R: How well does the factor model fit a correlation matrix. Part...

factor.fit {psych} | R Documentation

## 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.

### 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.

Let

R*= R - FF'

fit = 1 - sum(R*^2)/sum(R^2)

.

The sums are taken for the off diagonal elements.

### Value

fit

### Author(s)

William Revelle

### See Also

`VSS`, `ICLUST`

### Examples

    ## Not run:
    #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

    ## End(Not run)

[Package psych version 1.7.3.21 Index]