treatment groups (IVET and VRET) differ from controls in spider (vs neutral) mean amplitude in the first session (but not in any other picture category). The analysis compares the combined IVET and VRET to the control group and does not test whether the treatments differ from each other.
The formula was LPP ~ 1 + treat * Emo + (1 + Emo | fp).
Emo as random effect.
Intercept = treatment(control) / emotion(neutral).
The effect for the intercept = -0.52. This is the mean amplitude for the intercept that contains treatment(control) and emotion(neutral) and is thus the marginal mean for the control group for neutral pictures.
The first effect shows that there is an effect of spider (vs neutral). It shows that for the control group, spiders have higher amps than neutral pictures. This relative positivity supports an LPP. But, this effect is not of particular interest because it is only for the control group.
Emospider
In the model table with condition labels, this is number 3.
treatment (control) / emotion (spider).
- estimate: 0.65
- p value: 6.0601e-04
The main interest is to see whether the combined treatment groups (IVET and VRET) differ from controls in their amps to spiders. Particularly, the difference between spiders and neutral pictures should be more positive across treatment groups compared to controls. Because the intercept contains treatment(control) and emotion(neutral), we are interested in this test:
treatIVET/VRET:Emospider
In the model table with condition labels, this is number 6.
treatment (IVET/VRET) / emotion (spider).
- estimate: 0.88
- p value: 2.8616e-03
This is the interaction of treatment(IVET/VRET vs control) x emotion (spider vs neutral) across ratings.
estimated means
data %>%
modelr::data_grid(treat, Emo) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | neutral | spider | negative | positive |
|---|---|---|---|---|
| Control | -0.52 | 0.14 | -0.08 | -0.33 |
| IVET/VRET | -0.25 | 1.28 | 0.16 | -0.07 |
Bayes
only spider and neutral
gaussian model
# Prepare dataframe.
detect_sess1 <- detect_baseline_acrosstreatment %>%
select(Emo, EPN, LPP, fp, sess, treat) %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp),
Emo = factor(Emo, levels = c('neutral','spider'))) %>%
na.omit()
# Regression Model.
LPP.sess1.model <- brm(LPP ~ 1 + treat*Emo + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/LPP.sess1.model",
# file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(LPP.sess1.model)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: LPP ~ 1 + treat * Emo + (1 + Emo | fp)
## Data: detect_sess1 (Number of observations: 8677)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 89)
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## sd(Intercept) 0.80 0.11 0.60 1.02 1.00 4159
## sd(Emospider) 0.92 0.15 0.63 1.22 1.00 2018
## cor(Intercept,Emospider) 0.25 0.23 -0.16 0.73 1.00 1761
## Tail_ESS
## sd(Intercept) 6237
## sd(Emospider) 3326
## cor(Intercept,Emospider) 1922
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -0.51 0.15 -0.79 -0.22 1.00 6062
## treatIVETDVRET 0.27 0.22 -0.18 0.70 1.00 5441
## Emospider 0.66 0.18 0.30 1.02 1.00 7053
## treatIVETDVRET:Emospider 0.86 0.28 0.30 1.41 1.00 7334
## Tail_ESS
## Intercept 5503
## treatIVETDVRET 5996
## Emospider 6278
## treatIVETDVRET:Emospider 5674
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 4.66 0.04 4.59 4.73 1.00 13068 5756
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null.sess1.model <- brm(LPP ~ 1 + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/LPP.sess1.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
