##############################################################################
#----------------------------------------------------------------------------#
################################## LIBRARIES #################################
#----------------------------------------------------------------------------#
##############################################################################

library(TAM)
library(doMC)
library(parallel)
library(pbmcapply)
library(funprog)
library(plyr)
library(dplyr)
library(readxl)

lastChar <- function(str){
  substr(str, nchar(str)-2, nchar(str))
}

##############################################################################
#----------------------------------------------------------------------------#
############################# ANALYSIS FUNCTIONS #############################
#----------------------------------------------------------------------------#
##############################################################################
pcm_analysis <- function(df=NULL,treatment='TT',irtmodel='PCM2',method='MML') {
  nbitems <- sum(sapply(1:20,function(x) paste0('item',x)) %in% colnames(df))
  resp <- df[,sapply(seq(1,nbitems),function(x) paste0('item',x))]
  if (method=='MML') {
    tam1 <-  tam.mml(resp=resp,Y=df[,treatment],irtmodel = irtmodel,est.variance = T,verbose=F)
  }
  if (method=='JML') {
    tam1 <- tam.jml(resp=resp,group=1+df[,treatment])
  }
  if (method!='MML' & method!='JML') {
    stop('Invalid method. Please choose among MML or JML')
  }
  return(tam1)
}


replicate_pcm_analysis_m4 <- function(df=NULL,treatment='TT',irtmodel='PCM2',method='MML',sequence='replication',eff.size=0,difsize=NA,nbdif=0) {
  nbitems <- sum(sapply(1:20,function(x) paste0('item',x)) %in% colnames(df))
  resp <- df[,sapply(seq(1,nbitems),function(x) paste0('item',x))]
  truebeta <- eff.size
  if (method=='MML') {
    n <- max(df[,sequence])
    print(n)
    tam1 <- lapply(seq(1,n),
                   function(x) pcm_analysis(df=df[df[,sequence]==x,],treatment=treatment,irtmodel=irtmodel)
    )
  }
  listitems <- c(sapply(c('_1','_2','_3'),function(x) paste0(sapply(seq(1,nbitems),function(x) paste0('item',x)),x)))
  returndat <- data.frame(matrix(nrow=max(df[,sequence]),ncol=length(listitems)))
  colnames(returndat) <- listitems
  for (s in seq(1,max(df[,sequence]))) {
    for (k in seq(1,nbitems)) {
      returndat[s,paste0('item',k,'_1')] <- tam1[[s]]$item[k,'AXsi_.Cat1']
      returndat[s,paste0('item',k,'_2')] <- tam1[[s]]$item[k,'AXsi_.Cat2']-tam1[[s]]$item[k,'AXsi_.Cat1']
      returndat[s,paste0('item',k,'_3')] <- tam1[[s]]$item[k,'AXsi_.Cat3']-tam1[[s]]$item[k,'AXsi_.Cat2']
    }
  }
  returndat <- returndat[,sort_by(listitems, lastChar)]
  returndat$beta <- sapply(seq(1,max(df[,sequence])),function(k) tam1[[k]]$beta[2])
  returndat$se.beta <- 1.413612*sapply(seq(1,max(df[,sequence])),function(k) tam.se(tam1[[k]])$beta$se.Dim1[2] )
  returndat$low.ci.beta <- returndat$beta-1.96*returndat$se.beta
  returndat$high.ci.beta <- returndat$beta+1.96*returndat$se.beta
  returndat$true.value.in.ci <- 1*(truebeta>returndat$low.ci.beta & truebeta<returndat$high.ci.beta)
  returndat$h0.rejected <- 1*(0<returndat$low.ci.beta | 0>returndat$high.ci.beta)
  if (truebeta==0) {
    returndat$beta.same.sign.truebeta <- NA
  } else {
    returndat$beta.same.sign.truebeta <- 1*(sign(truebeta)==sign(returndat$beta))
  }
  returndat2 <- data.frame(J=rep(nbitems,max(df[,sequence])),
                           M=1+max(df$item1),
                           N=nrow(df[df$replication==1,])/2,
                           eff.size=truebeta,
                           dif.size= difsize,
                           nb.dif= nbdif
  )
  returndat <- cbind(returndat2,returndat)
  return(returndat)
}





replicate_pcm_analysis_m2 <- function(df=NULL,treatment='TT',irtmodel='PCM2',method='MML',sequence='replication',eff.size=0,difsize=NA,nbdif=0) {
  truebeta <- eff.size
  nbitems <- sum(sapply(1:20,function(x) paste0('item',x)) %in% colnames(df))
  resp <- df[,sapply(seq(1,nbitems),function(x) paste0('item',x))]
  if (method=='MML') {
    n <- max(df[,sequence])
    print(n)
    tam1 <- lapply(seq(1,n),
                   function(x) pcm_analysis(df=df[df[,sequence]==x,],treatment=treatment,irtmodel=irtmodel)
    )
  }
  listitems <- sapply(seq(1,nbitems),function(x) paste0('item',x))
  returndat <- data.frame(matrix(nrow=max(df[,sequence]),ncol=length(listitems)))
  colnames(returndat) <- listitems
  for (s in seq(1,max(df[,sequence]))) {
    for (k in seq(1,nbitems)) {
      returndat[s,paste0('item',k)] <- tam1[[s]]$xsi$xsi[k]
    }
  }
  returndat$beta <- sapply(seq(1,max(df[,sequence])),function(k) tam1[[k]]$beta[2])
  returndat$se.beta <- 1.413612*sapply(seq(1,max(df[,sequence])),function(k) tam.se(tam1[[k]])$beta$se.Dim1[2] )
  returndat$low.ci.beta <- returndat$beta-1.96*returndat$se.beta
  returndat$high.ci.beta <- returndat$beta+1.96*returndat$se.beta
  returndat$true.value.in.ci <- 1*(truebeta>returndat$low.ci.beta & truebeta<returndat$high.ci.beta)
  returndat$h0.rejected <- 1*(0<returndat$low.ci.beta | 0>returndat$high.ci.beta)
  if (truebeta==0) {
    returndat$beta.same.sign.truebeta <- NA
  } else {
    returndat$beta.same.sign.truebeta <- 1*(sign(truebeta)==sign(returndat$beta))
  }
  returndat2 <- data.frame(J=rep(nbitems,max(df[,sequence])),
                           M=1+max(df$item1),
                           N=nrow(df[df$replication==1,])/2,
                           eff.size=truebeta,
                           dif.size= difsize,
                           nb.dif= nbdif
  )
  returndat <- cbind(returndat2,returndat)
  return(returndat)
}


replicate_pcm_analysis<- function(df=NULL,treatment='TT',irtmodel='PCM2',method='MML',sequence='replication',eff.size=0,difsize=NA,nbdif=0) {
  j <- max(df$item1)
  if(j==1) {
    return(replicate_pcm_analysis_m2(df=df,treatment=treatment,irtmodel=irtmodel,method=method,sequence=sequence,eff.size=eff.size,difsize=difsize,nbdif=nbdif))
  } else {
    return(replicate_pcm_analysis_m4(df=df,treatment=treatment,irtmodel=irtmodel,method=method,sequence=sequence,eff.size=eff.size,difsize=difsize,nbdif=nbdif))
  }
}

