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.

`cluster.loadings(keys, r.mat, correct = TRUE,SMC=TRUE)`

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

A matrix of item-cluster correlations (loadings)

Correlation matrix of the clusters

Correlation matrix of the clusters, raw correlations below the diagonal, alpha on diagonal, corrected for reliability above the diagonal

Cluster standard deviations

alpha reliabilities of the clusters

G6* Modified estimated of Guttman Lambda 6

Number of items in the cluster

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 (https://www.sapa-project.org/) application where we are interested in item-whole correlations of items and composite scales.

For information about SAPA see Revelle et al, 2010, 2016. For information about SAPA based measures of ability, see https://icar-project.org.

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

).

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

Revelle, W., Wilt, J., and Rosenthal, A. (2010) Individual Differences in Cognition: New Methods for examining the Personality-Cognition Link In Gruszka, A. and Matthews, G. and Szymura, B. (Eds.) Handbook of Individual Differences in Cognition: Attention, Memory and Executive Control, Springer.

Revelle, W, Condon, D.M., Wilt, J., French, J.A., Brown, A., and Elleman, L.G. (2016) Web and phone based data collection using planned missing designs. In Fielding, N.G., Lee, R.M. and Blank, G. (Eds). SAGE Handbook of Online Research Methods (2nd Ed), Sage Publcations.

```
# NOT RUN {
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)
# }
```

Run the code above in your browser using DataLab