emo.sess1.model <- brm(LPP ~ 1 + Emo + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/LPP.sess1.emo",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
treat.sess1.model <- brm(LPP ~ 1 + treat + (1 + Emo | fp),
family = gaussian(),
data = detect_sess1,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/LPP.sess1.treat",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
full.sess1.bayes <- bayes_factor(LPP.sess1.model, null.sess1.model)## Iteration: 1
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## Iteration: 7treat.sess1.bayes <- bayes_factor(treat.sess1.model, null.sess1.model)## Iteration: 1
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## Iteration: 7emo.sess1.bayes <- bayes_factor(emo.sess1.model, null.sess1.model)## Iteration: 1
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## Iteration: 9full.sess1.bayes## Estimated Bayes factor in favor of LPP.sess1.model over null.sess1.model: 20045589.34571treat.sess1.bayes## Estimated Bayes factor in favor of treat.sess1.model over null.sess1.model: 0.25289emo.sess1.bayes## Estimated Bayes factor in favor of emo.sess1.model over null.sess1.model: 10633809.20049compare with null
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Null = format(c(full.sess1.bayes$bf,
treat.sess1.bayes$bf,
emo.sess1.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxEmo | 2.004559e+07 |
| Treat | 2.528901e-01 |
| Emo | 1.063381e+07 |
compare with Emo
tibble(model = c("TreatxEmo", "Treat", "Emo"),
Compared_To_Emo = format(c(full.sess1.bayes$bf/emo.sess1.bayes$bf,
treat.sess1.bayes$bf/emo.sess1.bayes$bf,
emo.sess1.bayes$bf/emo.sess1.bayes$bf),
scientific = TRUE),
BF01 = format(c(emo.sess1.bayes$bf/full.sess1.bayes$bf,
emo.sess1.bayes$bf/treat.sess1.bayes$bf,
emo.sess1.bayes$bf/emo.sess1.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Emo | BF01 |
|---|---|---|
| TreatxEmo | 1.885081e+00 | 5.304812e-01 |
| Treat | 2.378170e-08 | 4.204914e+07 |
| Emo | 1.000000e+00 | 1.000000e+00 |
check assumptions
Linear regression has these assumptions:
- Linear association
- Normality of residuals
- No heteroskedasticity
- No multicollinearity
linearity
# Check linearity
na.omit(detect_sess1) %>%
add_residual_draws(LPP.sess1.model, ndraws = 1) %>%
ggplot(aes(x = .row, y = .residual)) +
stat_pointinterval()
normality
# Check normality
na.omit(detect_sess1) %>%
add_residual_draws(LPP.sess1.model, ndraws = 1) %>%
median_qi() %>%
ggplot(aes(sample = .residual)) +
geom_qq() +
geom_qq_line()
multicollinearity
# Check vif and tolerance
check_collinearity(LPP.sess1.model)treatment comparison
- session 1 and session 2 (session 1 as reference)
- include only treatment groups
- IVET = -.5, VRET = .5
- use neutral pictures as reference emotion
model_name <- "only_treat_LPP"
model_formula <- formula("LPP ~ 1 + treat*sess*Emo + (1 + sess * Emo | fp)")
data <- detect_only_treat_recode
if (file.exists(sprintf("results/models/model_%s.RDS", model_name))) {
assign(get("model_name"), readRDS(sprintf("results/models/model_%s.RDS", model_name)))
} else {
assign(get("model_name"), lmerTest::lmer(model_formula,
control = lmerControl(optimizer = "Nelder_Mead",
optCtrl = list(maxfun = 1e7),
calc.derivs = FALSE),
data = data))
saveRDS(eval(parse(text = model_name)), sprintf("results/models/model_%s.RDS", model_name))
}
# nloptwrap: Model failed to converge with 4 negative eigenvalues: -1.3e-02 -7.1e-02 -1.7e-01 -7.8e+01
# Nelder_Mead: Model failed to converge with 2 negative eigenvalues: -3.5e+01 -4.4e+01plot
all categories
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nsession") +
plot_aes
spider and neutral
fits <- data %>%
modelr::data_grid(treat, sess, Emo, fp) %>%
