library(neuRosim)
library(ggplot2)
design <- simprepTemporal(totaltime=200, onsets=seq(1,200,40),
                          durations=10, effectsize=1, TR=1, hrf="double-gamma")
design_regressor <- simTSfmri(design=design, SNR=3, noise="none")

#create an ic timecourse that is aligned with the design
ictimecourse_aligned <- simTSfmri(design=design, SNR=2, noise="white")
summary(lm(ictimecourse_aligned ~ design_regressor)) #beta ~1.0

#decreasing response amplitude decreases beta by half
ictimecourse_smallamp <- ictimecourse_aligned / 2
summary(lm(ictimecourse_smallamp ~ design_regressor)) #beta ~ 0.5

#misaligning the regressor can also lead to a similar beta, but lower explained variance
ictimecourse_misaligned <- Hmisc::Lag(ictimecourse_aligned, 4)
summary(lm(ictimecourse_misaligned ~ design_regressor)) #beta ~ 0.5

#likewise, adding task-irrelevant activity can lower the beta somewhat while hammering R2
irrelevant <- simprepTemporal(totaltime=200, onsets=seq(20,200,40),
                          durations=5, effectsize=3, TR=1, hrf="double-gamma")
irrelevant_activity <- simTSfmri(design=irrelevant, SNR=3, noise="white")

ictimecourse_with_irrelevant <- ictimecourse_aligned + irrelevant_activity

summary(lm(ictimecourse_with_irrelevant ~ design_regressor)) #beta ~ 0.5

pdf("amplitude_versus_correspondence.pdf", width=12, height=5)
df <- data.frame(time=1:200, regressor=rep(c("design", "ic_tc", "ic_tc_small", "ic_tc_misalign", "ic_tc_irrel"), each=200),
                 activity=c(design_regressor, ictimecourse_aligned, ictimecourse_smallamp, ictimecourse_misaligned, ictimecourse_with_irrelevant))
ggplot(df, aes(x=time, y=activity, color=regressor)) + geom_line(size=1.3) + theme_bw(base_size=16) + scale_color_brewer(palette="Dark2")
dev.off()