nFactors (version 2.1)

parallel: PARALLEL ANALYSIS OF A CORRELATION MATRIX

Description

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

Usage

parallel(subject = 100, 
         var     = 10,
         rep     = 100, 
         cent    = 0.05)

Arguments

subject

Number of subjects (default is 100)

var

Number of variables (default is 10)

rep

Number of replication of the correlation matrix (default is 100)

cent

Centile of the distribution on which the decision is made (default is 0.05)

Value

• eigen
  Data frame consisting of mean and the centile of the eigenvalues distribution
• eigen$mevpea
  Mean of the eigenvalues distribution
• eigen$sevpea
  Standard deviation of the eigenvalues distribution
• eigen$qevpea
  Centile of the eigenvalues distribution
• eigen$sqevpea
  Standard error of the centile of the eigenvalues distribution
• subject
  Number of subjects
• variables
  Number of variables
• centile
  Selected centile
• Otherwise, returns a summary of the parallel analysis.

Details

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

References

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
 cent     <- 0.95
 results  <- parallel(subject,var,rep,cent)

 results

## IF THE DECISION IS BASED ON THE CENTILE USE qevpea INSTEAD
## OF mevpea ON THE FIRST LINE OF THE FOLLOWING CALL
 plotuScree(eig,
             main = "Parallel Analysis"
             )
 lines(1:var, 
       results$eigen$qevpea, 
       type="b", 
       col="green"
       )


## ANOTHER SOLUTION IS SIMPLY TO
 plotParallel(results)
 

## RESULTS
# $eigen
#        mevpea     sevpea    qevpea    sevpea.1
# V1  1.5421626 0.09781869 1.4037201 0.020670924
# V2  1.3604323 0.05728471 1.2768656 0.012105332
# V3  1.2249034 0.04704870 1.1482431 0.009942272
# V4  1.1189148 0.03662555 1.0605407 0.007739666
# V5  1.0221635 0.04048780 0.9599296 0.008555832
# V6  0.9318382 0.04053704 0.8647949 0.008566237
# V7  0.8381154 0.04026090 0.7758708 0.008507883
# V8  0.7493151 0.04729122 0.6727706 0.009993521
# V9  0.6568985 0.04664676 0.5756055 0.009857334
# V10 0.5552561 0.04942935 0.4800394 0.010445348

# $subject
# [1] 100

# $variables
# [1] 10

# $centile
# [1] 0.05

# attr(,"class")
# [1] "parallel"