mutate(predicted_re = predict(get(model_name), .),
fp_treat = sprintf("%s_%s", fp, treat)) %>%
filter(fp_treat %in% sprintf("%s_%s", data$fp, data$treat)) %>%
filter(Emo %in% c("neutral", "spider")) %>%
mutate(sess = ifelse(sess == 0, 'pre', 'post'),
sess = factor(sess, levels = c('pre', 'post')),
treat = ifelse(treat == -.5, "IVET", "VRET"))
ggeffects::ggpredict(get(model_name), c("treat", "sess", "Emo")) %>%
data.frame() %>%
filter(facet %in% c("neutral", "spider")) %>%
mutate(group = ifelse(group == 0, 'pre', 'post'),
group = factor(group, levels = c('pre', 'post')),
x = ifelse(x == -.5, "IVET", "VRET"),
Emo = facet) %>%
ggplot(aes(group, predicted, color = x)) +
geom_line(data = fits, aes(x = sess, y = predicted_re, color = treat,
group = interaction(fp, treat, Emo)), alpha = .3, size = .2) +
geom_line(aes(group = x), position = position_dodge(width = .1)) +
geom_pointrange(aes(ymin = conf.low, ymax = conf.high), position = position_dodge(width = .1)) +
facet_grid(~Emo) +
scale_color_manual(values = palette[2:3], name = "treatment") +
labs(y = "predicted mean amplitude (µV)\n", x = "\nsession") +
plot_aes
ggsave('results/figures/fig_estimated_LPP_treat.png', plot = last_plot())summarize model
summary(get(model_name))## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: model_formula
## Data: data
## Control:
## lmerControl(optimizer = "Nelder_Mead", optCtrl = list(maxfun = 10000000),
## calc.derivs = FALSE)
##
## REML criterion at convergence: 115533.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -6.2454 -0.5664 -0.0046 0.5526 6.1588
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## fp (Intercept) 0.4393 0.6628
## sess 0.8677 0.9315 0.38
## Emospider 16.5298 4.0657 0.21 0.47
## Emonegative 5.6218 2.3710 0.12 0.58 0.92
## Emopositive 4.6972 2.1673 0.55 0.81 0.71 0.79
## sess:Emospider 2.4732 1.5727 -0.08 -0.14 -0.26 -0.18 -0.05
## sess:Emonegative 3.3048 1.8179 0.20 0.07 0.52 0.35 0.38
## sess:Emopositive 64.4452 8.0278 -0.11 0.07 0.76 0.73 0.37
## Residual 16.6861 4.0849
##
##
##
##
##
##
##
## 0.42
## 0.06 0.68
##
## Number of obs: 20284, groups: fp, 70
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.26617 0.13650 37.96659 -1.950 0.05860 .
## treat -0.14925 0.27301 37.96659 -0.547 0.58778
## sess -0.26842 0.17489 35.98661 -1.535 0.13360
## Emospider 1.60677 0.53667 39.50463 2.994 0.00473 **
## Emonegative 0.40088 0.33752 16.58090 1.188 0.25167
## Emopositive 0.11616 0.30752 16.66537 0.378 0.71040
## treat:sess 0.46054 0.34979 35.98661 1.317 0.19629
## treat:Emospider -0.05195 1.07334 39.50463 -0.048 0.96164
## treat:Emonegative 0.13738 0.67504 16.58090 0.204 0.84121
## treat:Emopositive 0.41937 0.61504 16.66537 0.682 0.50470
## sess:Emospider 0.12642 0.32112 22.54868 0.394 0.69753
## sess:Emonegative 0.08597 0.30794 15.75335 0.279 0.78375
## sess:Emopositive 0.24476 0.99118 540.06088 0.247 0.80505
## treat:sess:Emospider -0.01792 0.64225 22.54868 -0.028 0.97799
## treat:sess:Emonegative -0.44355 0.61589 15.75335 -0.720 0.48196
## treat:sess:Emopositive -0.70398 1.98236 540.06084 -0.355 0.72264
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1tidied_model <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)model table
table of labels
effectlbls <- data.frame(
num = as.character(seq(1:16)),
original = tidied_model$term[1:16],
standard = c("intercept (avr_treat, session (1), neutral)",
"treatment (VRET vs IVET)",
"session (2)",
"emotion (spider)",
"emotion (negative)",
"emotion (positive)",
"treatment (VRET vs IVET) x session",
"treatment (VRET vs IVET) x emotion (spider)",
"treatment (VRET vs IVET) x emotion (negative)",
