Create a population or sample correlation matrix with hierachical structure.

Description

Create a population hierarchical correlation matrix from a set of factor loadings and factor intercorrelations. Samples of size n may be then be drawn from this population. Return either the sample data, sample correlations, or population correlations. This is used to create sample data sets for instruction and demonstration.

Usage

make.hierarchical(gload, fload, n = 0, raw = FALSE)

Arguments

Details

Many personality and cognitive tests have a hierarchical factor structure. For demonstration purposes, it is useful to be able to create such matrices, either with population values, or sample values.

Given a matrix of item factor loadings (fload) and of loadings of these factors on a general factor (gload), we create a population correlation matrix by using the general factor law (R = F' theta F where theta = g'g).

To create sample values, we use the mvrnorm function from MASS.

The default is to return population correlation matrices. Sample correlation matrices are generated if n >0. Raw data are returned if raw = TRUE.

Value

a matrix of correlations or a data matrix

Author(s)

William Revelle

References

http://personality-project.org/r/r.omega.html

See Also

omega, schmid, ICLUST, VSS, mvrnorm

Examples

## Not run: 
gload <-  gload<-matrix(c(.9,.8,.7),nrow=3)    # a higher order factor matrix
fload <-matrix(c(                    #a lower order (oblique) factor matrix
           .8,0,0,
           .7,0,.0,
           .6,0,.0,
            0,.7,.0,
            0,.6,.0,
            0,.5,0,
            0,0,.6,
            0,0,.5,
            0,0,.4),   ncol=3,byrow=TRUE)
            
jensen <- make.hierarchical(gload,fload)    #the test set used by omega
round(jensen,2)     
## End(Not run)

## The function is currently defined as
function (gload,fload,n=0,raw=FALSE) {
   require(MASS) 
  fcor <- gload %*% t(gload)           #the factor correlation matrix
  diag(fcor) <-1                       #put ones on the diagonal
  model <-  fload%*% fcor %*% t(fload) #the model correlation matrix for oblique factors
  diag(model)<- 1                       # put ones along the diagonal 
  if(n>0) {
        model <- mvrnorm(n = n,mu, Sigma=model, tol = 1e-6, empirical = FALSE)
        if (!raw ) { model <- cor(model) } }
  make.hierarchical <- model }