psych (version 1.0-17)

factor.fit: How well does the factor model fit a correlation matrix. Part of the VSS package

Description

The basic factor or principal components model is that a correlation or covariance matrix may be reproduced by the product of a factor loading matrix times its transpose: F'F or P'P. One simple index of fit is the 1 - sum squared residuals/sum squared original correlations. This fit index is used by VSS, ICLUST, etc.

Usage

factor.fit(r, f)

Arguments

r

a correlation matrix

f

A factor matrix of loadings.

Value

• fit

Details

There are probably as many fit indices as there are psychometricians. This fit is a plausible estimate of the amount of reduction in a correlation matrix given a factor model. Note that it is sensitive to the size of the original correlations. That is, if the residuals are small but the original correlations are small, that is a bad fit.

See Also

VSS, ICLUST

Examples

#compare the fit of 4 to 3 factors for the Harman 24 variables
fa4 <- factanal(x,4,covmat=Harman74.cor$cov)
round(factor.fit(Harman74.cor$cov,fa4$loading),2)
#[1] 0.9
fa3 <- factanal(x,3,covmat=Harman74.cor$cov)
round(factor.fit(Harman74.cor$cov,fa3$loading),2)
#[1] 0.88

## The function is currently defined as
function (r,f) {
     r2 <-sum( r*r)
     rstar <- factor.residuals(r,f)
     rstar2 <- sum(rstar*rstar)
     fit<- 1- rstar2/r2
     return(fit) }