"treatment (VRET vs IVET) x emotion (positive)",
"session x emotion (spider)",
"session x emotion (negative)",
"session x emotion (positive)",
"treatment (VRET vs IVET) x session x emotion (spider)",
"treatment (VRET vs IVET) x session x emotion (negative)",
"treatment (VRET vs IVET) x session x emotion (positive)"),
condition = c("treatment (avr_treat) / session (1) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (neutral)",
"treatment (avr_treat) / sess (2) / emotion (neutral)",
"treatment (avr_treat) / sess (1) / emotion (spider)",
"treatment (avr_treat) / sess (1) / emotion (negative)",
"treatment (avr_treat) / sess (1) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (neutral)",
"treatment (VRET vs IVET) / sess (1) / emotion (spider)",
"treatment (VRET vs IVET) / sess (1) / emotion (negative)",
"treatment (VRET vs IVET) / sess (1) / emotion (positive)",
"treatment (avr_treat) / sess (2) / emotion (spider)",
"treatment (avr_treat) / sess (2) / emotion (negative)",
"treatment (avr_treat) / sess (2) / emotion (positive)",
"treatment (VRET vs IVET) / sess (2) / emotion (spider)",
"treatment (VRET vs IVET) / sess (2) / emotion (negative)",
"treatment (VRET vs IVET) / sess (2) / emotion (positive)"),
stringsAsFactors = F)
effectlbls %>%
kable() %>%
kable_styling()| num | original | standard | condition |
|---|---|---|---|
| 1 | (Intercept) | intercept (avr_treat, session (1), neutral) | treatment (avr_treat) / session (1) / emotion (neutral) |
| 2 | treat | treatment (VRET vs IVET) | treatment (VRET vs IVET) / sess (1) / emotion (neutral) |
| 3 | sess | session (2) | treatment (avr_treat) / sess (2) / emotion (neutral) |
| 4 | Emospider | emotion (spider) | treatment (avr_treat) / sess (1) / emotion (spider) |
| 5 | Emonegative | emotion (negative) | treatment (avr_treat) / sess (1) / emotion (negative) |
| 6 | Emopositive | emotion (positive) | treatment (avr_treat) / sess (1) / emotion (positive) |
| 7 | treat:sess | treatment (VRET vs IVET) x session | treatment (VRET vs IVET) / sess (2) / emotion (neutral) |
| 8 | treat:Emospider | treatment (VRET vs IVET) x emotion (spider) | treatment (VRET vs IVET) / sess (1) / emotion (spider) |
| 9 | treat:Emonegative | treatment (VRET vs IVET) x emotion (negative) | treatment (VRET vs IVET) / sess (1) / emotion (negative) |
| 10 | treat:Emopositive | treatment (VRET vs IVET) x emotion (positive) | treatment (VRET vs IVET) / sess (1) / emotion (positive) |
| 11 | sess:Emospider | session x emotion (spider) | treatment (avr_treat) / sess (2) / emotion (spider) |
| 12 | sess:Emonegative | session x emotion (negative) | treatment (avr_treat) / sess (2) / emotion (negative) |
| 13 | sess:Emopositive | session x emotion (positive) | treatment (avr_treat) / sess (2) / emotion (positive) |
| 14 | treat:sess:Emospider | treatment (VRET vs IVET) x session x emotion (spider) | treatment (VRET vs IVET) / sess (2) / emotion (spider) |
| 15 | treat:sess:Emonegative | treatment (VRET vs IVET) x session x emotion (negative) | treatment (VRET vs IVET) / sess (2) / emotion (negative) |
| 16 | treat:sess:Emopositive | treatment (VRET vs IVET) x session x emotion (positive) | treatment (VRET vs IVET) / sess (2) / emotion (positive) |
standard labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,3]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 intercept (avr_treat, session (1), neutral) | -0.27 | -0.54 – 0.01 | 0.14 | -1.95 | 0.059 |
| 2 treatment (VRET vs IVET) | -0.15 | -0.70 – 0.40 | 0.27 | -0.55 | 0.588 |
| 3 session (2) | -0.27 | -0.62 – 0.09 | 0.17 | -1.53 | 0.134 |
| 4 emotion (spider) | 1.61 | 0.52 – 2.69 | 0.54 | 2.99 | 0.005 |
