structureSim {nFactors}R Documentation

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

Description

The structureSim function return 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 replication for the parallel analysis
repsim numeric: number of replication 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 print the recovered population matrix from the factor structure
details logical: if TRUE output details of the repsim simulations
r2limen numeric: R2 limen value for the R2 index of Nelson
all logical: if TRUE computes athe Bentler and Yuan index (very long computating 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 return the recovered factor structure

Author(s)

Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
raiche.gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

References

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

# .......................................................
# 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))
# ......................................................
 

[Package nFactors version 2.3.1 Index]