psych (version 1.0-17)

schmid: Apply the Schmid Leiman transformation to a correlation matrix

Description

One way to find omega is to do a factor analysis of the original data set, rotate the factors obliquely, do a Schmid Leiman transformation, and then find omega. Here is the code for Schmid Leiman. The S-L transform takes a factor or PC solution, transforms it to an oblique solution, factors the oblique solution to find a higher order (g ) factor, and then residualizes g out of the the group factors.

Usage

schmid(model, nfactors = 3, pc = "pa",...)

Arguments

model

A correlation matrix

nfactors

Number of facdtors to extract

pc

pc="pa" for principal axes, pc="pc" for principal components, pc="mle" for maximum likelihood

...

Allows additional parameters to be passed to the factoring routines

Value

• sl
  loadings on g + nfactors group factors, communalities, uniqueness
• orthog
  original orthogonal factor loadings
• fcor
  correlations among the transformed factors
• gload
  loadings of the lower order factors on g
• ...

Details

Schmid Leiman orthogonalizations are typical in the ability domain, but are not seen as often in the non-cognitive personality domain. S-L is one way of finding the loadings of items on the general factor for estimating omega.

References

http://personality-project.org/r/r.omega.html gives an example taken from Jensen and Weng, 1994 of a S-L transformation.

See Also

omega, ICLUST,VSS

Examples

##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function (model, nfactors = 3, pc = "pa",...) 
{
    if (pc=="pc") {
        fact <- principal(model, nfactors,...)
    } else {if (pc=="pa") {fact <- factor.pa(model, nfactors,...) } else {
        fact <- factanal(x, covmat = model, factors = nfactors,...)
    }}
       obminfact <- oblimin(loadings(fact))
    rownames(obminfact$loadings) <- attr(model,"dimnames")[[1]]
    fload <- obminfact$loadings
    factr <- t(obminfact$Th) %*% (obminfact$Th)
    gfactor <- factanal(x, covmat = factr, factors = 1)
    gload <- loadings(gfactor)
    gprimaryload <- fload %*% gload
    colnames(gprimaryload) <- "g factor"
    u2 <- 1 - diag(fload %*% t(fload))
    h2 <- 1 - u2
    uniq <- 1 - fload^2
    guniq <- 1 - gprimaryload^2
    Ig <- matrix(0, ncol = nfactors, nrow = nfactors)
    diag(Ig) <- gload
    primeload <- fload %*% Ig
    uniq2 <- 1 - uniq - primeload^2
    sm <- sqrt(uniq2)
    schmid <- list(sl = cbind(gprimaryload, sm, h2, u2), orthog = fload, 
        fcor = factr, gloading = gload)
}