| 5 emotion (negative) | 0.40 | -0.31 – 1.11 | 0.34 | 1.19 | 0.252 |
| 6 emotion (positive) | 0.12 | -0.53 – 0.77 | 0.31 | 0.38 | 0.710 |
| 7 treatment (VRET vs IVET) x session | 0.46 | -0.25 – 1.17 | 0.35 | 1.32 | 0.196 |
| 8 treatment (VRET vs IVET) x emotion (spider) | -0.05 | -2.22 – 2.12 | 1.07 | -0.05 | 0.962 |
| 9 treatment (VRET vs IVET) x emotion (negative) | 0.14 | -1.29 – 1.56 | 0.68 | 0.20 | 0.841 |
| 10 treatment (VRET vs IVET) x emotion (positive) | 0.42 | -0.88 – 1.72 | 0.62 | 0.68 | 0.505 |
| 11 session x emotion (spider) | 0.13 | -0.54 – 0.79 | 0.32 | 0.39 | 0.698 |
| 12 session x emotion (negative) | 0.09 | -0.57 – 0.74 | 0.31 | 0.28 | 0.784 |
| 13 session x emotion (positive) | 0.24 | -1.70 – 2.19 | 0.99 | 0.25 | 0.805 |
| 14 treatment (VRET vs IVET) x session x emotion (spider) | -0.02 | -1.35 – 1.31 | 0.64 | -0.03 | 0.978 |
| 15 treatment (VRET vs IVET) x session x emotion (negative) | -0.44 | -1.75 – 0.86 | 0.62 | -0.72 | 0.482 |
| 16 treatment (VRET vs IVET) x session x emotion (positive) | -0.70 | -4.60 – 3.19 | 1.98 | -0.36 | 0.723 |
| Random Effects | |||||
| σ2 | 16.69 | ||||
| τ00 fp | 0.44 | ||||
| τ11 fp.sess | 0.87 | ||||
| τ11 fp.Emospider | 16.53 | ||||
| τ11 fp.Emonegative | 5.62 | ||||
| τ11 fp.Emopositive | 4.70 | ||||
| τ11 fp.sess:Emospider | 2.47 | ||||
| τ11 fp.sess:Emonegative | 3.30 | ||||
| τ11 fp.sess:Emopositive | 64.45 | ||||
| ρ01 | 0.38 | ||||
| 0.21 | |||||
| 0.12 | |||||
| 0.55 | |||||
| -0.08 | |||||
| 0.20 | |||||
| -0.11 | |||||
| ICC | 0.59 | ||||
| N fp | 70 | ||||
| Observations | 20284 | ||||
| Marginal R2 / Conditional R2 | 0.011 / 0.591 | ||||
condition labels
table_model(get(model_name),
dv_labels = "only treat model",
pred_labels = paste(effectlbls[,1], effectlbls[,4]))| only treat model | |||||
|---|---|---|---|---|---|
| Parameter | B | 95% CI | SE | t | p |
| 1 treatment (avr_treat) / session (1) / emotion (neutral) | -0.27 | -0.54 – 0.01 | 0.14 | -1.95 | 0.059 |
| 2 treatment (VRET vs IVET) / sess (1) / emotion (neutral) | -0.15 | -0.70 – 0.40 | 0.27 | -0.55 | 0.588 |
| 3 treatment (avr_treat) / sess (2) / emotion (neutral) | -0.27 | -0.62 – 0.09 | 0.17 | -1.53 | 0.134 |
| 4 treatment (avr_treat) / sess (1) / emotion (spider) | 1.61 | 0.52 – 2.69 | 0.54 | 2.99 | 0.005 |
| 5 treatment (avr_treat) / sess (1) / emotion (negative) | 0.40 | -0.31 – 1.11 | 0.34 | 1.19 | 0.252 |
| 6 treatment (avr_treat) / sess (1) / emotion (positive) | 0.12 | -0.53 – 0.77 | 0.31 | 0.38 | 0.710 |
| 7 treatment (VRET vs IVET) / sess (2) / emotion (neutral) | 0.46 | -0.25 – 1.17 | 0.35 | 1.32 | 0.196 |
| 8 treatment (VRET vs IVET) / sess (1) / emotion (spider) | -0.05 | -2.22 – 2.12 | 1.07 | -0.05 | 0.962 |
| 9 treatment (VRET vs IVET) / sess (1) / emotion (negative) | 0.14 | -1.29 – 1.56 | 0.68 | 0.20 | 0.841 |
| 10 treatment (VRET vs IVET) / sess (1) / emotion (positive) | 0.42 | -0.88 – 1.72 | 0.62 | 0.68 | 0.505 |
| 11 treatment (avr_treat) / sess (2) / emotion (spider) | 0.13 | -0.54 – 0.79 | 0.32 | 0.39 | 0.698 |
| 12 treatment (avr_treat) / sess (2) / emotion (negative) | 0.09 | -0.57 – 0.74 | 0.31 | 0.28 | 0.784 |
| 13 treatment (avr_treat) / sess (2) / emotion (positive) | 0.24 | -1.70 – 2.19 | 0.99 | 0.25 | 0.805 |
| 14 treatment (VRET vs IVET) / sess (2) / emotion (spider) | -0.02 | -1.35 – 1.31 | 0.64 | -0.03 | 0.978 |
| 15 treatment (VRET vs IVET) / sess (2) / emotion (negative) | -0.44 | -1.75 – 0.86 | 0.62 | -0.72 | 0.482 |
| 16 treatment (VRET vs IVET) / sess (2) / emotion (positive) | -0.70 | -4.60 – 3.19 | 1.98 | -0.36 | 0.723 |
| Random Effects | |||||
| σ2 | 16.69 | ||||
| τ00 fp | 0.44 | ||||
| τ11 fp.sess | 0.87 | ||||