##############################################################################
#----------------------------------------------------------------------------#
################################# AGGREGATION ################################
#----------------------------------------------------------------------------#
##############################################################################

#### Create data.frame

results <- c(sapply(1:4,function(x) paste0(x,c('A','B','C','D','E'))),sapply(5:9,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results2 <- c(sapply(10:20,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results <- c(sapply(c(50,100,200,300),function(x) paste0(results,'_',x)))

results2 <- c(sapply(c(50,100,200,300),function(x) paste0(results2,'_',x)))

results <- sort(results)

results2 <- sort(results2)

results <- c(results,results2)

#### Compiler function

compile_simulation <- function(scenario) {
  name <- as.numeric(gsub("[^0-9.-]", "", substr(scenario,start=0,stop=2)))
  if (substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50" & name<=4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N50/scenario_',scenario,'.csv'))
  }
  if (substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50" & name>4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N50/scenario_',scenario,'.csv'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="100" & name<=4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N100/scenario_',scenario,'.csv'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="100" & name>4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N100/scenario_',scenario,'_nodif.csv'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="200" & name<=4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N200/scenario_',scenario,'.csv'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="200" & name>4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N200/scenario_',scenario,'_nodif.csv'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="300" & name<=4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N300/scenario_',scenario,'.csv'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="300" & name>4) {
    s <- read.csv(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/NoDIF/N300/scenario_',scenario,'_nodif.csv'))
  }
  if (unique(s$J)==4) {
    if (unique(s$M)==2) {
      a <- data.frame(m.item1=mean(s$item1),m.item2=mean(s$item2),m.item3=mean(s$item3),m.item4=mean(s$item4))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3)
                      )
    }
  } else {
    if (unique(s$M)==2) {
      a <- data.frame(m.item1=mean(s$item1),m.item2=mean(s$item2),m.item3=mean(s$item3),m.item4=mean(s$item4),
                      m.item5=mean(s$item5),m.item6=mean(s$item6),m.item7=mean(s$item7))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3),
                      m.item5_1=mean(s$item5_1),m.item5_2=mean(s$item5_2),m.item5_3=mean(s$item5_3),
                      m.item6_1=mean(s$item6_1),m.item6_2=mean(s$item6_2),m.item6_3=mean(s$item6_3),
                      m.item7_1=mean(s$item7_1),m.item7_2=mean(s$item7_2),m.item7_3=mean(s$item7_3)
      )
    }
  }
  N <- ifelse(substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50","50",substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario)))
  zz <- ifelse(N=="50",substr(scenario,start=0,stop=nchar(scenario)-3),substr(scenario,start=0,stop=nchar(scenario)-4)) 
  b <- data.frame(scenario=zz,
                  scenario.type=substr(zz,start=nchar(zz),stop=nchar(zz)),
                  N=N,
                  J=unique(s$J),
                  M=unique(s$M),
                  eff.size=unique(s$eff.size),
                  nb.dif=unique(s$nb.dif),
                  dif.size=unique(s$dif.size)
                  )
  z <- data.frame(m.beta=mean(s$beta),
                  se.empirical.beta=sd(s$beta),
                  se.analytical.beta=mean(s$se.beta),
                  m.low.ci.beta=mean(s$low.ci.beta),
                  m.high.ci.beta=mean(s$high.ci.beta),
                  true.value.in.ci.p=mean(s$true.value.in.ci),
                  h0.rejected.p=mean(s$h0.rejected),
                  beta.same.sign.truebeta.p=mean(s$beta.same.sign.truebeta,na.rm=T),
                  beta.same.sign.truebeta.signif.p=mean(s[s$h0.rejected==1,]$beta.same.sign.truebeta,na.rm=T))
  d <- cbind(b,a,z)
  d$prop.
  return(d)
}

#### Compiled results

res.dat <- compile_simulation('1A_100')

for (x in results[seq(2,length(results))]) {
  y <- compile_simulation(x)
  res.dat <- bind_rows(res.dat,y)
}
res.dat[res.dat$scenario.type=='A','dif.size'] <- -res.dat[res.dat$scenario.type=='A','dif.size']
res.dat[is.na(res.dat$dif.size),'dif.size'] <- 0
res.dat[193:417,'nb.dif'] <- 2
res.dat[417:528,'nb.dif'] <- 3
res.dat[res.dat$scenario.type=="B",]$eff.size <- 0.2
res.dat[res.dat$scenario.type=="C" & res.dat$dif.size==0,]$eff.size <- 0.4
res.dat[res.dat$scenario.type=="C" & res.dat$dif.size!=0,]$eff.size <- 0.2
res.dat[res.dat$scenario.type=="D" & res.dat$dif.size==0,]$eff.size <- -0.2
res.dat[res.dat$scenario.type=="D" & res.dat$dif.size!=0,]$eff.size <- 0.4
res.dat[res.dat$scenario.type=="E" & res.dat$dif.size==0,]$eff.size <- -0.4
res.dat[res.dat$scenario.type=="E" & res.dat$dif.size!=0,]$eff.size <- 0.4
res.dat[res.dat$scenario.type=="F",]$eff.size <- -0.2
res.dat[res.dat$scenario.type=="G",]$eff.size <- -0.4
View(res.dat)

res.dat.simple <- res.dat[,c(1:8,13,16:18)]
res.dat.simple$m.beta <- round(res.dat.simple$m.beta,3)
res.dat.simple

is.nan.data.frame <- function(x)
  do.call(cbind, lapply(x, is.nan))


res.dat[is.nan(res.dat)] <- NA
res.dat$bias <- res.dat$eff.size-res.dat$m.beta


##############################################################################
#----------------------------------------------------------------------------#
########################### AGGREGATION DIF MATRICES #########################
#----------------------------------------------------------------------------#
##############################################################################

#### Create data.frame

results <- c(sapply(1:4,function(x) paste0(x,c('A','B','C','D','E'))),sapply(5:9,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results2 <- c(sapply(10:20,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results <- c(sapply(c(50,100,200,300),function(x) paste0(results,'_',x)))

results2 <- c(sapply(c(50,100,200,300),function(x) paste0(results2,'_',x)))

results <- sort(results)

results2 <- sort(results2)

results <- c(results,results2)[81:528]


