1\name{Schmid} 2\Rdversion{1.1} 3\alias{Schmid} 4\alias{schmid.leiman} 5\alias{West} 6\alias{Chen} 7\docType{data} 8\title{12 variables created by Schmid and Leiman to show the Schmid-Leiman Transformation} 9 10\description{ 11John Schmid and John M. Leiman (1957) discuss how to transform a hierarchical factor structure to a bifactor structure. Schmid contains the example 12 x 12 correlation matrix. schmid.leiman is a 12 x 12 correlation matrix with communalities on the diagonal. This can be used to show the effect of correcting for attenuation. Two additional data sets are taken from Chen et al. (2006). 12} 13\usage{data(Schmid)} 14 15\details{ Two artificial correlation matrices from Schmid and Leiman (1957). One real and one artificial covariance matrices from Chen et al. (2006). 16\itemize{ 17\item Schmid: a 12 x 12 artificial correlation matrix created to show the Schmid-Leiman transformation. 18\item schmid.leiman: A 12 x 12 matrix with communalities on the diagonal. Treating this as a covariance matrix shows the 6 x 6 factor solution 19\item Chen: An 18 x 18 covariance matrix of health related quality of life items from Chen et al. (2006). Number of observations = 403. The first item is a measure of the quality of life. The remaining 17 items form four subfactors: The items are (a) Cognition subscale: ``Have difficulty reasoning 20and solving problems?" ``React slowly to things that were said or done?"; ``Become confused and start several actions at a time?" ``Forget where you 21put things or appointments?"; ``Have difficulty concentrating?" (b) Vitality 22subscale: ``Feel tired?" ``Have enough energy to do the things you want?" (R) 23``Feel worn out?" ; ``Feel full of pep?" (R). (c) Mental health subscale: ``Feel 24calm and peaceful?"(R) ``Feel downhearted and blue?"; ``Feel very 25happy"(R) ; ``Feel very nervous?" ; ``Feel so down in the dumps nothing could 26cheer you up? (d) Disease worry subscale: ``Were you afraid because of your health?"; ``Were you frustrated about your health?"; ``Was your health a worry in your life?" . 27\item West: A 16 x 16 artificial covariance matrix from Chen et al. (2006). 28} 29} 30\source{ 31John Schmid Jr. and John. M. Leiman (1957), The development of hierarchical factor solutions.Psychometrika, 22, 83-90. 32 33F.F. Chen, S.G. West, and K.H. Sousa.(2006) A comparison of bifactor and second-order models of quality of life. Multivariate Behavioral Research, 41(2):189-225, 2006. 34 35} 36\references{ 37 38Y.-F. Yung, D.Thissen, and L.D. McLeod. (1999) On the relationship between the higher-order factor model and the hierarchical factor model. Psychometrika, 64(2):113-128, 1999. 39 40 41 42} 43\examples{ 44data(Schmid) 45cor.plot(Schmid,TRUE) 46print(fa(Schmid,6,rotate="oblimin"),cut=0) #shows an oblique solution 47round(cov2cor(schmid.leiman),2) 48cor.plot(cov2cor(West),TRUE) 49} 50\keyword{datasets} 51