structureSim {nFactors}

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

Description

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

Usage

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)

Value

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

Author(s)

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

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

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)