R/StanORDM.script.R

In JihongZ/StanDCM: Diagnostic Classification Model using Stan

#' @title Generate Stan code and Run the estimation for ORDM
#'
#' @description
#' The StanLCDM.script Function to automate Stan code geneartion for LCDMs with binary resposnes
#'
#' @param Qmatrix the Q-matrix specified for the LCDM
#' @param save.path save the .stan file to somewhere; the default path is getwd()
#' @param save.name name the .stan
#' @return a. stan file saved at the specified path
#'
#' @author {Zhehan Jiang, University of Alabama, \email{zjiang17@@ua.edu}}
#'
#' @export

StanORDM.script<-function(Qmatrix,scale.num,save.path=getwd(),save.name="ORDM_uninf"){
  nc<-ncol(Qmatrix)
  nr<-nrow(Qmatrix)
  temp.table.col<-unique(apply(combn(rep(c(0,1),nc),nc),2,function(x){paste(x,collapse = "")}))
  temp.table.col<-temp.table.col[order(temp.table.col)]
  temp.table<-matrix(0,nr,length(temp.table.col))
  colnames(temp.table)<-temp.table.col
  rownames(temp.table)<-paste('item',c(1:nr),sep='')
  temp.table<-as.data.frame(temp.table)
  for (i in 1:nr){
    temp.table[i,]<-paste('l',i,'_0',sep='')
  }
  intercept<-temp.table[,1]

  #Generate attribute combinations
  comb.generator<-function(x.vector){
    if(length(x.vector)>1){
      temp.attr<-x.vector
      temp.attr.sav<-NULL
      for(i in 1:length(temp.attr)){
        temp.1<-combn(temp.attr,i)
        temp.2<-apply(temp.1,2,function(x){paste(x,collapse = "")})
        temp.attr.sav<-c(temp.attr.sav,temp.2)
      }
    }
    if(length(x.vector)==1){temp.attr.sav<-x.vector}
    temp.attr.sav
  }
  #vectors needed for combination.generator
  Item.load.id<-list()
  for ( i in 1:nr){
    Item.load.id[[i]]<-grep('1',Qmatrix[i,])}

  Attr.load.id<-list()
  attr.load.id<-matrix(0,length(temp.table.col),nc)
  for ( i in 1:length(temp.table.col)){
    attr.load.id[i,]<-unlist(strsplit(temp.table.col[i],split=''))
    Attr.load.id[[i]]<-grep('1',attr.load.id[i,])
  }

  #Generate Combination for both Item.load and Attr.load
  Item.Comb<-list()
  for ( i in 1:nr){
    Item.Comb[[i]]<-comb.generator(Item.load.id[[i]])
  }
  Attr.Comb<-list()
  for ( i in 2:length(temp.table.col)){
    Attr.Comb[[1]]<-0
    Attr.Comb[[i]]<-comb.generator(Attr.load.id[[i]])
  }
  constraints.list<-list()
  nway.inter.list<-list()
  for(i in 1:nr){
    for(a in 2:length(temp.table.col)){
      ifzero<-as.numeric(paste(Item.Comb[[i]][Item.Comb[[i]]%in%(Attr.Comb[[a]])],collapse=''))
      if((!is.na(ifzero))){
        temp.table[i,a]<-paste(c(temp.table[i,a],
                                 paste("S","l",i,"_",nchar(Item.Comb[[i]][Item.Comb[[i]]%in%(Attr.Comb[[a]])]),Item.Comb[[i]][Item.Comb[[i]]%in%(Attr.Comb[[a]])],sep='',collapse='')
        ),collapse='')
        if(a==length(temp.table.col)){
          nway.inter.list[[i]]<-nchar(Item.Comb[[i]][Item.Comb[[i]]%in%(Attr.Comb[[a]])])
          constraints.list[[i]]<-paste("l",i,"_",nchar(Item.Comb[[i]][Item.Comb[[i]]%in%(Attr.Comb[[a]])]),Item.Comb[[i]][Item.Comb[[i]]%in%(Attr.Comb[[a]])],sep='')
        }
      }
    }
  }

