R/entropy.lca.R

In CDM: Cognitive Diagnosis Modeling

## File Name: entropy.lca.R
## File Version: 0.194


#--- entropy for din, gdina and mcdina objects
entropy.lca <- function( object )
{
    posterior <- object$like
    data <- object$data
    weights <- object$control$weights
    pjk <- object$pjk
    if ( inherits(object,"mcdina") ){
        weights <- object$weights
        data <- object$dat
        data <- data - 1
        pjk <- object$pik[,,,1]
    }

    skillspace <- object$attribute.patt.splitted

    q.matrix <- object$q.matrix
    data.resp <- 1-is.na(data)
    data[is.na(data) ] <- 0

    N <- length(weights)
    weights <- N / sum(weights) * weights
    L <- nrow(skillspace )
    K <- ncol(skillspace)
    I <- ncol(data)
    eps <- 1E-10
    posterior <- posterior / rowSums( posterior )

    #*** calculate entropy for whole test
    entropy.total <- 1 +  sum( weights * posterior * log( posterior + eps) )/N/log(L)

    #*** maximum number of skills
    maxskill <- apply( skillspace, 2, max )

    #*** entropy for each skill
    entropy.skill <- rep(0,K)
    for (kk in 1:K){
        # kk <- 1
        Nkk <- maxskill[kk]
        posterior.kk <- matrix(NA, nrow=N, ncol=Nkk+1 )
        for (vv in 0:Nkk){
            posterior.kk[,vv+1] <- rowSums( posterior[, skillspace[,kk]==vv ]  )
        }
        entropy.skill[kk] <- 1 +
                sum( weights * posterior.kk * log(posterior.kk+eps))/ N / log(Nkk+1)
    }

    #******** entropy for each item
    entropyM <- matrix( NA, nrow=I+1, ncol=K +1 )
    entropyM[1,] <- c( entropy.total, entropy.skill )
    for (ii in 1:I){
        weights.ii <- weights * data.resp[,ii]
        N.ii <- sum(weights.ii)
        pjk.ii <- pjk[ii,,]
        pjkM <- pjk.ii[ data[,ii] +1, ]
        posterior.ii <- pjkM
        posterior.ii <- posterior.ii / rowSums( posterior.ii )
        entropyM[ii+1,1] <- 1 +
                sum( weights.ii * posterior.ii * log(posterior.ii + eps) )/N.ii/log(L)
        for (kk in 1:K){
            # skill kk and item ii
            Nkk <- maxskill[kk]
            posterior.kk <- matrix(NA, nrow=N, ncol=Nkk+1 )
            for (vv in 0:Nkk){
                posterior.kk[,vv+1] <- rowSums( posterior.ii[, skillspace[,kk]==vv ]  )
            }
            entropyM[ii+1,kk+1] <- 1 +
                    sum( weights * posterior.kk * log(posterior.kk + eps) )/N/log(Nkk+1)
        }
    }

    res <- data.frame( "item"=c("test", colnames(data) ), entropyM )
    colnames(res)[-1] <- c("entr_test",paste0("entr_skill", 1:K ) )
    res2 <- list( "entropy"=res )
    class(res2) <- "entropy.lca"
    return(res2)
}