| τ11 fp.Emospider | 16.53 | ||||
| τ11 fp.Emonegative | 5.62 | ||||
| τ11 fp.Emopositive | 4.70 | ||||
| τ11 fp.sess:Emospider | 2.47 | ||||
| τ11 fp.sess:Emonegative | 3.30 | ||||
| τ11 fp.sess:Emopositive | 64.45 | ||||
| ρ01 | 0.38 | ||||
| 0.21 | |||||
| 0.12 | |||||
| 0.55 | |||||
| -0.08 | |||||
| 0.20 | |||||
| -0.11 | |||||
| ICC | 0.59 | ||||
| N fp | 70 | ||||
| Observations | 20284 | ||||
| Marginal R2 / Conditional R2 | 0.011 / 0.591 | ||||
interpretation
tm <- get(model_name) %>%
broom.mixed::tidy(conf.int = TRUE)The goal is to examine whether IVET and VRET differ from each other in spider (vs neutral) mean amps in the first session and between the first and second session (but not in any other picture category).
The formula was LPP ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp).
Sess * Emo as random effects: This means that emo, session, and the 2-way interaction can differ between subjects.
Intercept = treatment(avr_treat) / session (1) / emotion (neutral).
avr_treat is the mean of IVET and VRET.
The effect for the intercept = -0.27. This is the mean amp for the intercept that contains the average across treatments in session 1 to neutral pictures.
The effect of the interaction is added to this together with lower-order terms to get the marginal mean. An interaction parameter is how much it differs from the lower order terms and the t test is for the null hypothesis that the difference between these parameters is 0. When testing higher effects, the lower effects are removed. That is, the higher effects test for something over and above the lower effects. Accordingly, the estimated marginal means are the intercept + lower effects + estimate for higher effect.
We want to see whether the groups showed higher amps to spiders than neutral pictures in session 1.
Emospider
In the model table with condition labels, this is number 4.
treatment (avr_treat) / sess (1) / emotion (spider).
- estimate: 1.61
- p value: 4.7331e-03
Indeed, mean amps are relatively positive to spiders.
Did the groups differ in how they responded to spiders versus neutral pictures in session 1? No.
treat:Emospider
In the model table with condition labels, this is number 8.
treatment (VRET vs IVET) / sess (1) / emotion (spider).
- estimate: -0.05
- p value: 9.6164e-01
Did the effect of spiders differ between sessions: No difference!
sess:Emospider
In the model table with condition labels, this is number 11.
treatment (avr_treat) / sess (2) / emotion (spider).
- estimate: 0.13
- p value: 6.9753e-01
Critically, did this effect vary with treatment? No difference!
treat:sess:Emospider
In the model table with condition labels, this is number 14.
treatment (VRET vs IVET) / sess (2) / emotion (spider).
- estimate: -0.02
- p value: 9.7799e-01
estimated means
data %>%
modelr::data_grid(treat, Emo, sess) %>%
mutate(marginal_mean = predict(get(model_name), ., re.form = NA),
treat = ifelse(treat == -.5, "IVET", "VRET"),
sess = ifelse(sess == 0, "1", "2")) %>%
pivot_wider(names_from = Emo, values_from = marginal_mean) %>%
kable(digits = 2) %>%
kable_styling()| treat | sess | neutral | spider | negative | positive |
|---|---|---|---|---|---|
| IVET | 1 | -0.19 | 1.44 | 0.14 | -0.29 |
| IVET | 2 | -0.69 | 1.08 | -0.05 | -0.19 |
| VRET | 1 | -0.34 | 1.24 | 0.13 | -0.01 |
| VRET | 2 | -0.38 | 1.32 | -0.05 | -0.16 |
Bayes
only spider and neutral
gaussian model
detect_treat <- detect_only_treat_recode %>%
select(Emo, EPN, LPP, fp, sess, treat) %>%
filter(Emo %in% c('spider', 'neutral')) %>%
mutate(fp = as.factor(fp),
Emo = factor(Emo, levels = c('neutral','spider'))) %>%
na.omit()