  #Create Lambda Table
  Lamda.Table<-temp.table
  for(i in 1:nr){
    for(a in 1:length(Lamda.Table)){
      t.ref<-unique(as.character(Lamda.Table[i,]))
      pos<-c(1:length(t.ref))[Lamda.Table[i,a]==t.ref]
      temp.table[i,a]<-paste("t",i,"_",pos,sep='')}}

  #Generate LCDM specification
  out<-list()
  out[[1]]<-Lamda.Table
  out[[2]]<-temp.table
  out[[3]]<-constraints.list
  out[[4]]<-nway.inter.list
  out[[5]]<-intercept
  OUTPUT<-out
  nclass<-ncol(OUTPUT[[1]]);Nc<-nclass

  #Produce kernel expressions across items and attributes
  Kernel.exp<-OUTPUT[[1]]
  for (i in 1:nrow(OUTPUT[[1]])){
    for ( j in 1:ncol(OUTPUT[[1]])){
      if(sum(grep('S',OUTPUT[[1]][i,j]))!=0){Kernel.exp[i,j]<-gsub('S','+',OUTPUT[[1]][i,j])}
    }
  }


  #Monotonicity constraint in terms of the interaction terms of the item effects
  Constrain.List1<-NULL
  name.inter<-unlist(OUTPUT[[3]])[unlist(OUTPUT[[4]])>=2]
  numway.inter<-unlist(OUTPUT[[4]])[unlist(OUTPUT[[4]])>=2]
  subname.inter<-substr((unlist(OUTPUT[[3]])[unlist(OUTPUT[[4]])>=2]), (nchar(unlist(OUTPUT[[3]])[unlist(OUTPUT[[4]])>=2])-unlist(OUTPUT[[4]])[unlist(OUTPUT[[4]])>=2]+1),
                        nchar(unlist(OUTPUT[[3]])[unlist(OUTPUT[[4]])>=2]))

  if(length(name.inter)!=0){
    for (inter in 1: length(name.inter)){
      temp.nw<-numway.inter[inter]
      temp.nm<-name.inter[inter]
      temp.subnm<-strsplit(subname.inter[inter],split='')[[1]]
      temp.sel<-paste(unlist(strsplit(temp.nm,split = '_'))[1],"_",(1:(temp.nw-1)),sep='')
      first.sel<-unlist(OUTPUT[[3]])[grep(paste((temp.sel),collapse="|"),unlist(OUTPUT[[3]]))]
      second.sel<-sub(".*_.", "", first.sel)
      for (sel in 1:length(temp.subnm)){
        SEL<-second.sel[sel]
        Constrain.List1<-rbind(
          paste(temp.nm,">-(0", paste("+",first.sel[grep(SEL,second.sel)],
                                      sep='',collapse=''),")",sep=''),Constrain.List1)
      }
    }
    Constrain.List1<-as.character(Constrain.List1)
  }else{
    Constrain.List1<-NULL
  }

  itemParmName<-c(unlist(OUTPUT[[3]])[unlist(OUTPUT[[4]])==1],unlist(OUTPUT[[3]])[unlist(OUTPUT[[4]])==2],OUTPUT[[5]])
  numMainEffect<-length(unlist(OUTPUT[[3]])[unlist(OUTPUT[[4]])==1])
  Constrain.List<-paste('  real<lower=0>',itemParmName[1:numMainEffect],';\n ')
  Unconstrain.List<-paste('  real',itemParmName[-(1:numMainEffect)],';\n ')

  Reparm<-array(rep(0,nr*nclass*(scale.num)),dim = c(nr,nclass,(scale.num)))

  #step parameters
  StepParmName<-paste('step',1:scale.num-1,sep='')
  StepParmName[1]<-0
  CulStepParmName<-StepParmName

  ##########0529update Kernal.exp is updated to a list so that list[[?]] is a PImat for a cate
  Kernel.exp.list<-list(scale.num)
  for(i in 1:scale.num){
    Kernel.exp.list[[i]]<-Kernel.exp
  }
  Kernel.exp.list.copy<-Kernel.exp.list
  for(i in 1:scale.num){
    for (j in 1:nr){
      for( z in 1:nclass){
        Kernel.exp.list[[i]][j,z]<-str_replace_all(Kernel.exp.list[[i]][j,z],Kernel.exp.list.copy[[i]][j,1],
                                                   paste(Kernel.exp.list.copy[[i]][j,1],"r",i-1,sep=''))

