#treating IHI data as a ratio of the unconditioned baseline condition is a bad idea
#these ratios have an extremely long right tail making their residuals asymmetric and badly non-normal
#the difference method has fewer problems, but ratios are more common in the literature
#probably because that's what Ferbert 1992 did and everybody followed suit
#here I do the ratio method to see whether it changes anything very important
#all results are the same, but test magnitude appears to reduce IHI

#the gap between conditioned and unconditioned MEPs grows with test pulse magnitude
#but unconditioned MEP sizes increase more (this should be obvious)
#the ratio therefore shrinks. 
#this makes it appear that strong tests pulses reduce IHI, but this is an artefact


library("tidyverse")
library("lme4")
library("merTools")
library("lmerTest")
library("boot")
library("pbkrtest")
setwd('~/your/working_directory/here')
getwd()
options(contrasts = c("contr.sum","contr.poly"))
set.seed(42)

dat<-read_csv("Belyk_exp1.csv")

#reference data
dat_TestOnly<-dat %>% 
  filter(IHI=="TestOnly") %>%
  group_by(TPower, Subject)

###############
###wrangle###
###############

Test_list<-list()
subjects <- unique(dat$Subject)
for(s in 1:length(subjects)){ #loop through subjects
  Test_list[[s]]<-dat_TestOnly %>% 
    filter(Subject == subjects[s]) %>%  #find data for this subject only
    summarise(Test = median(Test_EMG), Conditioning = median(Cond_EMG)) #get medians
}

#more useful data
dat_ihi<-dat %>% filter(IHI != "TestOnly")
dat_ihi$Inhibition_ratio <- NA
dat_ihi$Inhibition <- NA

for(i in 1:dim(dat_ihi)[1]) { #loop through rows
  sub_index<-which(subjects == dat_ihi$Subject[i]) #index for matching participant to test only medians
  
  #find relevant test only value specific to participant
  if(dat_ihi$TPower[i] == 1.0) TO <- Test_list[[sub_index]]$Test[1]
  if(dat_ihi$TPower[i] == 1.1) TO <- Test_list[[sub_index]]$Test[2]  
  if(dat_ihi$TPower[i] == 1.2) TO <- Test_list[[sub_index]]$Test[3]
  if(dat_ihi$TPower[i] == 1.3) TO <- Test_list[[sub_index]]$Test[4]
  
  #calculate inhibition
  dat_ihi$Inhibition_ratio[i] <- dat_ihi$Test_EMG[i] / TO #by ratio
  dat_ihi$Inhibition[i] <-       TO - dat_ihi$Test_EMG[i] #by subtraction, not clear which is more sensible
}

#fix classes
dat_ihi$TPower <- as.factor(dat_ihi$TPower)
dat_ihi$CPower <- as.factor(dat_ihi$CPower)
dat_ihi$IHI <- as.factor(dat_ihi$IHI)
dat_ihi$Subject <- as.factor(dat_ihi$Subject)

###normalize values within subject### #? is this smart?
#lets wait a second. I'm not convinced that variation within one subject means the same as variation within another


#######################################
###Filter data from experiment notes###
#######################################
##remove S2 trial 62, script failed to trigger stimulator
dat_ihi %>%  
  filter(Subject == "S2" & Trial == 61) #already removed

##S3, big head movement at trials 152
#doesn't appear all that sudden. Take no action.
dat_ihi %>%  
  filter(Subject == "S3") %>%
  gather(key = Dimension, value = measurement, 
         Cond_Dist_Target,Cond_Target_Error,Cond_Angular_Error,Cond_Twist_Error,
         Test_Dist_Target,Test_Target_Error,Test_Angular_Error,Test_Twist_Error) %>%
  ggplot(aes(x=Trial, y=measurement, colour= Dimension)) +
  geom_line()+
  geom_smooth(se=F)+
  geom_vline(xintercept=152)

