fareg {fungible}

Regularized Factor Analysis

Description

This function applies the regularized factoring method to extract an unrotated factor structure matrix.

Usage

fareg(R, numFactors = 1, facMethod = "rls")

Arguments

R

(Matrix) A correlation matrix to be analyzed.

numFactors

(Integer) The number of factors to extract. Default: numFactors = 1.

facMethod

(Character) "rls" for regularized least squares estimation or "rml" for regularized maximum likelihood estimation. Default: facMethod = "rls".

Value

The main output is the matrix of unrotated factor loadings.

• loadings: (Matrix) A matrix of unrotated factor loadings.

• h2: (Vector) A vector of estimated communality values.

• L: (Numeric) Value of the estimated penality parameter.

• Heywood (Logical) TRUE if a Heywood case is detected (this should never happen).

Author(s)

Niels G. Waller ([e-mail])

References

Jung, S. & Takane, Y. (2008). Regularized common factor analysis. New trends in psychometrics, 141-149.

See Also

Other Factor Analysis Routines: BiFAD(), Box26, GenerateBoxData(), Ledermann(), SLi(), SchmidLeiman(), faAlign(), faEKC(), faIB(), faLocalMin(), faMB(), faMain(), faScores(), faSort(), faStandardize(), faX(), fals(), fapa(), fsIndeterminacy(), orderFactors(), print.faMB(), print.faMain(), promaxQ(), summary.faMB(), summary.faMain()

Examples

data("HW")

# load first HW data set

RHW <- cor(x = HW$HW6)

# Compute principal axis factor analysis
fapaOut <- faMain(R = RHW, 
                 numFactors = 3, 
                 facMethod = "fapa", 
                 rotate = "oblimin",
                 faControl = list(treatHeywood = FALSE))


fapaOut$faFit$Heywood
round(fapaOut$h2, 2)

 # Conduct a regularized factor analysis
regOut <- fareg(R = RHW, 
               numFactors = 3,
               facMethod = "rls")
regOut$L
regOut$Heywood


# rotate regularized loadings and align with 
# population structure
regOutRot <- faMain(urLoadings = regOut$loadings,
                   rotate = "oblimin")

# ALign
FHW  <- faAlign(HW$popLoadings, fapaOut$loadings)$F2
Freg <- faAlign(HW$popLoadings, regOutRot$loadings)$F2

AllSolutions <- round(cbind(HW$popLoadings, Freg, FHW),2) 
colnames(AllSolutions) <- c("F1", "F2", "F3", "Fr1", "Fr2", "Fr3", 
                           "Fhw1", "Fhw2", "Fhw3")
AllSolutions


rmsdHW <- rmsd(HW$popLoadings, FHW, 
              IncludeDiag = FALSE, 
              Symmetric = FALSE)

rmsdReg <- rmsd(HW$popLoadings, Freg, 
               IncludeDiag = FALSE, 
               Symmetric = FALSE)

cat("\nrmsd HW =  ", round(rmsdHW,3),
    "\nrmsd reg = ", round(rmsdReg,3))