#### Compiler function

compile_simulation2 <- function(scenario) {
  name <- as.numeric(gsub("[^0-9.-]", "", substr(scenario,start=0,stop=2)))
  if (substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50" & name>4) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/DIF/N50/',scenario,'.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="100" & name>4) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/DIF/N100/',scenario,'.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="200" & name>4) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/DIF/N200/',scenario,'.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="300" & name>4) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/DIF/N300/',scenario,'.xls'))
  }
  J <- max(which(sapply(1:7,function(x) paste0('item',x) %in% colnames(s) | paste0('item',x,'_1') %in% colnames(s))))
  M <- 1+sum(sapply(1:3,function(x) paste0('item1_',x) %in% colnames(s) ))
  if (M==1) {M <- 2}
  nb.dif <- max(which(sapply(1:3,function(x) paste0('dif',x) %in% colnames(s) | paste0('dif',x,'_1') %in% colnames(s))))
  if (J==4) {
    if (M==2) {
      a <- data.frame(m.item1=mean(s$item1),m.item2=mean(s$item2),m.item3=mean(s$item3),m.item4=mean(s$item4))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3)
      )
    }
  } else {
    if (M==2) {
      a <- data.frame(m.item1=mean(s$item1),m.item2=mean(s$item2),m.item3=mean(s$item3),m.item4=mean(s$item4),
                      m.item5=mean(s$item5),m.item6=mean(s$item6),m.item7=mean(s$item7))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3),
                      m.item5_1=mean(s$item5_1),m.item5_2=mean(s$item5_2),m.item5_3=mean(s$item5_3),
                      m.item6_1=mean(s$item6_1),m.item6_2=mean(s$item6_2),m.item6_3=mean(s$item6_3),
                      m.item7_1=mean(s$item7_1),m.item7_2=mean(s$item7_2),m.item7_3=mean(s$item7_3)
      )
    }
  }
  N <- ifelse(substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50","50",substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario)))
  zz <- ifelse(N=="50",substr(scenario,start=0,stop=nchar(scenario)-3),substr(scenario,start=0,stop=nchar(scenario)-4))
  eff.size <- unique(res.dat[res.dat$scenario==zz & res.dat$N==N,'eff.size'])
  dif.size <- unique(res.dat[res.dat$scenario==zz & res.dat$N==N,'dif.size'])
  b <- data.frame(scenario=zz,
                  scenario.type=substr(zz,start=nchar(zz),stop=nchar(zz)),
                  N=N,
                  J=J,
                  M=M,
                  eff.size=eff.size,
                  nb.dif=nb.dif,
                  dif.size=dif.size
  )
  true.value.in.ci <- eff.size <= s$beta+1.96*s$se_beta & eff.size >= s$beta-1.96*s$se_beta
  beta.same.sign.truebeta.p <- ifelse(rep(eff.size,nrow(s))==0,NA,(rep(eff.size,nrow(s))/s$beta)>0)
  num.reject <- which((s$beta-1.96*s$se_beta)>0 | (s$beta+1.96*s$se_beta)<0)
  z <- data.frame(m.beta=mean(s$beta),
                  se.empirical.beta=sd(s$beta),
                  se.analytical.beta=mean(s$se_beta),
                  m.low.ci.beta=mean(s$beta-1.96*s$se_beta),
                  m.high.ci.beta=mean(s$beta+1.96*s$se_beta),
                  true.value.in.ci.p=mean(true.value.in.ci),
                  h0.rejected.p=mean( (s$beta-1.96*s$se_beta)>0 | (s$beta+1.96*s$se_beta)<0 ),
                  beta.same.sign.truebeta.p=mean(beta.same.sign.truebeta.p),
                  beta.same.sign.truebeta.signif.p=mean(beta.same.sign.truebeta.p[num.reject])
  )
  d <- cbind(b,a,z)
  d$prop.
  return(d)
}


#### Compiled results

res.dat.dif <- compile_simulation2('5A_100')

for (x in results[seq(2,length(results))]) {
  y <- compile_simulation2(x)
  res.dat.dif <- bind_rows(res.dat.dif,y)
}

res.dat$bias <- res.dat$eff.size-res.dat$m.beta
res.dat.dif$bias <- res.dat.dif$eff.size-res.dat.dif$m.beta

##############################################################################
#----------------------------------------------------------------------------#
####################### AGGREGATION DIF MATRICES ROSALI ######################
#----------------------------------------------------------------------------#
##############################################################################

#### Create data.frame

results <- c(sapply(1:4,function(x) paste0(x,c('A','B','C','D','E'))),sapply(5:9,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results2 <- c(sapply(10:20,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results <- c(sapply(c(50,100,200,300),function(x) paste0(results,'_',x)))

results2 <- c(sapply(c(50,100,200,300),function(x) paste0(results2,'_',x)))

results <- sort(results)

results2 <- sort(results2)

results <- c(results,results2)


