psych (version 1.0-97)

sim.structure: Create correlation matrices or data matrices with a particular measurement and structural model

Description

Structural Equation Models decompose correlation or correlation matrices into a measurement (factor) model and a structural (regression) model. sim.structural creates data sets with known measurement and structural properties. Population or sample correlation matrices with known properties are generated. Optionally raw data are produced.

It is also possible to specify a measurement model for a set of x variables separately from a set of y variables. They are then combined into one model with the correlation structure between the two sets.

Usage

sim.structural(fx=NULL,Phi=NULL,fy=NULL,f=NULL,n=0,raw=FALSE)																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																																		
make.structural(fx=NULL,Phi=NULL,fy=NULL,f=NULL,n=0,raw=FALSE)  #deprecated

Arguments

fx

The measurement model for x

Phi

The structure matrix of the latent variables

fy

The measurement model for y

f

The measurement model

n

Number of cases to simulate. If n=0, the population matrix is returned.

raw

if raw=TRUE, raw data are returned as well.

Value

• model
  The implied population correlation matrix
• reliability
  The population reliability values
• r
  The sample correlation matrix
• observed
  If raw=TRUE, a sample data matrix

Details

Given the measurement model, fx and the structure model Phi, the model is f Given the model, raw data are generated using the mvnorm function.

A special case of a structural model are one factor models such as parallel tests, tau equivalent tests, and congneneric tests. These may be created by letting the structure matrix = 1 and then defining a vector of factor loadings. Alternatively, make.congeneric will do the same.

References

Revelle, W. (in preparation) An Introduction to Psychometric Theory with applications in R. Springer. at http://personality-project.org/r/book/

See Also

make.hierarchical for another structural model and make.congeneric for the one factor case. structure.list and structure.list for making symbolic structures.

Examples

fx <-matrix(c( .9,.8,.6,rep(0,4),.6,.8,-.7),ncol=2)              
fy <- matrix(c(.6,.5,.4),ncol=1)
rownames(fx) <- c("V","Q","A","nach","Anx")
rownames(fy)<- c("gpa","Pre","MA")
Phi <-matrix( c(1,0,.7,.0,1,.7,.7,.7,1),ncol=3)
gre.gpa <- sim.structural(fx,Phi,fy)
print(gre.gpa,2)  
round(correct.cor(gre.gpa$model,gre.gpa$reliability),2)  #correct for attenuation to see structure

congeneric <- sim.structural(f=c(.9,.8,.7,.6)) # a congeneric model 
congeneric