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

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 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 R procedures using mat.regress.

The original correlation is pre and post multiplied by the (transpose) of the keys matrix.

Value

Note

See SAPA e.g., Revelle, W. (2006) Synthetic Aperture Personality Assessment. Invited paper at the Midwestern Psychological Association Annual Meeting, Chicago, May, 2006. pdf available at http://personality-project.org/revelle/publications/sapa.mpa.key.pdf

Author(s)

Maintainer: William Revelle revelle@northwestern.edu

References

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

See Also

factor2cluster, mat.regress, alpha.scale, score.items

Examples

## Not run: 
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)
## End(Not run)
#$cor
#       first second
#first    1.0    0.6
#second   0.6    1.0
#
#$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 

## The function is currently defined as
function(keys,r.mat,correct=TRUE) { #function to extract clusters according to the key vector
#default is to correct for attenuation and show this above the diagonal
#find the correlation matrix of scales made up of items defined in a keys matrix
#(e.g., extracted by factor2cluster) 
 #takes as input the keys matrix as well as a correlation matrix of all the items
 if(!is.matrix(keys)) keys <- as.matrix(keys) 
 #keys are sometimes a data frame - must be a matrix
 covar <- t(keys) %*% r.mat %*% keys    #matrix algebra is our friend
 var <- diag(covar)
 sd.inv <- 1/sqrt(var)
 ident.sd <- diag(sd.inv,ncol = length(sd.inv))
 cluster.correl <- ident.sd %*% covar  %*% ident.sd
 key.var <- diag(t(keys) %*% keys)
 key.alpha <- ((var-key.var)/var)*(key.var/(key.var-1))
 key.alpha[is.nan(key.alpha)] <- 1 #if only 1 variable to the cluster, then alpha is undefined
 key.alpha[!is.finite(key.alpha)] <- 1   
 colnames(cluster.correl) <- names(key.alpha)
 rownames(cluster.correl) <- names(key.alpha)
 if (correct) {cluster.corrected <- correct.cor(cluster.correl,t(key.alpha))
 return(list(cor=cluster.correl,sd=sqrt(var),corrected= cluster.corrected,size=key.var))
 }  #correct for attenuation
 else {
 return(list(cor=cluster.correl,sd=sqrt(var),alpha=key.alpha,size=key.var))}
 }