R/gdina_dif_compute.R

In CDM: Cognitive Diagnosis Modeling

## File Name: gdina_dif_compute.R
## File Version: 1.455


#-- auxiliary calculations in gdina model for
#-- detection of differential item functioning
gdina_dif_compute <- function( ocontrol, gg, data )
{
    aggr.patt.designmatrix <- ocontrol$aggr.patt.designmatrix
    Aj <- ocontrol$Aj
    Mj <- ocontrol$Mj
    Mj.index <- ocontrol$Mj.index
    linkfct <- ocontrol$linkfct
    rule <- ocontrol$rule
    method <- ocontrol$method
    aggr.attr.patt <- ocontrol$aggr.attr.patt
    IP <- ocontrol$IP
    p.aj.xi <- ocontrol$p.aj.xi[,,gg]

    ind1 <- match( ocontrol$item.patt[,1], ocontrol$item.patt.subj)
    ind1 <- stats::na.omit(ind1)
    # p.aj.xi <- p.aj.xi[ ind1, ]
    item.patt.split <- ocontrol$item.patt.split
    resp.patt <- ocontrol$resp.patt
    item.patt.freq <- ocontrol$item.patt.freq[,gg]
    freq.pattern <- ocontrol$freq.pattern
    invM.list <- ocontrol$invM.list
    eps <- eps2 <- 1E-10
    J <- length(Mj)
    prob_exp <- varmat.delta <- varmat.palj <- delta <- ndj <- as.list(1:J)
    R.lj <- ocontrol$R.lj.gg[,,gg]
    I.lj <- ocontrol$I.lj.gg[,,gg]
    # calculation of expected counts
    R.ljM <- R.lj %*% aggr.patt.designmatrix
    I.ljM <- I.lj %*% aggr.patt.designmatrix
    for (jj in 1:J){    # begin item
        Ajjj <- Aj[[jj]]
        Mjjj <- Mj[[jj]][[1]]
        Rlj.ast <- R.ljM[ jj, Mj.index[jj,5]:Mj.index[jj,6] ]
        Ilj.ast <- I.ljM[ jj, Mj.index[jj,5]:Mj.index[jj,6] ]
        pjjj <- Rlj.ast / ( Ilj.ast + eps2 )
        if (linkfct=="logit" ){
            pjjj[ pjjj > 1-eps ] <- 1 - eps
            pjjj[ pjjj < eps ] <- eps
            pjjj <- stats::qlogis( pjjj )
        }
        #*****
        if (linkfct=="log" ){
            pjjj[ pjjj < eps ] <- eps
            pjjj <- log( pjjj )
        }
        Wj <- diag( Ilj.ast )
        if ( ( rule[jj]=="GDINA" )| ( method=="ULS" ) ){
            invM <- invM.list[[jj]]
            delta.jj <- invM %*% crossprod(Mjjj,pjjj)
        } else {
            invM <- solve( crossprod(Mjjj, Wj ) %*% Mjjj + diag( rep( eps2, ncol(Mjjj) )) )
            delta.jj <- tcrossprod( invM, Mjjj ) %*% Wj %*% pjjj
        }
        pjj_exp <- ( Mjjj %*% delta.jj )[,1]
        if ( linkfct=="logit" ){
            pjj_exp <- stats::plogis( pjj_exp)
        }
        if ( linkfct=="log" ){
            pjj_exp <- exp( pjj_exp)
        }
        # data frame with counts and expected probabilities
        prob_exp[[jj]] <- data.frame( "freq"=Ilj.ast / sum( Ilj.ast), "prob"=pjj_exp )
        rownames(prob_exp[[jj]]) <- apply( Ajjj, 1,
                FUN=function(ll){ paste0("S", paste0( ll, collapse="") ) } )
        delta[[jj]] <- delta.jj[,1]

