R/gdm_est_normalskills.R

In CDM: Cognitive Diagnosis Modeling

## File Name: gdm_est_normalskills.R
## File Version: 0.15

##############################################################
# estimation of skill distribution under normality
gdm_est_normalskills <- function( pi.k, theta.k, irtmodel, G, D,
    mean.constraint, Sigma.constraint, standardized.latent,
    p.aj.xi, group, ind.group, weights, b, a )
{
    # mean.constraint [ dimension, group, value ]
    # Sigma.constraint [ dimension1, dimension2, group, value ]

    #-----------------------------------------
    #-------- unidimensional model -----------
    #-----------------------------------------
    if (D==1){
        for (gg in 1:G){
            res <- cdm_fit_normal(x=theta.k, w=pi.k[,gg])
            mg <- res$Mu
            sdg <- sqrt(res$Sigma)
            #--------- mean constraint
            if ( ( ! is.null ( mean.constraint )) ){
                i1 <- mean.constraint[ mean.constraint[,2]==gg,, drop=FALSE]
                if ( ( nrow(i1)==1 ) & (G>1) ){
                    if ( ( gg==1 ) & (i1[,1]==1) & (i1[,2]==1) ){
                        b <- b + ( mg - i1[3] )
                    }
                    mg <- i1[3]
                }
                if ( nrow(i1) > 0 ){
                    mg <- i1[,3]
                }
            }    # end mean constraint
            #--------- sigma constraint
            if ( ( ! is.null ( Sigma.constraint ) )  ){
                i1 <- Sigma.constraint[ Sigma.constraint[,3]==gg,, drop=FALSE]
                if ( ( nrow(i1)==1 ) & (G>1) ){
                    if ( ( gg==1 ) & (i1[,1]==1) & (i1[,2]==1) ){
                        a <- a * sdg / sqrt(i1[4])
                    }
                    sdg <- sqrt(i1[4])
                }
            }  # end sigma constraint
        pi.k[,gg] <- cdm_sumnorm( stats::dnorm( theta.k[,1],mean=mg, sd=sdg)    )
        }
    }
    #-----------------------------------------
    #-------- multidimensional model ---------
    #-----------------------------------------
    if (D>1){
        for (gg in 1:G){
            res <- cdm_fit_normal(x=theta.k, w=pi.k[,gg] )
            mean.gg <- res$Mu
            Sigma.gg <- res$Sigma
            Sigma.gg <- cdm_add_ridge_diagonal(x=Sigma.gg, eps=1E-10 )
            #----- mu constraint
            m.gg <- mean.constraint[ mean.constraint[,2]==1, ]
            if ( ! is.null(mean.constraint)){
                if( dim(m.gg)[1] > 0 ){
                    mean.gg[ m.gg[,1] ] <- m.gg[,3]
                }
            }
            s.gg <- Sigma.constraint[ Sigma.constraint[,3]==1, ]
            #----- sigma constraint
            if ( ! is.null(Sigma.constraint)){
                if( dim(s.gg)[1] > 0 ){
                    c1 <- stats::cov2cor( Sigma.gg )
                    d1 <- diag(Sigma.gg)
                    s.gg1 <- s.gg[ s.gg[,1]==s.gg[,2], ]
                    if ( nrow(s.gg1) > 0 ){
                        d1[ s.gg1[,1:2] ] <- s.gg[,4]
                    }
                    d1 <- outer( sqrt(d1), sqrt(d1) )*c1
                    s.gg2 <- s.gg[ s.gg[,1] !=s.gg[,2], ]
                    if ( nrow(s.gg1) > 0 ){
                        d1[ s.gg1[,1:2] ] <- s.gg[,4]
                        d1[ s.gg1[,c(2,1)] ] <- s.gg[,4]
                    }
                    Sigma.gg <- d1
                }
            }
            pi.k[,gg] <- cdm_sumnorm( mvtnorm::dmvnorm( theta.k, mean=mean.gg, sigma=Sigma.gg )    )
        }  # end gg
    }  # end multidimensional model
    #--- OUTPUT
    res <- list(pi.k=pi.k, b=b, a=a )
    return(res)
}
#*************************************************************

.gdm.est.normalskills <- gdm_est_normalskills