R/equivalent.dina.R

In CDM: Cognitive Diagnosis Modeling

## File Name: equivalent.dina.R
## File Version: 2.20
equivalent.dina <- function (q.matrix, reparameterization="B")
{
    reparametrization <- reparameterization
    K <- ncol(q.matrix)
    I <- nrow(q.matrix)
    if (is.null(colnames(q.matrix))) {
        colnames(q.matrix) <- paste("S", 1:K, sep="")
    }
    if (is.null(rownames(q.matrix))) {
        rownames(q.matrix) <- paste("I", 1:I, sep="")
    }
    L <- 2^K

    dich_vec <- c(0,1)
    dfr <- as.matrix( dich_vec, ncol=1)
    rownames(dfr) <- NULL
    for (kk in 2:K){
        dfr <- rbind( cbind( dfr, 0), cbind( dfr, 1) )
    }
    attr.patt <- as.matrix(dfr)

    alpha <- attr.patt
    l1 <- apply(alpha, 1, FUN=function(hh) {
            paste(hh, collapse="")
        })
    alpha <- matrix(NA, L, K)
    for (kk in 1:K) {
        alpha[, kk] <- as.numeric(substring(l1, kk, kk))
    }
    alpha <- data.frame(alpha)
    rownames(alpha) <- l1
    colnames(alpha) <- colnames(q.matrix)

    #*** link to alpha.ast
    alpha_ast_index <- alpha[,1]
    for ( kk in 2:K){
        alpha_ast_index <- alpha_ast_index + 2^(kk-1)*alpha[,kk]
    }

    #--- reparametrization B
    if (reparametrization=="B") {
        qclasses <- q.matrix[,1]
        for (kk in 2:K){
            qclasses <- qclasses + 2^(kk-1) * q.matrix[,kk]
        }
        uqclasses <- setdiff(unique(qclasses),0)
        qclasses <- match( qclasses,  uqclasses )
        L1 <- length( uqclasses )
        q.matrix.ast <- matrix(0, I, L1)
        q.matrix.ast[ cbind(1:I, qclasses) ] <- 1
        qclasses[ is.na(qclasses) ] <- -9
        rownames(q.matrix.ast) <- rownames(q.matrix)
        v1 <- rep( "", L1 )
        for (cc in 1:L1){
            q_cc <- q.matrix[ which(qclasses==cc),, drop=FALSE]
            q_cc <- q_cc[1,]
            v1[cc] <- paste0("S*", paste0( q_cc, collapse="" ) )
        }
        colnames(q.matrix.ast) <- v1
        alpha.ast <- matrix(0, L, L1)
        rownames(alpha.ast) <- rownames(alpha)
        colnames(alpha.ast) <- colnames(q.matrix.ast)
        for (tt in 1:L){
            alpha_tt <- alpha[ tt, ]
            for (ll in 1:L1){
                q_ll <- q.matrix[ qclasses==ll,, drop=FALSE]
                q_ll <- q_ll[1,]
                v_tt_ll <- prod( alpha_tt^q_ll )
                if (v_tt_ll==1 ){
                    alpha.ast[tt,ll] <- 1
                }
            }
        }
    }
    #----------------------------------------------
    #--- reparametrization A
    if (reparametrization=="A") {
        alpha.ast <- matrix(0, L, L)
        rownames(alpha.ast) <- rownames(alpha)
        colnames(alpha.ast) <- rownames(alpha)
        diag(alpha.ast) <- 1
        alpha.ast <- alpha.ast[, -1]
        q.matrix.ast <- matrix(0, I, L)
        rownames(q.matrix.ast) <- rownames(q.matrix)
        colnames(q.matrix.ast) <- paste("S*", rownames(alpha), sep="")
        for (ii in 1:I) {
            q.ii <- q.matrix[ii, ]
            a1 <- rep(0,L)
            for (hh in 1:L){
                v_hh <- prod( alpha[hh, ]^q.ii )
                if ( v_hh==1 ){
                    a1[hh] <- 1
                }
            }
            q.matrix.ast[ii, ] <- a1
        }
        q.matrix.ast[ rowSums(q.matrix)==0, ] <- 0
        q.matrix.ast <- q.matrix.ast[, -1]
    }
    #--- OUTPUT
    res <- list(q.matrix=q.matrix, q.matrix.ast=q.matrix.ast,
                    alpha=alpha, alpha.ast=alpha.ast )
    return(res)
}