#S4 first trial missing. Already absent
dat_ihi %>%  
  filter(Subject == "S4")

##s7 experiment stopped at trial 170
#earlier than that apparently, onlu 163 recorded
tail(dat_ihi %>%  
       filter(Subject == "S7"))

##s10 camera lost sight of markers
#several abrupt jumps remove trials 1-15, 85-95, 115-125

dat_ihi %>%  
  filter(Subject == "S10") %>%
  gather(key = Dimension, value = measurement, 
         Cond_Dist_Target,Cond_Target_Error,Cond_Angular_Error,Cond_Twist_Error,
         Test_Dist_Target,Test_Target_Error,Test_Angular_Error,Test_Twist_Error) %>%
  ggplot(aes(x=Trial, y=measurement, colour= Dimension)) +
  geom_line()+
  geom_smooth(se=F)+
  geom_vline(xintercept=1)+
  geom_vline(xintercept=15)+
  geom_vline(xintercept=85)+
  geom_vline(xintercept=95)+
  geom_vline(xintercept=115)+  
  geom_vline(xintercept=125) 

#remove ranges, some trials were already missing
dat_ihi<-dat_ihi %>%  
  filter((Subject == "S10" & Trial <=15)==F) %>%
  filter((Subject == "S10" & Trial >=85 & Trial <95)==F) %>% 
  filter((Subject == "S10" & Trial >=115 & Trial <125)==F)

##########################
###Normalize covariates###
##########################
#add columns
dat_ihi$Cond_Target_Norm <- NA
dat_ihi$Cond_Angular_Norm <- NA
dat_ihi$Cond_Twist_Norm <- NA

dat_ihi$Test_Target_Norm <- NA
dat_ihi$Test_Angular_Norm <- NA
dat_ihi$Test_Twist_Norm <- NA

#center and scale targeting error metric
for(s in subjects){ #loop through subjects
  sub_index <- which(dat_ihi == s) #get rows
  
  dat_ihi$Cond_Target_Norm[sub_index] <-scale(dat_ihi$Cond_Target_Error[sub_index])  
  dat_ihi$Cond_Angular_Norm[sub_index] <-scale(dat_ihi$Cond_Angular_Error[sub_index])  
  dat_ihi$Cond_Twist_Norm[sub_index] <-scale(dat_ihi$Cond_Twist_Error[sub_index])  
  
  dat_ihi$Test_Target_Norm[sub_index] <-scale(dat_ihi$Test_Target_Error[sub_index])  
  dat_ihi$Test_Angular_Norm[sub_index] <-scale(dat_ihi$Test_Angular_Error[sub_index])  
  dat_ihi$Test_Twist_Norm[sub_index] <-scale(dat_ihi$Test_Twist_Error[sub_index])    
}
#################################
###Hunt for targeting outliers###
#################################
#yes there are long positive tails
ggplot(dat_ihi, aes(x=Cond_Target_Norm))+
  geom_density()
ggplot(dat_ihi, aes(x=Cond_Angular_Norm))+
  geom_density()
ggplot(dat_ihi, aes(x=Cond_Twist_Norm))+
  geom_density()
ggplot(dat_ihi, aes(x=Cond_Target_Norm))+
  geom_density()
ggplot(dat_ihi, aes(x=Cond_Angular_Norm))+
  geom_density()
ggplot(dat_ihi, aes(x=Cond_Twist_Norm))+
  geom_density()

###############################
###Remove targeting outliers###
###############################
#q=0.99 is about right for loping of the long tails
q_Cond_Target_Norm <- quantile(dat_ihi$Cond_Target_Norm, probs=0.99)
q_Cond_Angular_Norm <- quantile(dat_ihi$Cond_Angular_Norm, probs=0.99)
q_Cond_Twist_Norm <- quantile(dat_ihi$Cond_Twist_Norm, probs=0.99)

q_Test_Target_Norm <- quantile(dat_ihi$Test_Target_Norm, probs=0.99)
q_Test_Angular_Norm <- quantile(dat_ihi$Test_Angular_Norm, probs=0.99)
q_Test_Twist_Norm <- quantile(dat_ihi$Test_Twist_Norm, probs=0.99)

