parallel function

Parallel Analysis of a Correlation or Covariance Matrix

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.

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

Returns

• 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.

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.

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)

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

Author(s)

Gilles Raiche

Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)

Universite du Quebec a Montreal

raiche.gilles@uqam.ca