factor.model {psych}

Find R = F F' + U2 is the basic factor model

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. Find this reproduced matrix. Used by factor.fit, VSS, ICLUST, etc.

Usage

factor.model(f,Phi=NULL,U2=TRUE)

Arguments

f

A matrix of loadings.

Phi

A matrix of factor correlations

U2

Should the diagonal be model by ff' (U2 = TRUE) or replaced with 1's (U2 = FALSE)

Value

A correlation or covariance matrix.

Author(s)

[e-mail]
https://personality-project.org/revelle.html

References

Gorsuch, Richard, (1983) Factor Analysis. Lawrence Erlebaum Associates.
Revelle, W. In preparation) An Introduction to Psychometric Theory with applications in R (https://personality-project.org/r/book/)

See Also

ICLUST.graph,ICLUST.cluster, cluster.fit , VSS, omega

Examples

f2 <- matrix(c(.9,.8,.7,rep(0,6),.6,.7,.8),ncol=2)
mod <- factor.model(f2)
round(mod,2)