#remove tail values
dat_ihi<-dat_ihi %>%
  filter(Cond_Target_Norm < q_Cond_Target_Norm) %>%
  filter(Cond_Angular_Norm < q_Cond_Angular_Norm) %>%
  filter(Cond_Twist_Norm < q_Cond_Twist_Norm) %>%
  
  filter(Test_Target_Norm < q_Test_Target_Norm) %>%
  filter(Test_Angular_Norm < q_Test_Angular_Norm) %>%
  filter(Test_Twist_Norm < q_Test_Twist_Norm) 

#Re-scale and re-center and scale targeting error metric after outlier
for(s in subjects){ #loop through subjects
  sub_index <- which(dat_ihi == s) #get rows
  
  dat_ihi$Cond_Target_Norm[sub_index] <-scale(dat_ihi$Cond_Target_Error[sub_index])  
  dat_ihi$Cond_Angular_Norm[sub_index] <-scale(dat_ihi$Cond_Angular_Error[sub_index])  
  dat_ihi$Cond_Twist_Norm[sub_index] <-scale(dat_ihi$Cond_Twist_Error[sub_index])  
  
  dat_ihi$Test_Target_Norm[sub_index] <-scale(dat_ihi$Test_Target_Error[sub_index])  
  dat_ihi$Test_Angular_Norm[sub_index] <-scale(dat_ihi$Test_Angular_Error[sub_index])  
  dat_ihi$Test_Twist_Norm[sub_index] <-scale(dat_ihi$Test_Twist_Error[sub_index])    
}

############################
###Linear model of ratios###
############################
dat_ihi$TPower_scaled<-scale(as.numeric(as.character(dat_ihi$TPower)))
dat_ihi$CPower_scaled<-scale(as.numeric(as.character(dat_ihi$CPower)))


mod_inhibit<-lmer(Inhibition_ratio ~  
                    CPower_scaled+
                    TPower_scaled+
                    IHI+
                    Cond_EMG + #considered log(Cond_EMG) but AIC was worse
                    CPower_scaled:TPower_scaled+ #plus some interactions
                    #CPower:IHI+
                    #TPower:IHI+
                    Cond_EMG:CPower_scaled+
                    #Cond_EMG:TPower_scaled+
                    Cond_EMG:IHI+
                    (1+Cond_EMG|Subject) #random slopes for TPower & CPower were too much to model
                  ,REML=F
                  ,control =lmerControl(optimizer = "bobyqa", optCtrl=list(maxfun=1e5)),  #fiddle with optimizers
                  #,verbose=T
                  ,data=dat_ihi)

relgrad <- with(mod_inhibit@optinfo$derivs,solve(Hessian,gradient)) #is this less than about 0.0001? If so can ignore convergence warnings
max(abs(relgrad))
AIC(mod_inhibit)

summary(mod_inhibit)

###diagnostics
#deviance residuals

pdf("Ratio_QQ.pdf", width = 3, height = 3) #start figure output
  qqnorm(y=residuals(mod_inhibit)) #not particularly normal. long tails. bootstrap?
  qqline(y=residuals(mod_inhibit)) #not particularly normal. long tails. bootstrap?
dev.off()
  
pdf("Ratio_distribution_of_residuals.pdf", width = 3, height = 3) #start figure output
  plot(density(residuals(mod_inhibit)), main="Distribution of Residuals")
dev.off()
####BOOTSTRAPPING CIs###