#### Compiler function

compile_simulation2_rosali <- function(scenario) {
  name <- as.numeric(gsub("[^0-9.-]", "", substr(scenario,start=0,stop=2)))
  if (substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/ROSALI-DIF/N50/',scenario,'_original.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="100" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/ROSALI-DIF/N100/',scenario,'_original.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="200" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/ROSALI-DIF/N200/',scenario,'_original.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="300" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/ROSALI-DIF/N300/',scenario,'_original.xls'))
  }
  J <- max(which(sapply(1:7,function(x) paste0('item',x) %in% colnames(s) | paste0('item',x,'_1') %in% colnames(s))))
  M <- 1+sum(sapply(1:3,function(x) paste0('item1_',x) %in% colnames(s) ))
  if (M==1) {M <- 2}
  nb.dif.true <- ifelse(name<=4,0,ifelse(name<=8,1,ifelse(name<=16,2,3)))
  if (name %in% c(3,4,13:20)) {
    m.nb.dif.detect <- mean(ifelse(is.na(s$dif_1_1),0,
                            ifelse(is.na(s$dif_2_1),1,
                                   ifelse(is.na(s$dif_3_1),2,
                                          ifelse(is.na(s$dif_4_1),3,
                                                 ifelse(is.na(s$dif_5_1),4,
                                                        ifelse(is.na(s$dif_6_1),5,
                                                               ifelse(is.na(s$dif_7_1),6,7))))))))
  }
  if (!(name %in% c(3,4,13:20))) {
    m.nb.dif.detect <- mean(ifelse(is.na(s$dif_1_1),0,
                            ifelse(is.na(s$dif_2_1),1,
                                   ifelse(is.na(s$dif_3_1),2,
                                          ifelse(is.na(s$dif_4_1),3,4)))))
  }
  if (J==4) {
    if (M==2) {
      a <- data.frame(m.item1=mean(s$item1_1),m.item2=mean(s$item2_1),m.item3=mean(s$item3_1),m.item4=mean(s$item4_1))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3)
      )
    }
  } else {
    if (M==2) {
      a <- data.frame(m.item1=mean(s$item1_1),m.item2=mean(s$item2_1),m.item3=mean(s$item3_1),m.item4=mean(s$item4_1),
                      m.item5=mean(s$item5_1),m.item6=mean(s$item6_1),m.item7=mean(s$item7_1))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3),
                      m.item5_1=mean(s$item5_1),m.item5_2=mean(s$item5_2),m.item5_3=mean(s$item5_3),
                      m.item6_1=mean(s$item6_1),m.item6_2=mean(s$item6_2),m.item6_3=mean(s$item6_3),
                      m.item7_1=mean(s$item7_1),m.item7_2=mean(s$item7_2),m.item7_3=mean(s$item7_3)
      )
    }
  }
  N <- ifelse(substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50","50",substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario)))
  zz <- ifelse(N=="50",substr(scenario,start=0,stop=nchar(scenario)-3),substr(scenario,start=0,stop=nchar(scenario)-4))
  eff.size <- unique(res.dat[res.dat$scenario==zz & res.dat$N==N,'eff.size'])
  dif.size <- unique(res.dat[res.dat$scenario==zz & res.dat$N==N,'dif.size'])
  b <- data.frame(scenario=zz,
                  scenario.type=substr(zz,start=nchar(zz),stop=nchar(zz)),
                  N=N,
                  J=J,
                  M=M,
                  eff.size=eff.size,
                  nb.dif=nb.dif.true,
                  m.nb.dif.detect=m.nb.dif.detect,
                  dif.size=dif.size
  )
  true.value.in.ci <- eff.size <= s$beta+1.96*s$se_beta & eff.size >= s$beta-1.96*s$se_beta
  beta.same.sign.truebeta.p <- ifelse(rep(eff.size,nrow(s))==0,NA,(rep(eff.size,nrow(s))/s$beta)>0)
  num.reject <- which((s$beta-1.96*s$se_beta)>0 | (s$beta+1.96*s$se_beta)<0)
  dif.d <- mean(sapply(1:1000,function(x) any(!is.na(s[x,paste0("dif_",1:unique(b$J),"_1")]))))
  if (nb.dif.true==0 & unique(b$J)==4) {
    prop.perfect <- NA
    flexible.detect <- NA
    moreflexible.detect <- NA
    any.detect <- NA
    thay.tpr <- NA
    thay.fpr <- mean(sapply(1:1000,function(x) sum( !is.na(s[x,paste0("dif_detect_",1:4)]) )/4 ))
  }
  if (nb.dif.true==0 & unique(b$J)==7) {
    prop.perfect <- NA
    flexible.detect <- NA
    moreflexible.detect <- NA
    any.detect <- NA
    thay.tpr <- NA
    thay.fpr <- mean(sapply(1:1000,function(x) sum( !is.na(s[x,paste0("dif_detect_",1:7)]) )/7 ))
  }
  if (nb.dif.true==1 & unique(b$J)==4 & unique(b$M)==4) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==1,s[x,"dif_detect_unif_1"]==1  & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1")])
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==1,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1")])
                                                        ,0)  )
    flexible.detect <- mean(flexible.detect)
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- moreflexible.detect
    thay.tpr <- moreflexible.detect
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])!=s[x,"real_dif_1"],na.rm=F)/4,0)  ))
  }
  if (nb.dif.true==2 & unique(b$J)==4 & unique(b$M)==4) {
      perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==2,s[x,"dif_detect_unif_1"]==1 & s[x,"dif_detect_unif_2"]==1 & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                            ,0)  )
      prop.perfect <- mean(perfect.detection)
      flexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
      flexible.detect <- mean(flexible.detect)
      moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) &
                                                                s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
      moreflexible.detect <- mean(moreflexible.detect)
      any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) |
                                                       s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0) )
      any.detect <- mean(any.detect)
      thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
      thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/4,0)  ))
      
  }
  if (nb.dif.true==2 & unique(b$J)==7 & unique(b$M)==4) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==2,s[x,"dif_detect_unif_1"]==1 & s[x,"dif_detect_unif_2"]==1 & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                        ,0)  )
    flexible.detect <- mean(flexible.detect)
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/7,0)  ))
    
  }
  if (nb.dif.true==3 & unique(b$J)==7 & unique(b$M)==4) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==3,s[x,"dif_detect_unif_1"]==1 & s[x,"dif_detect_unif_2"]==1 & s[x,"dif_detect_unif_3"]==1 & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[3])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <-  sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==3,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[3])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) 
                                                         ,0)  )
    flexible.detect <- mean(flexible.detect)
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) & s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) | s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"]),na.rm=F)/3,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"])),na.rm=F)/7,0)  ))
    
  }
  if (nb.dif.true==1 & unique(b$J)==4 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==1, s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1")])
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- moreflexible.detect
    thay.tpr <- moreflexible.detect
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])!=s[x,"real_dif_1"],na.rm=F)/4,0)  ))
  }
  if (nb.dif.true==2 & unique(b$J)==4 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) |
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/4,0)  ))
    
  }
  if (nb.dif.true==2 & unique(b$J)==7 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/7,0)  ))
    
  }
  if (nb.dif.true==3 & unique(b$J)==7 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==3,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[3])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) & s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) | s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"]),na.rm=F)/3,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"])),na.rm=F)/7,0)  ))
    
  }
  lrt.pass <- mean(s$lrt_passed)
  z <- data.frame(m.beta=mean(s$beta),
                  se.empirical.beta=sd(s$beta),
                  se.analytical.beta=mean(s$se_beta),
                  m.low.ci.beta=mean(s$beta-1.96*s$se_beta),
                  m.high.ci.beta=mean(s$beta+1.96*s$se_beta),
                  true.value.in.ci.p=mean(true.value.in.ci),
                  h0.rejected.p=mean( (s$beta-1.96*s$se_beta)>0 | (s$beta+1.96*s$se_beta)<0 ),
                  beta.same.sign.truebeta.p=mean(beta.same.sign.truebeta.p),
                  beta.same.sign.truebeta.signif.p=mean(beta.same.sign.truebeta.p[num.reject]),
                  dif.detected=dif.d,
                  prop.perfect=prop.perfect,
                  flexible.detect=flexible.detect,
                  moreflexible.detect=moreflexible.detect,
                  any.detect=any.detect,
                  thay.tpr=thay.tpr,
                  thay.fpr=thay.fpr,
                  lrt.pass=lrt.pass
  )
  d <- cbind(b,a,z)
  d$prop.
  return(d)
}


#### Compiled results

res.dat.dif.rosali <- compile_simulation2_rosali('1A_100')

for (x in results[seq(2,length(results))]) {
  y <- compile_simulation2_rosali(x)
  res.dat.dif.rosali <- bind_rows(res.dat.dif.rosali,y)
}

res.dat.dif.rosali$bias <- res.dat.dif.rosali$eff.size-res.dat.dif.rosali$m.beta


##############################################################################
#----------------------------------------------------------------------------#
####################### AGGREGATION DIF MATRICES RESALI ######################
#----------------------------------------------------------------------------#
##############################################################################

#### Create data.frame

results <- c(sapply(1:4,function(x) paste0(x,c('A','B','C','D','E'))),sapply(5:9,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results2 <- c(sapply(10:20,function(x) paste0(x,c('A','B','C','D','E','F','G'))))

results <- c(sapply(c(50,100,200,300),function(x) paste0(results,'_',x)))

results2 <- c(sapply(c(50,100,200,300),function(x) paste0(results2,'_',x)))

results <- sort(results)

results2 <- sort(results2)

results <- c(results,results2)


