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manuscript.R
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### R code from vignette source '/home/malsburg/Documents/Uni/Projekte/AnalyzingETMeasures/MalsburgAngele2016JML/manuscript.Rnw'
### Encoding: UTF-8
###################################################
### code chunk number 1: load-libraries
###################################################
library(knitr)
library(dplyr)
library(ggplot2)
library(PropCIs)
source("R/new_etmeasures.function.R")
source("R/compute_model_parameters.function.R")
###################################################
### code chunk number 2: calculate-parameters
###################################################
d1 <- read.csv("eyetracking_data/AngeleEtAl2013.csv")
parameters1 <- with(d1, compute.model.parameters(subject, item, condition, ffd_n1, gzd_n1, gopast_n1, tvt_n1))
d2 <- read.csv("eyetracking_data/MetznerEtAl2016.tsv", sep="\t", head=T)
parameters2 <- with(d2, compute.model.parameters(subj, item, cond, FFD, FPRT, RPD, TFT))
d <- data.frame(parameter=names(parameters1),
angele=unlist(parameters1),
metzner=unlist(parameters2))
d[1,2:3] <- c(20, 50)
d[2,2:3] <- c(20, 50)
###################################################
### code chunk number 3: table-parameters
###################################################
kable(d[c(1:2, 5:6, 7:9, 3, 10, 12, 14, 4, 11, 13, 15),], digits=2, row.names=F, col.names=c("Parameter", "Lower bound", "Upper bound"), format="latex", booktabs=T)
###################################################
### code chunk number 4: measure-correlations
###################################################
cor.angele <- cor(subset(d1, select=c(ffd_n1, gzd_n1, gopast_n1, tvt_n1)), use="complete")
cor.metzner <- cor(subset(d2, select=c(FFD, FPRT, RPD, TFT)), use="complete")
set.seed(1)
d1a <- new.etmeasures(parameters1)
set.seed(1)
d2a <- new.etmeasures(parameters2)
cor.angele.a <- cor(subset(d1a, select=c(ffd, gzd, gpd, tvt)))
cor.metzner.a <- cor(subset(d2a, select=c(ffd, gzd, gpd, tvt)))
colnames(cor.angele) <- rownames(cor.angele) <-
colnames(cor.metzner) <- rownames(cor.metzner) <-
colnames(cor.angele.a) <- rownames(cor.angele.a) <-
colnames(cor.metzner.a) <- rownames(cor.metzner.a) <- c("FFD", "GZD", "GPD", "TVT")
kable(cbind(cor.angele, cor.angele.a), digits=2, format="latex")
kable(cbind(cor.metzner, cor.metzner.a), digits=2, format="latex")
###################################################
### code chunk number 5: figure-scatter-plots-angele
###################################################
set.seed(1)
t <- as.logical(rbinom(nrow(d2), 1, 0.5))
par(mfrow=c(2, 3), mar=c(4,4,1,1))
with(d1[t,], plot(ffd_n1, gzd_n1, xlab="FFD", ylab="GZD", xlim=c(0, 800), ylim=c(0, 1500), cex=0.5, pch=20))
with(d1[t,], plot(gzd_n1, gopast_n1, xlab="GZD", ylab="GPD", xlim=c(0, 800), ylim=c(0, 1500), cex=0.5, pch=20))
with(d1[t,], plot(gzd_n1, tvt_n1, xlab="GZD", ylab="TVT", xlim=c(0, 800), ylim=c(0, 1500), cex=0.5, pch=20))
with(d1a[t,], plot(ffd, gzd, xlab="Artificial FFD", ylab="Artificial GZD", xlim=c(0, 800), ylim=c(0, 1500), cex=0.5, pch=20))
with(d1a[t,], plot(gzd, gpd, xlab="Artificial GZD", ylab="Artificial GPD", xlim=c(0, 800), ylim=c(0, 1500), cex=0.5, pch=20))
with(d1a[t,], plot(gzd, tvt, xlab="Artificial GZD", ylab="Artificial TVT", xlim=c(0, 800), ylim=c(0, 1500), cex=0.5, pch=20))
###################################################
### code chunk number 6: figure-scatter-plots-metzner
###################################################
set.seed(1)
t <- as.logical(rbinom(nrow(d2), 1, 0.1))
par(mfrow=c(2, 3), mar=c(4,4,1,1))
with(d2[t,], plot(FFD, FPRT, xlab="FFD", ylab="GZD", xlim=c(0, 2000), ylim=c(0, 4000), cex=0.5, pch=20))
with(d2[t,], plot(FPRT, RPD, xlab="GZD", ylab="GPD", xlim=c(0, 2000), ylim=c(0, 4000), cex=0.5, pch=20))
with(d2[t,], plot(FPRT, TFT, xlab="GZD", ylab="TVT", xlim=c(0, 2000), ylim=c(0, 4000), cex=0.5, pch=20))
t <- as.logical(rbinom(nrow(d2a), 1, 0.1))
with(d2a[t,], plot(ffd, gzd, xlab="Artificial FFD", ylab="Artificial GZD", xlim=c(0, 2000), ylim=c(0, 4000), cex=0.5, pch=20))
with(d2a[t,], plot(gzd, gpd, xlab="Artificial GZD", ylab="Artificial GPD", xlim=c(0, 2000), ylim=c(0, 4000), cex=0.5, pch=20))
with(d2a[t,], plot(gzd, tvt, xlab="Artificial GZD", ylab="Artificial TVT", xlim=c(0, 2000), ylim=c(0, 4000), cex=0.5, pch=20))
###################################################
### code chunk number 7: load-simulation-results
###################################################
load("simulation_results/results.Rda")