###bootsrap mean estiamtes and CI
TPowers_scaled<-unique(dat_ihi$TPower_scaled)
CPowers_scaled<-unique(dat_ihi$CPower_scaled)
IHIs<-as.factor(c(0.01, 0.05))

newdata <- expand.grid(TPowers_scaled,CPowers_scaled, IHIs, 0) #Condition hand regressed out
names(newdata)<-c("TPower_scaled", "CPower_scaled","IHI", "Cond_EMG")
newdata<-cbind(newdata,"Z") #a representative subject
names(newdata)[5]  <- "Subject"

PredFun <- function(.) predict(.,newdata=newdata, type="response", allow.new.levels=T) #added type arg later. used unlogodds to make up for it
system.time(mod_inhibit_boot<-bootMer(mod_inhibit, PredFun, nsim = 1000,  #about 90 minutes by a workhorse
                                      re.form=NULL, type="parametric", 
                                      #.progress = "txt", PBargs=list(style=3),#progress bar. silenced by parallel :()
                                      parallel = "multicore", ncpus = 4)) #parallel computing
mod_inhibit_boot.mean = apply(mod_inhibit_boot$t, 2, function(x) mean(x))
mod_inhibit_boot.lower = apply(mod_inhibit_boot$t, 2, function(x) as.numeric(quantile(x, probs=.025, na.rm=TRUE)))
mod_inhibit_boot.upper = apply(mod_inhibit_boot$t, 2, function(x) as.numeric(quantile(x, probs=.975, na.rm=TRUE)))

mod_inhibit_ci<-tibble(Inhibition=mod_inhibit_boot.mean, Lower=mod_inhibit_boot.lower, Upper=mod_inhibit_boot.upper)
mod_inhibit_ci<-cbind(newdata,mod_inhibit_ci)

#unscale for interpretable plotting    
unscale<-function(vector,dataframe,digits=2){
  center<-attr(dataframe, "scaled:center")
  scale<-attr(dataframe, "scaled:scale")
  out<- round(vector*scale+center, digits)
  return(out)
}

mod_inhibit_ci$CPower<-unscale(mod_inhibit_ci$CPower_scaled, dat_ihi$CPower_scaled)  
mod_inhibit_ci$TPower<-unscale(mod_inhibit_ci$TPower_scaled, dat_ihi$TPower_scaled)  

mod_inhibit_ci<-mutate(mod_inhibit_ci,IHI = paste("IHI", IHI,"S", sep=" "))


#########################
###Bootstrap inference###
#########################
#make new models
mod_inhibit_main<-lmer(Inhibition ~  
                         CPower_scaled+
                         TPower_scaled+
                         IHI+
                         Cond_EMG + #considered log(Cond_EMG) but AIC was worse
                         #CPower:TPower_scaled+ #plus some interactions
                         #CPower:IHI+
                         #TPower:IHI+
                         #Cond_EMG:CPower_scaled+
                         #Cond_EMG:TPower_scaled+
                         #Cond_EMG:IHI+
                         (1+Cond_EMG|Subject) #random slopes for TPower & CPower were too much to model
                       ,REML=F
                       ,control =lmerControl(optimizer = "bobyqa", optCtrl=list(maxfun=1e5)),  #fiddle with optimizers
                       #,verbose=T
                       ,data=dat_ihi)


#C=conditioning power, T = test power, H = IHI, E = conditioning EMG
mod_inhibit_CT<-update(mod_inhibit, .~. -CPower_scaled:TPower_scaled)
mod_inhibit_EC<-update(mod_inhibit, .~. -Cond_EMG:CPower_scaled)
mod_inhibit_EH<-update(mod_inhibit, .~. -Cond_EMG:IHI)
mod_inhibit_C<-update(mod_inhibit_main, .~. -CPower_scaled)
mod_inhibit_T<-update(mod_inhibit_main, .~. -TPower_scaled)
mod_inhibit_H<-update(mod_inhibit_main, .~. -IHI)
mod_inhibit_E<-update(mod_inhibit_main, .~. -Cond_EMG)

