psych (version 1.0-17)

cluster.fit: cluster Fit: fit of the cluster model to a correlation matrix

Description

How well does the cluster model found by ICLUST fit the original correlation matrix? A similar algorithm factor.fit is found in VSS. This function is internal to ICLUST but has more general use as well. In general, the cluster model is a Very Simple Structure model of complexity one. That is, every item is assumed to represent only one factor/cluster. Cluster fit is an analysis of how well this model reproduces a correlation matrix. Two measures of fit are given: cluster fit and factor fit. Cluster fit assumes that variables that define different clusters are orthogonal. Factor fit takes the loadings generated by a cluster model, finds the cluster loadings on all clusters, and measures the degree of fit of this somewhat more complicated model. Because the cluster loadings are similar to, but not identical to factor loadings, the factor fits found here and by factor.fit will be similar.

Usage

cluster.fit(original, load, clusters, diagonal = FALSE, digits = 2)

Arguments

original

The original correlation matrix being fit

load

Cluster loadings -- that is, the correlation of individual items with the clusters, corrected for item overlap

clusters

The cluster structure

diagonal

Should we fit the diagonal as well?

digits

Number of digits to be used in the output

Value

• clusterfit
  The cluster model is a reduced form of the factor loading matrix. That is, it is the product of the elements of the cluster matrix * the loading matrix.
• factorfit
  How well does the complete loading matrix reproduce the correlation matrix?

Details

The cluster model is similar to the factor model: R is fitted by C'C. Where C <- Cluster definition matrix x the loading matrix. How well does this model approximate the original correlation matrix and how does this compare to a factor model?

The fit statistic is a comparison of the original (squared) correlations to the residual correlations. Fit = 1 - r*2/r2 where r* is the residual correlation of data - model and model = C'C.

References

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

See Also

VSS, ICLUST, factor2cluster, cluster.cor, factor.fit

Examples

r.mat<- Harman74.cor$cov
 iq.clus <- ICLUST(r.mat,nclusters =2)
 fit <- cluster.fit(r.mat,iq.clus$loadings,iq.clus$clusters)
 fit
 

## The function is currently defined as
function (original, load, clusters, diagonal = FALSE, digits = 2) 
{
    sqoriginal <- original * original
    totaloriginal <- sum(sqoriginal) - diagonal * sum(diag(sqoriginal))
    model <- load %*% t(load)
    residual <- original - model
    sqresid <- residual * residual
    totalresid <- sum(sqresid) - diagonal * sum(diag(sqresid))
    fit <- 1 - totalresid/totaloriginal
    model.1 <- (load * clusters) %*% t(load * clusters)
    residual <- original - model.1
    sqresid <- residual * residual
    totalresid <- sum(sqresid) - diagonal * sum(diag(sqresid))
    fit.1 <- 1 - totalresid/totaloriginal
    cluster.fit <- list(clusterfit = round(fit.1, digits), factorfit = round(fit, 
        digits))
  }