psych (version 1.0-17)

cluster.loadings: Find item by cluster correlations, corrected for overlap and reliability

Description

Given a n x n correlation matrix and a n x c matrix of -1,0,1 cluster weights for those n items on c clusters, find the correlation of each item with each cluster. If the item is part of the cluster, correct for item overlap. Part of the ICLUST set of functions, but useful for many item analysis problems.

Usage

cluster.loadings(keys, r.mat, correct = TRUE, digits = 2)

Arguments

keys

Cluster keys: a matrix of -1,0,1 cluster weights

r.mat

A correlation matrix

correct

Correct for reliability

digits

Number of digits output

Value

• loadings
  A matrix of item-cluster correlations (loadings)
• cor
  Correlation matrix of the clusters
• corrected
  Correlation matrix of the clusters, raw correlations below the diagonal, alpha on diagonal, corrected for reliability above the diagonal
• sd
  Cluster standard deviations
• alpha
  alpha reliabilities of the clusters
• count
  Number of items in the cluster

Details

Given a set of items to be scored as (perhaps overlapping) clusters and the intercorrelation matrix of the items, find the clusters and then the correlations of each item with each cluster. Correct for item overlap by replacing the item variance with its average within cluster inter-item correlation.

Although part of ICLUST, this may be used in any SAPA application where we are interested in item- whole correlations of items and composite scales.

These loadings are particularly interpretable when sorted by absolute magnitude for each cluster (see ICLUST.sort).

References

ICLUST: http://personality-project.org/r/r.iclust.html

See Also

ICLUST, factor2cluster, cluster.cor

Examples

r.mat<- Harman74.cor$cov
 clusters <- matrix(c(1,1,1,rep(0,24),1,1,1,1,rep(0,17)),ncol=2)
 cluster.loadings(clusters,r.mat)
 
## The function is currently defined as
function (keys, r.mat, correct = TRUE, digits = 2) 
{
    if (!is.matrix(keys)) 
        keys <- as.matrix(keys)
    item.covar <- r.mat %*% keys
    covar <- t(keys) %*% item.covar
    var <- diag(covar)
    sd.inv <- 1/sqrt(var)
    key.count <- diag(t(keys) %*% keys)
    if (correct) {
        cluster.correct <- diag((key.count/(key.count - 1)))
        for (i in 1:ncol(keys)) {
            if (key.count[i] == 1) {
                cluster.correct[i, i] <- 1
            }
            else {
                item.covar[, i] <- item.covar[, i] - keys[, i]
            }
        }
        correction.factor <- keys %*% cluster.correct
        correction.factor[correction.factor < 1] <- 1
        item.covar <- item.covar * correction.factor
    }
    ident.sd <- diag(sd.inv, ncol = length(sd.inv))
    cluster.loading <- item.covar %*% ident.sd
    cluster.correl <- ident.sd %*% covar %*% ident.sd
    key.alpha <- ((var - key.count)/var) * (key.count/(key.count - 
        1))
    key.alpha[is.nan(key.alpha)] <- 1
    key.alpha[!is.finite(key.alpha)] <- 1
    colnames(cluster.loading) <- colnames(keys)
    colnames(cluster.correl) <- colnames(keys)
    rownames(cluster.correl) <- colnames(keys)
    rownames(cluster.loading) <- rownames(r.mat)
    if (ncol(keys) > 1) {
        cluster.corrected <- correct.cor(cluster.correl, t(key.alpha))
    }
    else {
        cluster.corrected <- cluster.correl
    }
    return(list(loadings = round(cluster.loading, digits), cor = round(cluster.correl, 
        digits), corrected = round(cluster.corrected, digits), 
        sd = round(sqrt(var), digits), alpha = round(key.alpha, 
            digits), size = key.count))
  }