        #**** variance matrix
        PAJXI <-  p.aj.xi
        Ajjj <- Aj[[jj]]
        Mjjj <- Mj[[jj]][[1]]
        Mjj2 <- Mj[[jj]][[2]]
        apjj <- aggr.attr.patt[[jj]]
        M1 <- max( apjj )
        p.ajast.xi <- matrix( 0, nrow=IP, ncol=M1 )
        for (kk in 1:M1){
            pg1 <-  PAJXI[, apjj==kk  ]
            if ( is.vector(pg1) ){
                p.ajast.xi[,kk] <- pg1
            } else {
                p.ajast.xi[,kk] <- rowSums( pg1 )
            }
        }
        se_version <- ocontrol$se_version
        res_jj <- gdina_se_itemwise( R.lj_jj=R.lj[jj,], I.lj_jj=I.lj[jj,],
                    apjj=apjj, Mjjj=Mjjj, Mjj2=Mjj2, PAJXI=PAJXI, IP=IP,
                    item.patt.split_jj=item.patt.split[,jj],
                    resp.patt_jj=resp.patt[,jj], freq.pattern=item.patt.freq,
                    item.patt.freq=item.patt.freq, avoid.zeroprobs=FALSE,
                    data=data, jj=jj, method=method, linkfct=linkfct,
                    delta_jj=delta[[jj]], se_version=se_version )

        Rlj.ast <- stats::aggregate( R.lj[jj,], list( aggr.attr.patt[[jj]]), sum )
        Ilj.ast <- stats::aggregate( I.lj[jj,], list( aggr.attr.patt[[jj]]), sum )
        pjjj <- Rlj.ast[,2] / Ilj.ast[,2]
        pjjjM <- outer( rep(1,IP), pjjj ) + eps
        nM <- ncol(pjjjM)
        x1 <- outer( item.patt.split[,jj], rep(1,nM) )
        r1 <- outer( resp.patt[,jj] * item.patt.freq, rep(1,ncol(pjjjM) ) )
        # Formula (17) for calculating the standard error
        mat.jj <- p.ajast.xi * ( x1 - pjjjM) / ( pjjjM * ( 1 - pjjjM ) )
        infomat.jj <- matrix( 0, nM, nM )
        for (kk1 in 1:nM){
            for (kk2 in kk1:nM){
                # frequency weights must be taken into account
                hh1 <- sum( mat.jj[,kk1] * mat.jj[,kk2] * item.patt.freq *
                            resp.patt[,jj] * item.patt.split[,jj] )
                infomat.jj[kk2,kk1] <- infomat.jj[kk1,kk2] <-  hh1
            }
        }
        try( a1 <- solve( infomat.jj + diag( eps2, ncol(infomat.jj) ) ) )
        if ( is.null(a1)){
            cat( "Item", colnames(data)[jj], "Singular item parameter covariance matrix\n")
            a1 <- NA*infomat.jj
        }
        varmat.palj[[jj]] <- Ijj <- a1
        Wj <- diag( Ilj.ast[,2] )
        if ( ( method=="ULS" ) ){
            x1 <- t(Mjjj) %*% Mjjj
            diag(x1) <- diag(x1) + eps
            Wjjj <- solve(x1) %*% t(Mjjj)
        } else {
            x1 <- t(Mjjj) %*% Wj %*% Mjjj
            diag(x1) <- diag(x1) + eps
            Wjjj <- solve(x1) %*% t(Mjjj) %*% Wj
        }
        if ( linkfct=="logit" ){
            pjjj.link <- 1 / ( ( pjjj * ( 1 - pjjj ) ) + eps2 )
            pjjj.link <- diag( pjjj.link )
            Wjjj <- Wjjj %*% pjjj.link
        }
        if ( linkfct=="log" ){
            pjjj.link <- 1 /  ( pjjj  + eps2 )
            pjjj.link <- diag( pjjj.link )
            Wjjj <- Wjjj %*% pjjj.link
        }
        varmat.delta[[jj]] <- Wjjj %*% Ijj %*% t(Wjjj)
        # varmat.delta[[jj]] <- t(Wjjj) %*% Ijj %*% Wjjj  # this is wrong!!
        varmat.delta[[jj]] <- res_jj$varmat.delta_jj
        ndj[[jj]] <- length( delta[[jj]] )
    }  # end jj

    #-- output
    res <- list( delta=delta, varmat.delta=varmat.delta,
                    ndj=ndj, prob_exp=prob_exp )
    return(res)
}