(PB.C<-PBmodcomp(mod_inhibit_main, mod_inhibit_C,  nsim=1000))
(PB.T<-PBmodcomp(mod_inhibit_main, mod_inhibit_T,  nsim=1000))
(PB.H<-PBmodcomp(mod_inhibit_main, mod_inhibit_H,  nsim=1000))
(PB.E<-PBmodcomp(mod_inhibit_main, mod_inhibit_E,  nsim=1000))
(PB.CT<-PBmodcomp(mod_inhibit, mod_inhibit_CT,  nsim=1000))
(PB.EC<-PBmodcomp(mod_inhibit, mod_inhibit_EC,  nsim=1000))
(PB.EH<-PBmodcomp(mod_inhibit, mod_inhibit_EH,  nsim=1000))

#CONFIDENCE INTERVALS AROUND ESTIMATE
ci<-confint.merMod(mod_inhibit, method="boot", nsim=1000)

#####FIGURES#####
##OPTIMIZATION
ggplot(mod_inhibit_ci,aes(x=TPower, y=CPower, colour=Inhibition, fill=Inhibition))+
  scale_color_gradient2(low="#2c7fb8",mid="#addd8e", high="#dd1c77")+
  scale_fill_gradient2(low="#2c7fb8",mid="#addd8e", high="#dd1c77")+
  # scale_size(range = c(2, 25), limits=c(-50,200), guide=guide_legend(reverse = TRUE))+
  geom_tile(alpha=1)+ #alpha=0.35
  #geom_point(aes(size=Inhibition))+
  facet_grid(IHI~.)+
  labs(x="Test pulse power (x MT)", y="Conditioning pulse power (x MT)", fill="Inhibition\nRation", colour ="Inhibition\nRation")+
  ggtitle("Heat map of parameter space")+
  theme_bw(base_size=14)
ggsave("heatMap_ratio_Variant.pdf", height=8,width=6)


###bootstrap for plotting
mod_merBoot <- bootMer(mod_inhibit, predict, nsim = 1000, re.form = NA)
CI.lower = apply(mod_merBoot$t, 2, function(x) as.numeric(quantile(x, probs=.025, na.rm=TRUE)))
CI.upper = apply(mod_merBoot$t, 2, function(x) as.numeric(quantile(x, probs=.975, na.rm=TRUE)))
CI.mean = apply(mod_merBoot$t, 2, mean)

ci.dat<-cbind(CI.mean, CI.upper, CI.lower, dat_ihi)
ci.dat<-mutate(ci.dat, IHI = paste("IHI",IHI, "S", sep=" "), TPower = paste("TPower", TPower, sep= " "))

#bootstrapped trendlines with 95% confidence intervals
ggplot(ci.dat,aes(x=Cond_EMG, y=CI.mean, colour=CPower))+
  geom_ribbon(aes(ymin=CI.lower,ymax=CI.upper, fill=CPower), alpha=0.25)+
  geom_line()+
  labs(x="Conditioning pulse MEP (uV)", y="Inhibition (uV)")+
  scale_x_continuous(breaks=c(0, 500, 1000))+
  ggtitle("Paradoxcial Conditioning Pulse EMG")+
  facet_grid(IHI~TPower)+
  theme_bw(base_size=12)

#individual differences
intercepts<-ranef(mod_inhibit)$Subject[,1] + fixef(mod_inhibit)[1] #intercepts
slopes<-ranef(mod_inhibit)$Subject[,2] + fixef(mod_inhibit)["Cond_EMG"] #intercepts
plot(NA,ylim=c(-150,150),xlim=c(0,900), ylab="Inhibition (uV)", xlab= "Conditioning EMG",main="Individual differences in cMEP-Inhibition slope")
abline(h=0, col="lightgrey", lty=1)
for(i in 1: length(slopes)){
  abline(a=intercepts[i], b=slopes[i],lty=i)
}