#### Compiler function

compile_simulation2_resali <- function(scenario) {
  name <- as.numeric(gsub("[^0-9.-]", "", substr(scenario,start=0,stop=2)))
  if (substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/RESALI/Results/N50/',scenario,'_original.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="100" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/RESALI/Results/N100/',scenario,'_original.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="200" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/RESALI/Results/N200/',scenario,'_original.xls'))
  }
  if (substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario))=="300" & name>0) {
    s <- read_excel(paste0('/home/corentin/Documents/These/Recherche/Simulations/Analysis/RESALI/Results/N300/',scenario,'_original.xls'))
  }
  J <- max(which(sapply(1:7,function(x) paste0('item',x) %in% colnames(s) | paste0('item',x,'_1') %in% colnames(s))))
  M <- 1+sum(sapply(1:3,function(x) paste0('item1_',x) %in% colnames(s) ))
  if (M==1) {M <- 2}
  nb.dif.true <- ifelse(name<=4,0,ifelse(name<=8,1,ifelse(name<=16,2,3)))
  if (name %in% c(3,4,13:20)) {
    m.nb.dif.detect <- mean(ifelse(is.na(s$dif_1_1),0,
                                   ifelse(is.na(s$dif_2_1),1,
                                          ifelse(is.na(s$dif_3_1),2,
                                                 ifelse(is.na(s$dif_4_1),3,
                                                        ifelse(is.na(s$dif_5_1),4,
                                                               ifelse(is.na(s$dif_6_1),5,
                                                                      ifelse(is.na(s$dif_7_1),6,7))))))))
  }
  if (!(name %in% c(3,4,13:20))) {
    m.nb.dif.detect <- mean(ifelse(is.na(s$dif_1_1),0,
                                   ifelse(is.na(s$dif_2_1),1,
                                          ifelse(is.na(s$dif_3_1),2,
                                                 ifelse(is.na(s$dif_4_1),3,4)))))
  }
  if (J==4) {
    if (M==2) {
      a <- data.frame(m.item1=mean(s$item1_1),m.item2=mean(s$item2_1),m.item3=mean(s$item3_1),m.item4=mean(s$item4_1))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3)
      )
    }
  } else {
    if (M==2) {
      a <- data.frame(m.item1=mean(s$item1_1),m.item2=mean(s$item2_1),m.item3=mean(s$item3_1),m.item4=mean(s$item4_1),
                      m.item5=mean(s$item5_1),m.item6=mean(s$item6_1),m.item7=mean(s$item7_1))
    } else {
      a <- data.frame(m.item1_1=mean(s$item1_1),m.item1_2=mean(s$item1_2),m.item1_3=mean(s$item1_3),
                      m.item2_1=mean(s$item2_1),m.item2_2=mean(s$item2_2),m.item2_3=mean(s$item2_3),
                      m.item3_1=mean(s$item3_1),m.item3_2=mean(s$item3_2),m.item3_3=mean(s$item3_3),
                      m.item4_1=mean(s$item4_1),m.item4_2=mean(s$item4_2),m.item4_3=mean(s$item4_3),
                      m.item5_1=mean(s$item5_1),m.item5_2=mean(s$item5_2),m.item5_3=mean(s$item5_3),
                      m.item6_1=mean(s$item6_1),m.item6_2=mean(s$item6_2),m.item6_3=mean(s$item6_3),
                      m.item7_1=mean(s$item7_1),m.item7_2=mean(s$item7_2),m.item7_3=mean(s$item7_3)
      )
    }
  }
  N <- ifelse(substr(scenario,start=nchar(scenario)-1,stop=nchar(scenario))=="50","50",substr(scenario,start=nchar(scenario)-2,stop=nchar(scenario)))
  zz <- ifelse(N=="50",substr(scenario,start=0,stop=nchar(scenario)-3),substr(scenario,start=0,stop=nchar(scenario)-4))
  eff.size <- unique(res.dat[res.dat$scenario==zz & res.dat$N==N,'eff.size'])
  dif.size <- unique(res.dat[res.dat$scenario==zz & res.dat$N==N,'dif.size'])
  b <- data.frame(scenario=zz,
                  scenario.type=substr(zz,start=nchar(zz),stop=nchar(zz)),
                  N=N,
                  J=J,
                  M=M,
                  eff.size=eff.size,
                  nb.dif=nb.dif.true,
                  m.nb.dif.detect=m.nb.dif.detect,
                  dif.size=dif.size
  )
  true.value.in.ci <- eff.size <= s$beta+1.96*s$se_beta & eff.size >= s$beta-1.96*s$se_beta
  beta.same.sign.truebeta.p <- ifelse(rep(eff.size,nrow(s))==0,NA,(rep(eff.size,nrow(s))/s$beta)>0)
  num.reject <- which((s$beta-1.96*s$se_beta)>0 | (s$beta+1.96*s$se_beta)<0)
  dif.d <- mean(sapply(1:1000,function(x) any(!is.na(s[x,paste0("dif_",1:unique(b$J),"_1")]))))
  if (nb.dif.true==0 & unique(b$J)==4) {
    prop.perfect <- NA
    flexible.detect <- NA
    moreflexible.detect <- NA
    any.detect <- NA
    thay.tpr <- NA
    thay.fpr <- mean(sapply(1:1000,function(x) sum( !is.na(s[x,paste0("dif_detect_",1:4)]) )/4 ))
  }
  if (nb.dif.true==0 & unique(b$J)==7) {
    prop.perfect <- NA
    flexible.detect <- NA
    moreflexible.detect <- NA
    any.detect <- NA
    thay.tpr <- NA
    thay.fpr <- mean(sapply(1:1000,function(x) sum( !is.na(s[x,paste0("dif_detect_",1:7)]) )/7 ))
  }
  if (nb.dif.true==1 & unique(b$J)==4 & unique(b$M)==4) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==1,s[x,"dif_detect_unif_1"]==1  & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1")])
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==1,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1")])
                                                        ,0)  )
    flexible.detect <- mean(flexible.detect)
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- moreflexible.detect
    thay.tpr <- moreflexible.detect
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])!=s[x,"real_dif_1"],na.rm=F)/4,0)  ))
  }
  if (nb.dif.true==2 & unique(b$J)==4 & unique(b$M)==4) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==2,s[x,"dif_detect_unif_1"]==1 & s[x,"dif_detect_unif_2"]==1 & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                        ,0)  )
    flexible.detect <- mean(flexible.detect)
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) |
                                                     s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0) )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/4,0)  ))
    
  }
  if (nb.dif.true==2 & unique(b$J)==7 & unique(b$M)==4) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==2,s[x,"dif_detect_unif_1"]==1 & s[x,"dif_detect_unif_2"]==1 & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                        ,0)  )
    flexible.detect <- mean(flexible.detect)
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                     s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/7,0)  ))
    
  }
  if (nb.dif.true==3 & unique(b$J)==7 & unique(b$M)==4) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==3,s[x,"dif_detect_unif_1"]==1 & s[x,"dif_detect_unif_2"]==1 & s[x,"dif_detect_unif_3"]==1 & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[3])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <-  sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==3,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[3])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) 
                                                         ,0)  )
    flexible.detect <- mean(flexible.detect)
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) & s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                     s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) | s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"]),na.rm=F)/3,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"])),na.rm=F)/7,0)  ))
    