# Regression Model.
LPP.treat.model <- brm(LPP ~ 1 + treat*sess*Emo + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/LPP.treat.model",
# file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
# Model Summary.
summary(LPP.treat.model)## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: LPP ~ 1 + treat * sess * Emo + (1 + sess * Emo | fp)
## Data: detect_treat (Number of observations: 10145)
## Draws: 4 chains, each with iter = 3000; warmup = 1000; thin = 1;
## total post-warmup draws = 8000
##
## Group-Level Effects:
## ~fp (Number of levels: 70)
## Estimate Est.Error l-95% CI u-95% CI Rhat
## sd(Intercept) 0.70 0.13 0.46 0.97 1.00
## sd(sess) 0.49 0.21 0.06 0.89 1.00
## sd(Emospider) 1.22 0.21 0.85 1.66 1.00
## sd(sess:Emospider) 0.81 0.32 0.15 1.43 1.00
## cor(Intercept,sess) -0.24 0.32 -0.72 0.50 1.00
## cor(Intercept,Emospider) 0.18 0.23 -0.26 0.62 1.00
## cor(sess,Emospider) -0.19 0.31 -0.75 0.48 1.01
## cor(Intercept,sess:Emospider) -0.33 0.28 -0.82 0.24 1.00
## cor(sess,sess:Emospider) 0.27 0.35 -0.46 0.87 1.00
## cor(Emospider,sess:Emospider) -0.45 0.25 -0.82 0.17 1.00
## Bulk_ESS Tail_ESS
## sd(Intercept) 4022 5894
## sd(sess) 997 942
## sd(Emospider) 3558 5699
## sd(sess:Emospider) 903 1316
## cor(Intercept,sess) 2836 2829
## cor(Intercept,Emospider) 1722 3494
## cor(sess,Emospider) 852 1073
## cor(Intercept,sess:Emospider) 2812 4190
## cor(sess,sess:Emospider) 1495 2570
## cor(Emospider,sess:Emospider) 3669 3809
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
## Intercept -0.27 0.14 -0.55 0.02 1.00 5930
## treat -0.17 0.29 -0.74 0.40 1.00 6077
## sess -0.29 0.15 -0.60 0.01 1.00 9030
## Emospider 1.64 0.23 1.20 2.09 1.00 5680
## treat:sess 0.51 0.31 -0.09 1.12 1.00 7133
## treat:Emospider -0.08 0.45 -0.99 0.80 1.00 6774
## sess:Emospider 0.08 0.23 -0.37 0.53 1.00 7294
## treat:sess:Emospider 0.03 0.46 -0.88 0.91 1.00 8037
## Tail_ESS
## Intercept 6006
## treat 5598
## sess 6688
## Emospider 5623
## treat:sess 5640
## treat:Emospider 6084
## sess:Emospider 5998
## treat:sess:Emospider 6145
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 4.07 0.03 4.01 4.12 1.00 16735 5357
##
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).Bayes factor
only spider and neutral
computations
null.treat.model <- brm(LPP ~ 1 + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = prior(normal(0, 4), class = Intercept),
chains = 4,
file = "results/models/LPP.treat.null",
# Specify file to save/reuse model
cores = 4,
iter = 3000,
warmup = 1000,
init_r = 0.5,
save_pars = save_pars(all = TRUE))
sess_emo.treat.model <- brm(LPP ~ 1 + sess*Emo + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/LPP.treat.sess_emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))
emo.treat.model <- brm(LPP ~ 1 + Emo + (1 + sess*Emo | fp),
family = gaussian(),
data = detect_treat,
prior = c(prior(normal(0, 4), class = Intercept),
prior(normal(0, 4), class = b)),
chains = 4,
file = "results/models/LPP.treat.emo",
cores = 4,
iter = 3000,
warmup = 1000,
save_pars = save_pars(all = TRUE))Compute bayes factor approximations (via bridge sampling)
