psych (version 1.0-23)

fa.parallel: Scree plots of data or correlation matrix compared to random ``parallel" matrix

Description

One way to determine the number of factors or components in a data matrix or a correlation matrix is to examine the ``scree" plot of the successive eigenvalues. Sharp breaks in the plot suggest the appropriate number of components or factors to extract. ``Parallel" analyis is an alternative technique that compares the scree of the observed data with that of a random data matrix of the same size as the original.

Usage

fa.parallel(x, ncases = 0, main = "Parallel Analysis Scree Plots")

Arguments

x

A data.frame or data matrix of scores. If the matrix is square, it is assumed to be a correlation matrix. Otherwise, correlations (with pairwise deletion) will be found

ncases

ncases=0 implies a data matrix/data.frame. Otherwise, how many cases were used to find the correlations.

main

a title for the analysis

Value

• A plot of the eigen values for the original data, a resampling of the original data, and of a equivalent size matrix of random normal deviates.

Details

Cattell's ``scree" test is one of most simple tests for the number of factors problem. Humphreys and Montanelli's ``parallel" analysis is an equally compelling procedure. Other procedures for determining the most optimal number of factors include finding the Very Simple Structure (VSS) criterion (VSS).

See Also

VSS,VSS.plot, VSS.parallel

Examples

#not run
#test.data <- Harman74.cor$cov 
#fa.parallel(test.data,ncases=200)
#
#fa.parallel(attitude) 
#


## The function is currently defined as
function(x,ncases=0,main="Parallel Analysis Scree Plots")  {     
 nsub <- dim(x)[1]
 nvariables <- dim(x)[2]
 if (ncases >0) { nsub <- ncases 
  rx <- x} else {
  rx <- cor(x,use="pairwise")
  }
 if((ncases ==0) && (nsub==nvariables)) {warning("It seems as if you are using a correlation matrix, but have not specified the number of cases")}
  if(ncases == 0) {sampledata <- matrix(sample(unlist(x),size=nsub*nvariables,replace=TRUE),nrow=nsub,ncol=nvariables)
  values.samp <- eigen(cor(sampledata,use="pairwise"))$values}
  simdata=matrix(rnorm(nsub*nvariables),nrow=nsub,ncol=nvariables)    #make up simulated data
  values.sim <- eigen(cor(simdata))$values

 valuesx  <- eigen(rx)$values 

plot(valuesx,type="b", main = main ) 
points(values.sim,type ="b",lty="dotted")
if(ncases ==0) {points(values.samp,type ="b",lty="dashed")}
legend("topright", c("Actual Data", "Simulated Data", "Resampled Data"), col = c(3,4,5),
       text.col = "green4", lty = c("solid","dotted", "dashed"),
       merge = TRUE, bg = 'gray90')
abline(h=1) }