R: Parallel Analysis of a Correlation or Covariance Matrix
parallel
R Documentation
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.
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.
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)