# Multiply the p-values with the sign of the coefficient for the
# effect of condition if there was a true effect. In the power
# analysis, we only consider effects that are significant and in the
# correct direction.
sims$ps <- with(sims, p * sign(mer1.cond))
###################################################
### code chunk number 8: one-effect
###################################################
# Rate of simulations in which at least one single-variable model
# shows an effect. The uncorrected alpha level (0.05) is used to
# determine significance.
# Determine significance:
r <- sims %>%
mutate(significant = 0<=p & p <=0.05,
hit = 0<=ps & ps<=0.05,
significant.bf = 0<=p & p <=0.05/4,
hit.bf = 0<=ps & ps<=0.05/4)
r.ffd <- r %>%
group_by(effect.size, sim) %>%
summarize(significant = sum(significant),
hit = sum(hit),
significant.bf = sum(significant.bf),
hit.bf = sum(hit.bf))
r.gzd <- r %>%
filter(variable != "ffd") %>%
group_by(effect.size, sim) %>%
summarize(significant = sum(significant),
hit = sum(hit),
significant.bf = sum(significant.bf),
hit.bf = sum(hit.bf))
r.gpd <- r %>%
filter(variable == "gpd") %>%
select(sim, effect.size, significant, hit, significant.bf, hit.bf)
r.tvt <- r %>%
filter(variable == "tvt") %>%
select(sim, effect.size, significant, hit, significant.bf, hit.bf)
# Calculate rates and confidence intervals:
one.effect.ffd <- r.ffd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>0),
ht.ci.lower = exactci(sum(hit>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>0), n(), 0.95)$conf.int[2])
two.effects.ffd <- r.ffd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>1),
dr.ci.lower = exactci(sum(significant>1), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>1), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>1),
ht.ci.lower = exactci(sum(hit>1), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>1), n(), 0.95)$conf.int[2])
bonferroni.effect.ffd <- r.ffd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant.bf>0),
dr.ci.lower = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit.bf>0),
ht.ci.lower = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[2])
one.effect.gzd <- r.gzd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>0),
ht.ci.lower = exactci(sum(hit>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>0), n(), 0.95)$conf.int[2])
two.effects.gzd <- r.gzd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>1),
dr.ci.lower = exactci(sum(significant>1), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>1), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>1),
ht.ci.lower = exactci(sum(hit>1), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>1), n(), 0.95)$conf.int[2])
bonferroni.effect.gzd <- r.gzd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant.bf>0),
dr.ci.lower = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit.bf>0),
ht.ci.lower = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[2])
one.effect.gpd <- r.gpd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>0),
ht.ci.lower = exactci(sum(hit>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>0), n(), 0.95)$conf.int[2])
two.effects.gpd <- r.gpd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>1),
dr.ci.lower = exactci(sum(significant>1), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>1), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>1),
ht.ci.lower = exactci(sum(hit>1), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>1), n(), 0.95)$conf.int[2])
bonferroni.effect.gpd <- r.gpd %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant.bf>0),
dr.ci.lower = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit.bf>0),
ht.ci.lower = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[2])
one.effect.tvt <- r.tvt %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>0),
ht.ci.lower = exactci(sum(hit>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>0), n(), 0.95)$conf.int[2])
two.effects.tvt <- r.tvt %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant>1),
dr.ci.lower = exactci(sum(significant>1), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>1), n(), 0.95)$conf.int[2],
hit.rate = mean(hit>1),
ht.ci.lower = exactci(sum(hit>1), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit>1), n(), 0.95)$conf.int[2])
bonferroni.effect.tvt <- r.tvt %>%
group_by(effect.size) %>%
summarize(detection.rate = mean(significant.bf>0),
dr.ci.lower = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant.bf>0), n(), 0.95)$conf.int[2],
hit.rate = mean(hit.bf>0),
ht.ci.lower = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[1],
ht.ci.upper = exactci(sum(hit.bf>0), n(), 0.95)$conf.int[2])
###################################################
### code chunk number 9: decision-criteria
###################################################
all.criteria <- rbind(one.effect.ffd, two.effects.ffd, bonferroni.effect.ffd,
