R/rmsd_chisquare.R

In CDM: Cognitive Diagnosis Modeling

## File Name: rmsd_chisquare.R
## File Version: 0.09


##########################################
# auxiliary function
rmsd_chisquare <- function( n.ik, pi.k, probs, eps=10^(-30) )
{
    # probs ... [ classes, items, categories ]
    # n.ik ... [ classes, items, categories, groups ]
    # N.ik ... [ classes, items, categories]
    N.ik <- n.ik[,,,1]
    G <- dim(n.ik)[4]
    pitot <- pi.k[,1]
    eps <- 1E-10
    if (G>1){
        for (gg in 2:G ){
            N.ik <- N.ik + n.ik[,,,gg]
            pitot <- pitot + pi.k[,gg]
        }
    }

    #*** extract maximum number of categories
    maxK <- apply( N.ik, c(2,3), sum, na.rm=TRUE )
    maxK <- rowSums( maxK > eps )

    # calculate summed counts
    N.ik_tot <- array( 0, dim=dim(N.ik) )
    N.ik_tot[,,1] <- N.ik[,,1,drop=FALSE]
    K <- dim(N.ik)[3]
    for (kk in 2:K){
        N.ik_tot[,,1] <- N.ik_tot[,,1,drop=FALSE] + N.ik[,,kk,drop=FALSE]
    }

    for (kk in 2:K){
        N.ik_tot[,,kk] <- N.ik_tot[,,1]
    }
    E.ik <- N.ik_tot*probs
    #--- calculate chi square
    chisq_stat0 <- ( N.ik - E.ik )^2 / E.ik
    chisq_stat <- chisq_stat0[,,1]
    for (kk in 2:K){
        chisq_stat <- chisq_stat + chisq_stat0[,,kk]
    }
    chisq_stat <- colSums(chisq_stat)
    return(chisq_stat)
}