psych (version 1.0-77)

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, fm = "minres",digits=2,rotate="oblimin",n.obs=NA,option="equal",...)

Arguments

model

A correlation matrix

nfactors

Number of factors to extract

fm

fm="pa" for principal axes, fm="pc" for principal components, fm = "minres" for minimum residual (OLS), pc="mle" for maximum likelihood

digits

if digits not equal NULL, rounds to digits

rotate

The default, oblimin, produces somewhat more correlated factors than the alternative, simplimax. The third option is the promax criterion

n.obs

Number of observations, used to find fit statistics if specified. Will be calculated if input is raw data

option

When asking for just two group factors, option can be for "equal", "first" or "second"

...

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
• oblique
  oblique factor loadings
• phi
  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.

A typical example would be in the study of anxiety and depression. A general neuroticism factor (g) accounts for much of the variance, but smaller group factors of tense anxiety, panic disorder, depression, etc. also need to be considerd.

An alternative model is to consider hierarchical cluster analysis techniques such as ICLUST.

Requires the GPArotation package.

Although 3 factors are the minimum number necessary to define the solution uniquely, it is occasionally useful to allow for a two factor solution. There are three possible options for this condition: setting the general factor loadings between the two lower order factors to be "equal" which will be the sqrt(oblique correlations between the factors) or to "first" or "second" in which case the general factor is equated with either the first or second group factor. A message is issued suggesting that the model is not really well defined.

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, omega.graph, fa.graph, ICLUST,VSS

Examples

jen <- sim.hierarchical()  #create a hierarchical demo
if(!require(GPA.rotation)) {message("I am sorry, you must have GPArotation installed to use schmid.")} else {jen <- schmid(jen,digits=2)   #use the oblimin rotation
p.jen <- schmid(jen,rotate="promax") #use the promax rotation
}