one.effect.gzd, two.effects.gzd, bonferroni.effect.gzd,
one.effect.gpd, two.effects.gpd, bonferroni.effect.gpd,
one.effect.tvt, two.effects.tvt, bonferroni.effect.tvt)
all.criteria$measure <- factor(rep(c("ffd", "gzd", "gpd", "tvt"), each=21),
c("ffd", "gzd", "gpd", "tvt"))
all.criteria$criterion <- factor(rep(c("One effect", "Two effects", "Bonferroni"), each=7),
c("One effect", "Two effects", "Bonferroni"))
###################################################
### code chunk number 10: decision-criteria-table
###################################################
kable(subset(all.criteria, effect.size==0&measure=="ffd", select=c(criterion, detection.rate, dr.ci.lower, dr.ci.upper)), digits=3, format="latex")
###################################################
### code chunk number 11: figure-false-positives-by-parameters
###################################################
r0 <- subset(r.ffd, effect.size==0)[c("sim", "significant")]
s0 <- subset(sims, effect.size==0, select=c(sim, p.refix, p.regr, p.reread, mean.ffd, mean.gazediff, mean.gopastdiff, mean.tvtdiff))
s0 <- unique(s0)
r0 <- merge(r0, s0)
for (parameter.name in colnames(r0)[-(1:2)]) {
r0[[parameter.name]] <- cut(
r0[[parameter.name]],
quantile(r0[[parameter.name]], seq(0, 1, 1/2)),
c("low", "high"),
T)
}
x1 <- r0 %>%
group_by(p.refix) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
x2 <- r0 %>%
group_by(p.regr) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
x3 <- r0 %>%
group_by(p.reread) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
x4 <- r0 %>%
group_by(mean.ffd) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
x5 <- r0 %>%
group_by(mean.gazediff) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
x6 <- r0 %>%
group_by(mean.gopastdiff) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
x7 <- r0 %>%
group_by(mean.tvtdiff) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
colnames(x1)[1] <- colnames(x2)[1] <- colnames(x3)[1] <- colnames(x4)[1] <- colnames(x5)[1] <- colnames(x6)[1] <- colnames(x7)[1] <- "Parametervalue"
x <- rbind(x1, x2, x3, x4, x5, x6, x7)
x$parameter <- rep(colnames(r0)[-(1:2)], each=2)
x$detection.rate <- 100 * x$detection.rate
x$dr.ci.lower <- 100 * x$dr.ci.lower
x$dr.ci.upper <- 100 * x$dr.ci.upper
print(ggplot(x, aes(Parametervalue, detection.rate)) +
geom_point() +
geom_pointrange(aes(ymax=dr.ci.lower, ymin=dr.ci.upper)) +
ylab("False positive rate (%)") +
xlab("Parameter value") +
facet_wrap( ~ parameter, nrow=2, as.table=F) +
theme_bw())
###################################################
### code chunk number 12: table:false-positives-max-effect
###################################################
xl <- subset(r0, p.regr=="low" & p.reread=="low" & mean.gopastdiff=="low")
xh <- subset(r0, p.regr=="high" & p.reread=="high" & mean.gopastdiff=="high")
xl$params <- "low"
xh$params <- "high"
x <- rbind(xl, xh)
xx <- x %>%
group_by(params) %>%
summarize(detection.rate = mean(significant>0),
dr.ci.lower = exactci(sum(significant>0), n(), 0.95)$conf.int[1],
dr.ci.upper = exactci(sum(significant>0), n(), 0.95)$conf.int[2])
kable(xx, format="latex", digits=3)
###################################################
### code chunk number 13: figure-power-by-criterion
###################################################
ggplot(filter(all.criteria, measure=="ffd")) +
aes(factor(effect.size), hit.rate, group=criterion, linetype=criterion) +
geom_line() +
guides(linetype = guide_legend(title="Criterion:")) +
scale_x_discrete() +
ylim(0, 1) +
xlab("True effect (ms)") +
ylab("Power") +
theme_bw()
###################################################
### code chunk number 14: figure-power-by-stage
###################################################
# Plot how the power changes when effects are introduced at later stages:
ggplot(filter(all.criteria)) +
aes(factor(effect.size), hit.rate, group=criterion, linetype=criterion) +
geom_line() +
guides(linetype = guide_legend(title="Criterion:")) +
scale_x_discrete() +
ylim(0, 1) +
xlab("True effect (ms)") +
ylab("Power") +
theme_bw() +
facet_wrap(~measure, nrow=1, as.table=F)
###################################################
### code chunk number 15: figure-power-by-measure
###################################################
detection.rate.individual.models <- sims %>%
group_by(effect.size, variable) %>%
summarize(detection.rate=mean (0<=ps & ps<=0.05),
ci.lower=exactci(sum(0<=ps & ps<=0.05), n(), 0.95)$conf.int[1],
ci.upper=exactci(sum(0<=ps & ps<=0.05), n(), 0.95)$conf.int[2])
levels(detection.rate.individual.models$variable) <- toupper(levels(detection.rate.individual.models$variable))
ggplot(detection.rate.individual.models) +
aes(factor(effect.size), detection.rate, group=variable, linetype=variable) +
geom_line() +
guides(linetype = guide_legend(title="Measure:")) +
scale_x_discrete() +
ylim(0, 1) +
xlab("True effect (ms)") +
ylab("Power") +
theme_bw()