R/tam_mml_3pl_distributionmoments.R

In TAM: Test Analysis Modules

## File Name: tam_mml_3pl_distributionmoments.R
## File Version: 9.11

#######################################################################
# moments of distribution
tam_mml_3pl_distributionmoments <- function( D, G, pi.k, theta.k )
{
    D <- ncol(theta.k)
    if ( is.vector( theta.k) ){
        D <- 1
        theta.k <- matrix( theta.k, ncol=1 )
    }
    mean.trait <- sd.trait <- skewness.trait <- matrix( 0, nrow=D, ncol=G )
    for (dd in 1:D){
        for (gg in 1:G){
            mean.trait[dd,gg] <- sum( theta.k[,dd] * pi.k[, gg ] )
            sd.trait[dd,gg] <- sqrt( sum( theta.k[,dd]^2 * pi.k[, gg ] ) - mean.trait[dd,gg]^2 )
            skewness.trait[dd,gg] <- sum( ( theta.k[,dd] - mean.trait[dd,gg] )^3 * pi.k[, gg ] ) /
                            sd.trait[dd,gg]^3
        }
    }
    rownames(skewness.trait) <- rownames(sd.trait) <-
                rownames(mean.trait) <- colnames(theta.k)
    colnames(skewness.trait) <- colnames(sd.trait) <-
                colnames(mean.trait) <- paste0("Group",1:G)
    #*****
    # correlation matrices
    correlation.trait <- as.list(1:G)
    names(correlation.trait) <- colnames(mean.trait)
    for (gg in 1:G){
        # gg <- 1
        mean.gg <- rep(0,D)
        Sigma.gg <- diag(0,D)
        for (dd in 1:D){
            mean.gg[dd] <- sum( pi.k[,gg] * theta.k[,dd] )
        }
        for (dd1 in 1:D){
            for (dd2 in dd1:D){
                Sigma.gg[dd1,dd2] <- sum( pi.k[,gg] * (theta.k[,dd1] - mean.gg[dd1] )*(theta.k[,dd2] - mean.gg[dd2] ) )
                Sigma.gg[dd2,dd1] <- Sigma.gg[dd1,dd2]
            }
        }
        rownames(Sigma.gg) <- colnames(Sigma.gg) <- rownames(mean.trait)
        correlation.trait[[gg]] <- stats::cov2cor(Sigma.gg + diag(10^(-5),D) )
    }
    res <- list( "mean.trait"=mean.trait, "sd.trait"=sd.trait,
                "skewness.trait"=skewness.trait, "correlation.trait"=correlation.trait)
    return(res)
}

.mml.3pl.distributionmoments  <- tam_mml_3pl_distributionmoments