R/Rasch.R

In vthorrf/CIRM: Procedures for IRT modeling

Rasch <- function(x,l){
  require(R2jags)

  ### Assemble data into list for JAGS====
  y = x
  itemID = colnames(y)
  subjID = rownames(y)
  Nitem = ncol(y)
  Nsubj = nrow(y)
  v = ncol(y)
  n = nrow(y)
  L = (l - 1)
  dataList = list( y=y , Nsubj=Nsubj, Nitem=Nitem , L=L)

  # Define the model====
  modelString = "
  model {
  for ( i in 1:Nsubj ) {
    for ( j in 1:Nitem ) {
      y[i,j] ~ dbin( pCorr[i,j] , L)
      pCorr[i,j] <- ilogit( subjAbil[i] - itemDiff[j] )
    }
  }
  for ( subjIdx in 1:Nsubj ) {
  subjAbil[subjIdx] ~ dnorm( muAbil , sigmaAbil )
  }
  for ( itemIdx in 1:Nitem ) {
  itemDiff[itemIdx] ~ dnorm( muDiff , sigmaDiff )
  }
  muAbil    ~ dnorm(0,.001)
  sigmaAbil ~ dgamma(.01,.01)
  muDiff    ~ dnorm(0,.001)
  sigmaDiff ~ dgamma(.01,.01)
  }
  " # close quote for modelString
  model = textConnection(modelString)

  # Run the chains====
  # Name the parameters to be monitored
  params <- c("pCorr","subjAbil","itemDiff")
  # Random initial values
  inits <- function(){list("subjAbil"=stats::rnorm(Nsubj,0,1),
                           "itemDiff"=stats::rnorm(Nitem,0,1))}
  # Define some MCMC parameters for JAGS
  nthin    = 1    # How Much Thinning?
  nchains  = 3    # How Many Chains?
  nburnin  = 100  # How Many Burn-in Samples?
  nsamples = 1100 # How Many Recorded Samples?
  ### Calling JAGS to sample
  startTime = proc.time()
  samples <- R2jags::jags(dataList, NULL, params, model.file =model,
                          n.chains=nchains, n.iter=nsamples, n.burnin=nburnin,
                          n.thin=nthin, DIC=T, jags.seed=666)
  stopTime = proc.time(); elapsedTime = stopTime - startTime; methods::show(elapsedTime)

  ### Inspect and diagnose the run
  REs <- colMeans(samples$BUGSoutput$sims.list$pCorr[,,])
  abil <- colMeans(samples$BUGSoutput$sims.list$subjAbil)
  diff <- colMeans(samples$BUGSoutput$sims.list$itemDiff)
  dic <- samples$BUGSoutput$DIC
  full <- samples
  matrix <- ordering(REs,abil,diff)$matrix
  Result <- list("matrix"=matrix,"abil"=abil,"diff"=diff,"dic"=dic,"full"=full)
  return(Result)
}