  }
  if (nb.dif.true==1 & unique(b$J)==4 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==1, s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1")])
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- moreflexible.detect
    thay.tpr <- moreflexible.detect
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])!=s[x,"real_dif_1"],na.rm=F)/4,0)  ))
  }
  if (nb.dif.true==2 & unique(b$J)==4 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:4),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:4)]) |
                                                     s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:4)]),0)  )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:4)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:4)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/4,0)  ))
    
  }
  if (nb.dif.true==2 & unique(b$J)==7 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==2,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                     s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]),0)  )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"]),na.rm=F)/2,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"])),na.rm=F)/7,0)  ))
    
  }
  if (nb.dif.true==3 & unique(b$J)==7 & unique(b$M)==2) {
    perfect.detection <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))==3,s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[1])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[2])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) & s[x,paste0('dif_detect_',which(sapply(paste0("dif_detect_",1:7),function(y) !is.na(s[x,y])))[3])]%in%c(s[x,c("real_dif_1","real_dif_2","real_dif_3")]) 
                                                          ,0)  )
    prop.perfect <- mean(perfect.detection)
    flexible.detect <- prop.perfect
    moreflexible.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) &
                                                              s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) & s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    moreflexible.detect <- mean(moreflexible.detect)
    any.detect <- sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,s[x,"real_dif_1"]%in%c(s[x,paste0("dif_detect_",1:7)]) |
                                                     s[x,"real_dif_2"]%in%c(s[x,paste0("dif_detect_",1:7)]) | s[x,"real_dif_3"]%in%c(s[x,paste0("dif_detect_",1:7)]),0) )
    any.detect <- mean(any.detect)
    thay.tpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"]),na.rm=F)/3,0)  ))
    thay.fpr <- mean(sapply(1:1000,function(x) ifelse(sum(!is.na(s[x,paste0("dif_detect_",1:7)]))!=0,sum(!(unlist(s[x,paste0("dif_detect_",1:7)])%in%c(s[x,"real_dif_1"],s[x,"real_dif_2"],s[x,"real_dif_3"])),na.rm=F)/7,0)  ))
    
  }
  z <- data.frame(m.beta=mean(s$beta),
                  se.empirical.beta=sd(s$beta),
                  se.analytical.beta=mean(s$se_beta),
                  m.low.ci.beta=mean(s$beta-1.96*s$se_beta),
                  m.high.ci.beta=mean(s$beta+1.96*s$se_beta),
                  true.value.in.ci.p=mean(true.value.in.ci),
                  h0.rejected.p=mean( (s$beta-1.96*s$se_beta)>0 | (s$beta+1.96*s$se_beta)<0 ),
                  beta.same.sign.truebeta.p=mean(beta.same.sign.truebeta.p),
                  beta.same.sign.truebeta.signif.p=mean(beta.same.sign.truebeta.p[num.reject]),
                  dif.detected=dif.d,
                  prop.perfect=prop.perfect,
                  flexible.detect=flexible.detect,
                  moreflexible.detect=moreflexible.detect,
                  any.detect=any.detect
  )
  d <- cbind(b,a,z)
  d$prop.
  return(d)
}


#### Compiled results

res.dat.dif.resali <- compile_simulation2_resali('1A_100')

for (x in results[seq(2,length(results))]) {
  y <- compile_simulation2_resali(x)
  res.dat.dif.resali <- bind_rows(res.dat.dif.resali,y)
}

res.dat.dif.resali$bias <- res.dat.dif.resali$eff.size-res.dat.dif.resali$m.beta



##############################################################################
#----------------------------------------------------------------------------#
################################## RASCHPOWER ################################
#----------------------------------------------------------------------------#
##############################################################################

###### Puissance théorique

res.dat$theoretical.power <- 0

### Scénarios N=100

## Scénarios J=4 / M=2

res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'A') & res.dat$N==100,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'B') & res.dat$N==100,]$theoretical.power <- 0.1543
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'C') & res.dat$N==100,]$theoretical.power <- 0.1543
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'D') & res.dat$N==100,]$theoretical.power <- 0.4627
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'E') & res.dat$N==100,]$theoretical.power <- 0.4627
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'F') & res.dat$N==100,]$theoretical.power <- 0.1543
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'G') & res.dat$N==100,]$theoretical.power <- 0.4627

res.dat[res.dat$scenario %in% paste0(1,'C') & res.dat$N==100,]$theoretical.power <- 0.4627
res.dat[res.dat$scenario %in% paste0(1,'D') & res.dat$N==100,]$theoretical.power <- 0.1543
res.dat[res.dat$scenario %in% paste0(1,'E') & res.dat$N==100,]$theoretical.power <- 0.4627

## Scénarios J=4 / M=4

res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'A') & res.dat$N==100,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'B') & res.dat$N==100,]$theoretical.power <- 0.2177
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'C') & res.dat$N==100,]$theoretical.power <- 0.2177
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'D') & res.dat$N==100,]$theoretical.power <- 0.6586
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'E') & res.dat$N==100,]$theoretical.power <- 0.6586
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'F') & res.dat$N==100,]$theoretical.power <- 0.2177
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'G') & res.dat$N==100,]$theoretical.power <- 0.6586

res.dat[res.dat$scenario %in% paste0(2,'C') & res.dat$N==100,]$theoretical.power <- 0.6586
res.dat[res.dat$scenario %in% paste0(2,'D') & res.dat$N==100,]$theoretical.power <- 0.2177
res.dat[res.dat$scenario %in% paste0(2,'E') & res.dat$N==100,]$theoretical.power <- 0.6586

## Scénarios J=7 / M=2

res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'A') & res.dat$N==100,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'B') & res.dat$N==100,]$theoretical.power <- 0.1870
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'C') & res.dat$N==100,]$theoretical.power <- 0.1870
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'D') & res.dat$N==100,]$theoretical.power <- 0.5666
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'E') & res.dat$N==100,]$theoretical.power <- 0.5666
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'F') & res.dat$N==100,]$theoretical.power <- 0.1870
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'G') & res.dat$N==100,]$theoretical.power <- 0.5666

res.dat[res.dat$scenario %in% paste0(3,'C') & res.dat$N==100,]$theoretical.power <- 0.5666
res.dat[res.dat$scenario %in% paste0(3,'D') & res.dat$N==100,]$theoretical.power <- 0.1870
res.dat[res.dat$scenario %in% paste0(3,'E') & res.dat$N==100,]$theoretical.power <- 0.5666

## Scénarios J=7 / M=4

res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'A') & res.dat$N==100,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'B') & res.dat$N==100,]$theoretical.power <- 0.2450
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'C') & res.dat$N==100,]$theoretical.power <- 0.2450
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'D') & res.dat$N==100,]$theoretical.power <- 0.7136
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'E') & res.dat$N==100,]$theoretical.power <- 0.7136
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'F') & res.dat$N==100,]$theoretical.power <- 0.2450
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'G') & res.dat$N==100,]$theoretical.power <- 0.7136

res.dat[res.dat$scenario %in% paste0(4,'C') & res.dat$N==100,]$theoretical.power <- 0.7136
res.dat[res.dat$scenario %in% paste0(4,'D') & res.dat$N==100,]$theoretical.power <- 0.2450
res.dat[res.dat$scenario %in% paste0(4,'E') & res.dat$N==100,]$theoretical.power <- 0.7136


