structureSim function

Population or Simulated Sample Correlation Matrix from a Given Factor Structure Matrix

The structureSim function returns a population and a sample correlation matrices from a predefined congeneric factor structure.

structureSim(fload, reppar = 30, repsim = 100, N, quantile = 0.95,
  model = "components", adequacy = FALSE, details = TRUE,
  r2limen = 0.75, all = FALSE)

Arguments

• fload: matrix: loadings of the factor structure

• reppar: numeric: number of replications for the parallel analysis

• repsim: numeric: number of replications of the matrix correlation simulation

• N: numeric: number of subjects

• quantile: numeric: quantile for the parallel analysis

• model: character: "components" or "factors"

• adequacy: logical: if TRUE prints the recovered population matrix from the factor structure

• details: logical: if TRUE outputs details of the repsim

  simulations

• r2limen: numeric: R2 limen value for the R2 Nelson index

• all: logical: if TRUE computes the Bentler and Yuan index (very long computing time to consider)

Returns

• values: the output depends of the logical value of details. If FALSE, returns only statistics about the eigenvalues: mean, median, quantile, standard deviation, minimum and maximum. If TRUE, returns also details about the repsim simulations. If adequacy = TRUE returns the recovered factor structure

Examples

## Not run:

# .......................................................
# Example inspired from Zwick and Velicer (1986, table 2, p. 437)
## ...................................................................
 nFactors  <- 3
 unique    <- 0.2
 loadings  <- 0.5
 nsubjects <- 180
 repsim    <- 30
 zwick     <- generateStructure(var=36, mjc=nFactors, pmjc=12,
                                loadings=loadings,
                                unique=unique)
## ...................................................................

# Produce statistics about a replication of a parallel analysis on
# 30 sampled correlation matrices

 mzwick.fa <-  structureSim(fload=as.matrix(zwick), reppar=30,
                            repsim=repsim, N=nsubjects, quantile=0.5,
                            model="factors")

 mzwick    <-  structureSim(fload=as.matrix(zwick), reppar=30,
                            repsim=repsim, N=nsubjects, quantile=0.5, all=TRUE)

# Very long execution time that could be used only with model="components"
# mzwick    <-  structureSim(fload=as.matrix(zwick), reppar=30,
#                            repsim=repsim, N=nsubjects, quantile=0.5, all=TRUE)

 par(mfrow=c(2,1))
 plot(x=mzwick,    nFactors=nFactors, index=c(1:14), cex.axis=0.7, col="red")
 plot(x=mzwick.fa, nFactors=nFactors, index=c(1:11), cex.axis=0.7, col="red")
 par(mfrow=c(1,1))

 par(mfrow=c(2,1))
 boxplot(x=mzwick,    nFactors=3, cex.axis=0.8, vLine="blue", col="red")
 boxplot(x=mzwick.fa, nFactors=3, cex.axis=0.8, vLine="blue", col="red",
         xlab="Components")
 par(mfrow=c(1,1))
# ......................................................
## End(Not run)

References

Raiche, G., Walls, T. A., Magis, D., Riopel, M. and Blais, J.-G. (2013). Non-graphical solutions for Cattell's scree test. Methodology, 9(1), 23-29.

Zwick, W. R. and Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99, 432-442.

See Also

principalComponents, iterativePrincipalAxis, rRecovery

Author(s)

Gilles Raiche

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

Universite du Quebec a Montreal

raiche.gilles@uqam.ca