      }
    }
  }
  for(i in 1:scale.num){
    for (j in 1:nr){
      for( z in 2:nclass){
        Kernel.exp.list[[i]][j,z]<-str_replace_all(Kernel.exp.list[[i]][j,z],"\\+",
                                                   paste("+",i-1,"*",sep=''))

      }
    }
  }
  Kernel.exp.list[[1]]<-0
  for(loopi in 1:nr){
    for( loopc in 1:nclass){
      for( loops in 1:1){Reparm[loopi,loopc,loops]<-paste('  PImat[',loopi,',',loopc,'][',loops,']=0;\n',sep='')}
      for( loops in 2:scale.num){
        Reparm[loopi,loopc,loops]<-paste('  PImat[',loopi,',',loopc,'][',loops,']=',
                                         paste(Kernel.exp.list[[loops]][loopi,loopc]),';\n',sep='')
      }
    }
  }
  itemParmName<-c(unlist(OUTPUT[[3]]))
  for( i in 2:scale.num){
    itemParmName<-c(itemParmName,c(Kernel.exp.list[[i]][,1]))
  }
  Unconstrain.List<-paste('  real',itemParmName[-(1:numMainEffect)],';\n ')

  Modelcontainer<-paste('   vector[Nc] contributionsC;\n','    vector[Ni] contributionsI;\n\n',sep='')
  Parmprior<-paste(c(paste('   //Prior\n'),paste('   ',itemParmName,'~normal(0,15)',';\n',sep=''),paste('   Vc~dirichlet(rep_vector(2.0, Nc));',sep='')))
  #Likelihood Stan code
  Likelihood<-'
  \n
  //Likelihood
  for (iterp in 1:Np){
    for (iterc in 1:Nc){
      for (iteri in 1:Ni){
        contributionsI[iteri]= categorical_lpmf(Y[iterp,iteri]| softmax(((PImat[iteri,iterc]))));
      }
      contributionsC[iterc]=log(Vc[iterc])+sum(contributionsI);
    }
    target+=log_sum_exp(contributionsC);
  }
  '
  data.spec<-'
  data{
  int Np;
  int Ni;
  int Nc;
  int Ns;
  matrix[Np, Ni] Y;
  }
  '
  parm.spec<-paste(c('
                     parameters{
                     simplex[Nc] Vc;\n ',paste0(Constrain.List),paste0(Unconstrain.List),
                     '}\n'),collapse='')

  #Parameter Specification
  parm.spec<-paste(c('parameters{
                     simplex[Nc] Vc;\n ',paste0(Constrain.List),paste0(Unconstrain.List),'}\n'),collapse='')

  #Reparameter Specification

  transparm.spec<-paste(c('transformed parameters{
                          vector[Ns] PImat[Ni, Nc];\n',
                          paste0(unlist(Reparm)),'}\n'),collapse='')

  #Model Specification
  model.spec<-paste(c('\nmodel {\n',paste(c(Modelcontainer,Parmprior,Likelihood),sep=''),'\n}',sep=''))
  model.spec<-model.spec[!startsWith(str_remove_all(model.spec," "),"~")]

  generatedQuantities.spec<-'
  \n
  generated quantities {
  vector[Ni] log_lik[Np];
  vector[Ni] contributionsI;
  matrix[Ni,Nc] contributionsIC;
  //Posterior
  for (iterp in 1:Np){
    for (iteri in 1:Ni){
      for (iterc in 1:Nc){
        contributionsI[iteri]= categorical_lpmf(Y[iterp,iteri]| softmax(((PImat[iteri,iterc]))));
        contributionsIC[iteri,iterc]=log(Vc[iterc])+contributionsI[iteri];
      }
      log_lik[iterp,iteri]=log_sum_exp(contributionsIC[iteri,]);
    }
  }
  }
  '
  if (.Platform$OS.type == "unix") {
    filename = paste(paste(save.path,save.name,sep='/'),'.stan',sep='')
  }else{
    filename = paste(paste(save.path,save.name,sep='\\'),'.stan',sep='')
  }

  sink(file= filename,append=FALSE)
  cat(
    paste(c('   ',
            data.spec,parm.spec,transparm.spec,model.spec,generatedQuantities.spec)
    ))
  sink(NULL)

}