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,SMC=TRUE)

Arguments

keys

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

r.mat

A correlation matrix

correct

Correct for reliability

SMC

Use the squared multiple correlation as a communality estimate, otherwise use the greatest correlation for each variable

Value

loadingsA matrix of item-cluster correlations (loadings)
corCorrelation matrix of the clusters
correctedCorrelation matrix of the clusters, raw correlations below the diagonal, alpha on diagonal, corrected for reliability above the diagonal
sdCluster standard deviations
alphaalpha reliabilities of the clusters
G6G6* Modified estimated of Guttman Lambda 6
countNumber 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 (http://sapa-project.org) 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

Examples

Run this code

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)

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