R/IRT_se_gdina.R

In CDM: Cognitive Diagnosis Modeling

## File Name: IRT_se_gdina.R
## File Version: 0.21

IRT_se_gdina <- function(object, h=1E-4)
{
    dat <- object$dat
    resp.ind.list <- object$resp.ind.list
    delta <- object$delta
    attr.prob <- object$attr.prob
    aggr.attr.patt <- object$control$aggr.attr.patt
    Aj <- object$Aj
    Mj <- object$Mj
    p.xi.aj <- object$like
    J <- ncol(dat)
    linkfct <- object$control$linkfct
    item.patt.split <- object$control$item.patt.split
    item.patt.freq  <- object$item.patt.freq
    IP <- nrow(item.patt.split)
    zeroprob.skillclasses <- object$zeroprob.skillclasses
    resp.ind.list <- object$resp.ind.list
    G <- object$G
    L <- object$Nskillclasses
    group <- object$G
    reduced.skillspace <- object$reduced.skillspace
    beta <- object$beta
    Z.skillspace <- object$Z.skillspace

    if (G==1){
        item.patt.freq <- as.vector(item.patt.freq)
    }

    progress <- FALSE
    iter <- 1E2

    #-- handle reduced skill space
    if (reduced.skillspace){
        if (G==1){
            attr.prob <- reduced_skillspace_beta_2_probs( Z=Z.skillspace, beta=beta )
        }
        if (G>1){
            attr.prob <- matrix(NA, nrow=L, ncol=G)
            for (gg in 1:G){
                attr.prob[,gg] <- reduced_skillspace_beta_2_probs( Z=Z.skillspace, beta=beta[,gg] )
            }
        }
    }
    # no reduced skillspace
    if (! reduced.skillspace){
        eps <- 2*h
        beta <- matrix( 0, nrow=L-1, ncol=G)
        bounds <- c(eps, 1E3)
        if (G==1){
            beta[,1] <- cdm_sumnorm_squeeze( vec=attr.prob, bounds=bounds )[-L]
        } else {
            for (gg in 1:G){
                beta[,gg] <- cdm_sumnorm_squeeze( vec=attr.prob[,gg], bounds=bounds )[-L]
            }
        }
    }

    arglist <- list( J=J, L=L, aggr.attr.patt=aggr.attr.patt, Mj=Mj,
                    delta=delta, linkfct=linkfct, IP=IP,
                    item.patt.split=item.patt.split, resp.ind.list=resp.ind.list,
                    zeroprob.skillclasses=zeroprob.skillclasses, G=G, item.patt.freq=item.patt.freq,
                    beta=beta, Z.skillspace=Z.skillspace, reduced.skillspace=reduced.skillspace,
                    return_all=TRUE)
    res <- do.call( what=IRT_se_gdina_calc_individual_likelihood, args=arglist )
    loglike <- res$loglike
    p.xi.aj <- res$p.xi.aj
    p.aj.xi <- res$p.aj.xi
    like_ind <- res$like_ind

    #--- derivatives based with respect to delta

    delta1 <- delta

    jj <- 5  # item
    pp <- 1  # parameter
    delta1[[jj]][[pp]] <- delta[[jj]][[pp]] + h
    arglist1 <- arglist
    arglist1$return_all <- FALSE
    arglist1$delta <- delta1
    loglike1 <- do.call( what=IRT_se_gdina_calc_individual_likelihood, args=arglist1 )

    d1 <- ( loglike1 - loglike ) / h

# Revalpr("d1")

    eps <- 1E-20

    prob_args <- list( J=J, jj=jj, L=L, aggr.attr.patt=aggr.attr.patt, Mj=Mj, delta=delta, linkfct=linkfct)
    pj0 <- do.call( gdina_calc_prob_one_item, args=prob_args )

    prob_args1 <- prob_args
    delta1 <- delta
    delta1[[jj]][[pp]] <- delta[[jj]][[pp]] + h
    prob_args1$delta <- delta1
    pj1 <- do.call( gdina_calc_prob_one_item, args=prob_args1 )

    delta1 <- delta
    delta1[[jj]][[pp]] <- delta[[jj]][[pp]] - h
    prob_args1$delta <- delta1
    pj2 <- do.call( gdina_calc_prob_one_item, args=prob_args1 )

    like_der <- matrix( 0, nrow=IP, ncol=L)
    resp_jj <- resp.ind.list[[jj]]
    data_jj <- item.patt.split[ resp_jj, jj ] + 1
    like_der[ resp_jj, ] <- ( pj1[ data_jj, ] - pj2[ data_jj, ] ) / (2*h) / pj0[ data_jj, ]

    if (G==1){
        d1a <- sum( rowSums( p.aj.xi * like_der ) * item.patt.freq )
    } else {
        d1a <- 0
        for (gg in 1:G){
            d1a <- d1a + sum( rowSums( p.aj.xi[,,gg] * like_der ) * item.patt.freq[,gg] )
        }
    }

    #---- derivatives with respect to beta

    bb <- 4
    gg <- 1

    beta1 <- beta
    beta1[bb,gg] <- beta[bb,gg] + h
    arglist1 <- arglist
    arglist1$return_all <- FALSE
    arglist1$beta <- beta1
    loglike1 <- do.call( what=IRT_se_gdina_calc_individual_likelihood, args=arglist1 )
    d1 <- ( loglike1 - loglike ) / h

    beta1 <- beta
    beta1[bb,gg] <- beta[bb,gg] - h
    arglist1 <- arglist
    arglist1$return_all <- FALSE
    arglist1$beta <- beta1
    loglike2 <- do.call( what=IRT_se_gdina_calc_individual_likelihood, args=arglist1 )
    d1b <- ( loglike1 - loglike2 ) / (2*h)

# Revalpr("d1b")

    beta1[bb,gg] <- beta[bb,gg] + h
    skill_args <- list( beta=beta1, Z.skillspace=Z.skillspace, reduced.skillspace=reduced.skillspace, G=G)
    attr.prob1 <- do.call( what=IRT_se_gdina_calc_skill_distribution, args=skill_args )

    beta1[bb,gg] <- beta[bb,gg] - h
    skill_args$beta <- beta1
    attr.prob2 <- do.call( what=IRT_se_gdina_calc_skill_distribution, args=skill_args )

    if (G==1){
        attr_prob1 <- attr.prob1
        attr_prob2 <- attr.prob2
        attr_prob <- attr.prob
        post <- p.aj.xi
        freq <- item.patt.freq
    } else {
        attr_prob1 <- attr.prob1[,gg]
        attr_prob2 <- attr.prob2[,gg]
        attr_prob <- attr.prob[,gg]
        post <- p.aj.xi[,,gg]
        freq <- item.patt.freq[,gg]
    }
    M1 <- cdm_matrix2( ( attr_prob1 - attr_prob2 ) / (2*h) / ( attr_prob + eps ), nrow=IP)
    d1a <- sum( rowSums( post * M1 ) * freq )

    ### This function is yet incomplete. But the remaining derivatives can be simply calculated.

}