### Scénarios N=200

## Scénarios J=4 / M=2

res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'A') & res.dat$N==200,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'B') & res.dat$N==200,]$theoretical.power <- 0.2618
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'C') & res.dat$N==200,]$theoretical.power <- 0.2618
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'D') & res.dat$N==200,]$theoretical.power <- 0.7507
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'E') & res.dat$N==200,]$theoretical.power <- 0.7507
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'F') & res.dat$N==200,]$theoretical.power <- 0.2618
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'G') & res.dat$N==200,]$theoretical.power <- 0.7507

res.dat[res.dat$scenario %in% paste0(1,'C') & res.dat$N==200,]$theoretical.power <- 0.7507
res.dat[res.dat$scenario %in% paste0(1,'D') & res.dat$N==200,]$theoretical.power <- 0.2618
res.dat[res.dat$scenario %in% paste0(1,'E') & res.dat$N==200,]$theoretical.power <- 0.7507

## Scénarios J=4 / M=4

res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'A') & res.dat$N==200,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'B') & res.dat$N==200,]$theoretical.power <- 0.3875
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'C') & res.dat$N==200,]$theoretical.power <- 0.3875
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'D') & res.dat$N==200,]$theoretical.power <- 0.9161
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'E') & res.dat$N==200,]$theoretical.power <- 0.9161
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'F') & res.dat$N==200,]$theoretical.power <- 0.3875
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'G') & res.dat$N==200,]$theoretical.power <- 0.9161

res.dat[res.dat$scenario %in% paste0(2,'C') & res.dat$N==200,]$theoretical.power <- 0.9161
res.dat[res.dat$scenario %in% paste0(2,'D') & res.dat$N==200,]$theoretical.power <- 0.3875
res.dat[res.dat$scenario %in% paste0(2,'E') & res.dat$N==200,]$theoretical.power <- 0.9161

## Scénarios J=7 / M=2

res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'A') & res.dat$N==200,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'B') & res.dat$N==200,]$theoretical.power <- 0.3258
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'C') & res.dat$N==200,]$theoretical.power <- 0.3258
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'D') & res.dat$N==200,]$theoretical.power <- 0.8538
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'E') & res.dat$N==200,]$theoretical.power <- 0.8538
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'F') & res.dat$N==200,]$theoretical.power <- 0.3258
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'G') & res.dat$N==200,]$theoretical.power <- 0.8538

res.dat[res.dat$scenario %in% paste0(3,'C') & res.dat$N==200,]$theoretical.power <- 0.8538
res.dat[res.dat$scenario %in% paste0(3,'D') & res.dat$N==200,]$theoretical.power <- 0.3258
res.dat[res.dat$scenario %in% paste0(3,'E') & res.dat$N==200,]$theoretical.power <- 0.8538

## Scénarios J=7 / M=4

res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'A') & res.dat$N==200,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'B') & res.dat$N==200,]$theoretical.power <- 0.4321
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'C') & res.dat$N==200,]$theoretical.power <- 0.4321
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'D') & res.dat$N==200,]$theoretical.power <- 0.9471
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'E') & res.dat$N==200,]$theoretical.power <- 0.9471
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'F') & res.dat$N==200,]$theoretical.power <- 0.4321
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'G') & res.dat$N==200,]$theoretical.power <- 0.9471

res.dat[res.dat$scenario %in% paste0(4,'C') & res.dat$N==200,]$theoretical.power <- 0.9471
res.dat[res.dat$scenario %in% paste0(4,'D') & res.dat$N==200,]$theoretical.power <- 0.4321
res.dat[res.dat$scenario %in% paste0(4,'E') & res.dat$N==200,]$theoretical.power <- 0.9471




### Scénarios N=300

## Scénarios J=4 / M=2

res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'A') & res.dat$N==300,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'B') & res.dat$N==300,]$theoretical.power <- 0.3660
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'C') & res.dat$N==300,]$theoretical.power <- 0.3660
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'D') & res.dat$N==300,]$theoretical.power <- 0.8981
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'E') & res.dat$N==300,]$theoretical.power <- 0.8981
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'F') & res.dat$N==300,]$theoretical.power <- 0.3660
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'G') & res.dat$N==300,]$theoretical.power <- 0.8981

res.dat[res.dat$scenario %in% paste0(1,'C') & res.dat$N==300,]$theoretical.power <- 0.8981
res.dat[res.dat$scenario %in% paste0(1,'D') & res.dat$N==300,]$theoretical.power <- 0.3660
res.dat[res.dat$scenario %in% paste0(1,'E') & res.dat$N==300,]$theoretical.power <- 0.8981

## Scénarios J=4 / M=4

res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'A') & res.dat$N==300,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'B') & res.dat$N==300,]$theoretical.power <- 0.5373
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'C') & res.dat$N==300,]$theoretical.power <- 0.5373
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'D') & res.dat$N==300,]$theoretical.power <- 0.9834
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'E') & res.dat$N==300,]$theoretical.power <- 0.9834
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'F') & res.dat$N==300,]$theoretical.power <- 0.5373
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'G') & res.dat$N==300,]$theoretical.power <- 0.9834

res.dat[res.dat$scenario %in% paste0(2,'C') & res.dat$N==300,]$theoretical.power <- 0.9834
res.dat[res.dat$scenario %in% paste0(2,'D') & res.dat$N==300,]$theoretical.power <- 0.5373
res.dat[res.dat$scenario %in% paste0(2,'E') & res.dat$N==300,]$theoretical.power <- 0.9834

## Scénarios J=7 / M=2

res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'A') & res.dat$N==300,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'B') & res.dat$N==300,]$theoretical.power <- 0.4550
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'C') & res.dat$N==300,]$theoretical.power <- 0.4550
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'D') & res.dat$N==300,]$theoretical.power <- 0.9584
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'E') & res.dat$N==300,]$theoretical.power <- 0.9584
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'F') & res.dat$N==300,]$theoretical.power <- 0.4550
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'G') & res.dat$N==300,]$theoretical.power <- 0.9584

res.dat[res.dat$scenario %in% paste0(3,'C') & res.dat$N==300,]$theoretical.power <- 0.9584
res.dat[res.dat$scenario %in% paste0(3,'D') & res.dat$N==300,]$theoretical.power <- 0.4550
res.dat[res.dat$scenario %in% paste0(3,'E') & res.dat$N==300,]$theoretical.power <- 0.9584

