parallel: Parallel Analysis of a Correlation or Covariance Matrix

In nFactors: Parallel Analysis and Other Non Graphical Solutions to the Cattell Scree Test

Parallel Analysis of a Correlation or Covariance Matrix

Description

This function gives the distribution of the eigenvalues of correlation or a covariance matrices of random uncorrelated standardized normal variables. The mean and a selected quantile of this distribution are returned.

Usage

parallel(subject = 100, var = 10, rep = 100, cent = 0.05,
  quantile = cent, model = "components", sd = diag(1, var), ...)

Arguments

subject	numeric: nmber of subjects (default is 100)
var	numeric: number of variables (default is 10)
rep	numeric: number of replications of the correlation matrix (default is 100)
cent	depreciated numeric (use quantile instead): quantile of the distribution on which the decision is made (default is 0.05)
quantile	numeric: quantile of the distribution on which the decision is made (default is 0.05)
model	character: "components" or "factors"
sd	numeric: vector of standard deviations of the simulated variables (for a parallel analysis on a covariance matrix)
...	variable: other parameters for the "mvrnorm", corr or cov functions

Details

Note that if the decision is based on a quantile value rather than on the mean, care must be taken with the number of replications (rep). In fact, the smaller the quantile (cent), the bigger the number of necessary replications.

Value

eigen	Data frame consisting of the mean and the quantile of the eigenvalues distribution
eigen$mevpea	Mean of the eigenvalues distribution
eigen$sevpea	Standard deviation of the eigenvalues distribution
eigen$qevpea	quantile of the eigenvalues distribution
eigen$sqevpea	Standard error of the quantile of the eigenvalues distribution
subject	Number of subjects
variables	Number of variables
centile	Selected quantile

Otherwise, returns a summary of the parallel analysis.

Author(s)

Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
[e-mail]

References

Drasgow, F. and Lissak, R. (1983) Modified parallel analysis: a procedure for examining the latent dimensionality of dichotomously scored item responses. Journal of Applied Psychology, 68(3), 363-373.

Hoyle, R. H. and Duvall, J. L. (2004). Determining the number of factors in exploratory and confirmatory factor analysis. In D. Kaplan (Ed.): The Sage handbook of quantitative methodology for the social sciences. Thousand Oaks, CA: Sage.

Horn, J. L. (1965). A rationale and test of the number of factors in factor analysis. Psychometrika, 30, 179-185.

See Also

plotuScree, nScree, plotnScree, plotParallel

Examples

## SIMPLE EXAMPLE OF A PARALLEL ANALYSIS
## OF A CORRELATION MATRIX WITH ITS PLOT
 data(dFactors)
 eig      <- dFactors$Raiche$eigenvalues
 subject  <- dFactors$Raiche$nsubjects
 var      <- length(eig)
 rep      <- 100
 quantile <- 0.95
 results  <- parallel(subject, var, rep, quantile)

 results

## IF THE DECISION IS BASED ON THE CENTILE USE qevpea INSTEAD
## OF mevpea ON THE FIRST LINE OF THE FOLLOWING CALL
 plotuScree(x    = eig,
            main = "Parallel Analysis"
            )

 lines(1:var,
       results$eigen$qevpea,
       type="b",
       col="green"
       )


## ANOTHER SOLUTION IS SIMPLY TO
 plotParallel(results)

nFactors documentation built on Oct. 10, 2022, 5:07 p.m.