# Bayes factor comparisons are in favor of alternative hypothesis.
full.treat.bayes <- bayes_factor(LPP.treat.model, null.treat.model)## Iteration: 1
## Iteration: 2
## Iteration: 3
## Iteration: 4
## Iteration: 5
## Iteration: 6
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## Iteration: 1full.treat.bayes## Estimated Bayes factor in favor of LPP.treat.model over null.treat.model: 35070233.10941sess_emo.treat.bayes## Estimated Bayes factor in favor of sess_emo.treat.model over null.treat.model: 229742538642.90051emo.treat.bayes## Estimated Bayes factor in favor of emo.treat.model over null.treat.model: 3152655368753433.50000compare with null
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Null = format(c(full.treat.bayes$bf,
sess_emo.treat.bayes$bf,
emo.treat.bayes$bf), scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Null |
|---|---|
| TreatxSessxEmo | 3.507023e+07 |
| SessxEmo | 2.297425e+11 |
| Emo | 3.152655e+15 |
compare with Treat x Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Treat.Sess.Emo =
format(c(full.treat.bayes$bf/full.treat.bayes$bf,
sess_emo.treat.bayes$bf/full.treat.bayes$bf,
emo.treat.bayes$bf/full.treat.bayes$bf),
scientific = TRUE),
BF01 =
format(c(full.treat.bayes$bf/full.treat.bayes$bf,
full.treat.bayes$bf/sess_emo.treat.bayes$bf,
full.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Treat.Sess.Emo | BF01 |
|---|---|---|
| TreatxSessxEmo | 1.000000e+00 | 1.000000e+00 |
| SessxEmo | 6.550927e+03 | 1.526502e-04 |
| Emo | 8.989548e+07 | 1.112403e-08 |
compare with Sess x Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Sess.Emo = format(c(full.treat.bayes$bf/sess_emo.treat.bayes$bf,
sess_emo.treat.bayes$bf/sess_emo.treat.bayes$bf,
emo.treat.bayes$bf/sess_emo.treat.bayes$bf),
scientific = TRUE),
BF01 = format(c(sess_emo.treat.bayes$bf/full.treat.bayes$bf,
sess_emo.treat.bayes$bf/sess_emo.treat.bayes$bf,
sess_emo.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Sess.Emo | BF01 |
|---|---|---|
| TreatxSessxEmo | 1.526502e-04 | 6.550927e+03 |
| SessxEmo | 1.000000e+00 | 1.000000e+00 |
| Emo | 1.372256e+04 | 7.287271e-05 |
compare with Emo
tibble(model = c("TreatxSessxEmo", "SessxEmo", "Emo"),
Compared_To_Emo = format(c(full.treat.bayes$bf/emo.treat.bayes$bf,
sess_emo.treat.bayes$bf/emo.treat.bayes$bf,
emo.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE),
BF01 = format(c(emo.treat.bayes$bf/full.treat.bayes$bf,
emo.treat.bayes$bf/sess_emo.treat.bayes$bf,
emo.treat.bayes$bf/emo.treat.bayes$bf),
scientific = TRUE)) %>%
kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"),
full_width = F, position = 'left')| model | Compared_To_Emo | BF01 |
|---|---|---|
| TreatxSessxEmo | 1.112403e-08 | 8.989548e+07 |
| SessxEmo | 7.287271e-05 | 1.372256e+04 |
| Emo | 1.000000e+00 | 1.000000e+00 |
check assumptions
Linear regression has these assumptions:
- Linear association
- Normality of residuals
- No heteroskedasticity
- No multicollinearity
linearity
# Check linearity
na.omit(detect_treat) %>%
add_residual_draws(LPP.treat.model, ndraws = 1) %>%
ggplot(aes(x = .row, y = .residual)) +
stat_pointinterval()
normality
# Check normality
na.omit(detect_treat) %>%
add_residual_draws(LPP.treat.model, ndraws = 1) %>%
median_qi() %>%
ggplot(aes(sample = .residual)) +
geom_qq() +
geom_qq_line()
multicollinearity
# Check vif and tolerance
check_collinearity(LPP.treat.model)