cluster.cor: Find correlations of composite variables from a larger matrix

Description

Given a n x c cluster definition matrix of -1s, 0s, and 1s (the keys) , and a n x n correlation matrix, find the correlations of the composite clusters. The keys matrix can be entered by hand, copied from the clipboard (read.clipboard), or taken as output from the factor2cluster function.

Usage

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

Arguments

keys

A matrix of cluster keys

r.mat

A correlation matrix

correct

TRUE shows both raw and corrected for attenuation correlations

digits

round off answer to digits

Value

corthe (raw) correlation matrix of the clusters
sdstandard deviation of the cluster scores
correctedraw correlations below the diagonal, alphas on diagonal, disattenuated above diagonal
alphaThe (standardized) alpha reliability of each scale.
sizeHow many items are in each cluster?

Details

This is one of the functions used in the SAPA procedures to form synthetic correlation matrices. Given any correlation matrix of items, it is easy to find the correlation matrix of scales made up of those items. This can also be done from the original data matrix using score.items.

A typical use in the SAPA project is to form item composites by clustering or factoring (see factor.pa, ICLUST, principal), extract the clusters from these results (factor2cluster), and then form the composite correlation matrix using cluster.cor. The variables in this reduced matrix may then be used in multiple correlatin procedures using mat.regress. The original correlation is pre and post multiplied by the (transpose) of the keys matrix. If some correlations are missing from the original matrix this will lead to missing values (NA) for scale intercorrelations based upon those lower level correlations. Because the alpha estimate of reliability is based upon the correlations of the items rather than upon the covariances, this estimate of alpha is sometimes called ``standardized alpha". If the raw items are available, it is useful to compare standardized alpha with the raw alpha found using score.items. They will differ substantially only if the items differ a great deal in their variances.

Examples

Run this code

data(attitude)
keys <- matrix(c(1,1,1,0,0,0,0,
                 0,0,0,1,1,1,1),ncol=2)
colnames(keys) <- c("first","second")
r.mat <- cor(attitude)
cluster.cor(keys,r.mat)
#$cor
#       first second
#first    1.0    0.6
#second   0.6    1.0
#
#$sd
# first second 
#  2.57   3.01 
#
#$corrected
#       first second
#first   0.82   0.77
#second  0.60   0.74
#
#$size
# first second 
#     3      4

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