nFactors (version 2.3.3)

generateStructure: Generate a Factor Structure Matrix.

Description

The generateStructure function returns a mjc factor structure matrix. The number of variables per major factor pmjc is equal for each factor. The argument pmjc must be divisible by nVar. The arguments are strongly inspired from Zick and Velicer (1986, p. 435-436) methodology.

Usage

generateStructure(var, mjc, pmjc, loadings, unique)

Arguments

var

numeric: number of variables

mjc

numeric: number of major factors (factors with practical significance)

pmjc

numeric: number of variables that load significantly on each major factor

loadings

numeric: loadings on the significant variables on each major factor

unique

numeric: loadings on the non significant variables on each major factor

Value

values

numeric matrix: factor structure

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

# NOT RUN {
# .......................................................
# Example inspired from Zwick and Velicer (1986, table 2, p. 437)
## ...................................................................
 unique=0.2; loadings=0.5
 zwick1 <- generateStructure(var=36, mjc=6, pmjc= 6, loadings=loadings,
                             unique=unique)
 zwick2 <- generateStructure(var=36, mjc=3, pmjc=12, loadings=loadings,
                             unique=unique)
 zwick3 <- generateStructure(var=72, mjc=9, pmjc= 8, loadings=loadings,
                             unique=unique)
 zwick4 <- generateStructure(var=72, mjc=6, pmjc=12, loadings=loadings,
                             unique=unique)
 sat=0.8
## ...................................................................
 zwick5 <- generateStructure(var=36, mjc=6, pmjc= 6, loadings=loadings,
                             unique=unique)
 zwick6 <- generateStructure(var=36, mjc=3, pmjc=12, loadings=loadings,
                             unique=unique)
 zwick7 <- generateStructure(var=72, mjc=9, pmjc= 8, loadings=loadings,
                             unique=unique)
 zwick8 <- generateStructure(var=72, mjc=6, pmjc=12, loadings=loadings,
                             unique=unique)
## ...................................................................

# nsubjects <- c(72, 144, 180, 360)
# require(psych)
# Produce an usual correlation matrix from a congeneric model
 nsubjects <- 72
 mzwick5   <- sim.structure(fx=as.matrix(zwick5), n=nsubjects)
 mzwick5$r

# Factor analysis: recovery of the factor structure
 iterativePrincipalAxis(mzwick5$model, nFactors=6,
                        communalities="ginv")$loadings
 iterativePrincipalAxis(mzwick5$r    , nFactors=6,
                        communalities="ginv")$loadings
 factanal(covmat=mzwick5$model,         factors=6)
 factanal(covmat=mzwick5$r    ,         factors=6)
 
# Number of components to retain
 eigenvalues  <- eigen(mzwick5$r)$values
 aparallel    <- parallel(var      = length(eigenvalues),
                          subject  = nsubjects,
                          rep      = 30,
                          quantile = 0.95,
                          model="components")$eigen$qevpea
 results <- nScree(x         = eigenvalues,
                   aparallel = aparallel)
 results$Components
 plotnScree(results)
 
# Number of factors to retain
 eigenvalues.fa  <- eigen(corFA(mzwick5$r))$values
 aparallel.fa    <- parallel(var      = length(eigenvalues.fa),
                             subject  = nsubjects,
                             rep      = 30,
                             quantile = 0.95,
                             model="factors")$eigen$qevpea
 results.fa <- nScree(x      = eigenvalues.fa,
                   aparallel = aparallel.fa,
                   model     ="factors")
 results.fa$Components
 plotnScree(results.fa)
# ......................................................
 
# }