## Scénarios J=7 / M=4

res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'A') & res.dat$N==300,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'B') & res.dat$N==300,]$theoretical.power <- 0.5907
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'C') & res.dat$N==300,]$theoretical.power <- 0.5907
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'D') & res.dat$N==300,]$theoretical.power <- 0.9919
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'E') & res.dat$N==300,]$theoretical.power <- 0.9919
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'F') & res.dat$N==300,]$theoretical.power <- 0.5907
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'G') & res.dat$N==300,]$theoretical.power <- 0.9919

res.dat[res.dat$scenario %in% paste0(4,'C') & res.dat$N==300,]$theoretical.power <- 0.9919
res.dat[res.dat$scenario %in% paste0(4,'D') & res.dat$N==300,]$theoretical.power <- 0.5907
res.dat[res.dat$scenario %in% paste0(4,'E') & res.dat$N==300,]$theoretical.power <- 0.9919


### Scénarios N=50

## Scénarios J=4 / M=2

res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'A') & res.dat$N==50,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(1,5,7,9,11),'B') & res.dat$N==50,]$theoretical.power <- 0.1013
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'C') & res.dat$N==50,]$theoretical.power <- 0.1013
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'D') & res.dat$N==50,]$theoretical.power <- 0.2615
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'E') & res.dat$N==50,]$theoretical.power <- 0.2615
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'F') & res.dat$N==50,]$theoretical.power <- 0.1013
res.dat[res.dat$scenario %in% paste0(c(5,7,9,11),'G') & res.dat$N==50,]$theoretical.power <- 0.2615

res.dat[res.dat$scenario %in% paste0(1,'C') & res.dat$N==50,]$theoretical.power <- 0.2615
res.dat[res.dat$scenario %in% paste0(1,'D') & res.dat$N==50,]$theoretical.power <- 0.1013
res.dat[res.dat$scenario %in% paste0(1,'E') & res.dat$N==50,]$theoretical.power <- 0.2615

## Scénarios J=4 / M=4

res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'A') & res.dat$N==50,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(2,6,8,10,12),'B') & res.dat$N==50,]$theoretical.power <- 0.1339
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'C') & res.dat$N==50,]$theoretical.power <- 0.1339
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'D') & res.dat$N==50,]$theoretical.power <- 0.3863
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'E') & res.dat$N==50,]$theoretical.power <- 0.3863
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'F') & res.dat$N==50,]$theoretical.power <- 0.1339
res.dat[res.dat$scenario %in% paste0(c(6,8,10,12),'G') & res.dat$N==50,]$theoretical.power <- 0.3863

res.dat[res.dat$scenario %in% paste0(2,'C') & res.dat$N==50,]$theoretical.power <- 0.3863
res.dat[res.dat$scenario %in% paste0(2,'D') & res.dat$N==50,]$theoretical.power <- 0.1339
res.dat[res.dat$scenario %in% paste0(2,'E') & res.dat$N==50,]$theoretical.power <- 0.3863

## Scénarios J=7 / M=2

res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'A') & res.dat$N==50,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(3,13,15,17,19),'B') & res.dat$N==50,]$theoretical.power <- 0.1171
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'C') & res.dat$N==50,]$theoretical.power <- 0.1171
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'D') & res.dat$N==50,]$theoretical.power <- 0.3236
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'E') & res.dat$N==50,]$theoretical.power <- 0.3236
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'F') & res.dat$N==50,]$theoretical.power <- 0.1171
res.dat[res.dat$scenario %in% paste0(c(13,15,17,19),'G') & res.dat$N==50,]$theoretical.power <- 0.3236

res.dat[res.dat$scenario %in% paste0(3,'C') & res.dat$N==50,]$theoretical.power <- 0.3236
res.dat[res.dat$scenario %in% paste0(3,'D') & res.dat$N==50,]$theoretical.power <- 0.1171
res.dat[res.dat$scenario %in% paste0(3,'E') & res.dat$N==50,]$theoretical.power <- 0.3236

## Scénarios J=7 / M=4

res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'A') & res.dat$N==50,]$theoretical.power <- 0.05
res.dat[res.dat$scenario %in% paste0(c(4,14,16,18,20),'B') & res.dat$N==50,]$theoretical.power <- 0.1448
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'C') & res.dat$N==50,]$theoretical.power <- 0.1448
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'D') & res.dat$N==50,]$theoretical.power <- 0.4328
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'E') & res.dat$N==50,]$theoretical.power <- 0.4328
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'F') & res.dat$N==50,]$theoretical.power <- 0.1448
res.dat[res.dat$scenario %in% paste0(c(14,16,18,20),'G') & res.dat$N==50,]$theoretical.power <- 0.4328

res.dat[res.dat$scenario %in% paste0(4,'C') & res.dat$N==50,]$theoretical.power <- 0.4328
res.dat[res.dat$scenario %in% paste0(4,'D') & res.dat$N==50,]$theoretical.power <- 0.1448
res.dat[res.dat$scenario %in% paste0(4,'E') & res.dat$N==50,]$theoretical.power <- 0.4328


### DIF scenarios

res.dat.dif$theoretical.power <- res.dat[81:nrow(res.dat),]$theoretical.power
res.dat.dif.rosali$theoretical.power <- res.dat$theoretical.power
res.dat.dif.resali$theoretical.power <- res.dat$theoretical.power


##############################################################################
#----------------------------------------------------------------------------#
######################### AGGREGATION OF ALL METHODS #########################
#----------------------------------------------------------------------------#
##############################################################################



# Correction of N=50 scenarios

res.dat[res.dat$N==50,]$dif.size <- sapply(which(res.dat$N==50),function(k) res.dat[k-1,]$dif.size)
res.dat.dif[res.dat.dif$N==50,]$dif.size <- sapply(which(res.dat.dif$N==50),function(k) res.dat.dif[k-1,]$dif.size)
res.dat.dif.rosali[res.dat.dif.rosali$N==50,]$dif.size <- sapply(which(res.dat.dif.rosali$N==50),function(k) res.dat.dif.rosali[k-1,]$dif.size)
res.dat.dif.resali[res.dat.dif.resali$N==50,]$dif.size <- sapply(which(res.dat.dif.resali$N==50),function(k) res.dat.dif.resali[k-1,]$dif.size)


# Items dichotomiques

res.dat$method <- "NONE"
res.dat.dif$method <- "PERFECT"
res.dat.dif.rosali$method <- "ROSALI"
res.dat.dif.resali$method <- "RESIDUS"

res.dat.dicho <- res.dat[res.dat$M==2,]
res.dat.dicho <- rbind(res.dat.dicho,res.dat.dif[res.dat.dif$M==2,])
res.dat.dicho <- rbind.fill(res.dat.dicho,res.dat.dif.rosali[res.dat.dif.rosali$M==2,])
res.dat.dicho <- rbind(res.dat.dicho,res.dat.dif.resali[res.dat.dif.resali$M==2,])

# Items polytomiques

res.dat.poly <- res.dat[res.dat$M==4,]
res.dat.poly <- rbind(res.dat.poly,res.dat.dif[res.dat.dif$M==4,])
res.dat.poly <- rbind.fill(res.dat.poly,res.dat.dif.rosali[res.dat.dif.rosali$M==4,])
res.dat.poly <- rbind(res.dat.poly,res.dat.dif.resali[res.dat.dif.resali$M==4,])
