iterativePrincipalAxis {nFactors}R Documentation

Iterative Principal Axis Analysis

Description

The iterativePrincipalAxis function return a principal axis analysis with iterated communalities estimates. Three different choices of initial communalities estimates are given: maximum corelation, multiple correlation or estimates based on the sum of the sqared principal component analysis loadings. Generally statistical packages initialize the the communalities at the multiple correlation value. Unfortunately, this strategy cannot deal with singular correlation or covariance matrices. If the maximum correlation or the estimated communalities based on the sum of loading are used insted, then a solution can be computed.

Usage

 iterativePrincipalAxis(R,
                        nFactors=2,
                        communalities="component",
                        iterations=20,
                        tolerance=0.001)
 

Arguments

R numeric: correlation or covariance matrix
nFactors numeric: number of factors to retain
communalities character: initial values for communalities ("component", "maxr", or "multiple")
iterations numeric: maximum number of iterations to obtain a solution
tolerance numeric: minimal difference in the estimated communalities after a given iteration

Value

values numeric: variance of each component
varExplained numeric: variance explained by each component
varExplained numeric: cumulative variance explained by each component
loadings numeric: loadings of each variable on each component
iterations numeric: maximum number of iterations to obtain a solution
tolerance numeric: minimal difference in the estimated communalities after a given iteration

Author(s)

Gilles Raiche, Universite du Quebec a Montreal raiche.gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

See Also

componentAxis, principalAxis, rRecovery

Examples

# .......................................................
# Exemple from Kim and Mueller (1978, p. 10)
# Population: upper diagonal
# Simulated sample: lower diagnonal
 R <- matrix(c( 1.000, .6008, .4984, .1920, .1959, .3466,
                .5600, 1.000, .4749, .2196, .1912, .2979,
                .4800, .4200, 1.000, .2079, .2010, .2445,
                .2240, .1960, .1680, 1.000, .4334, .3197,
                .1920, .1680, .1440, .4200, 1.000, .4207,
                .1600, .1400, .1200, .3500, .3000, 1.000),
                nrow=6, byrow=TRUE)

# Factor analysis: Principal axis factoring with iterated communalities -
# Kim and Mueller (1978, p. 23)
# Replace upper diagonal by lower diagonal
 RU         <- diagReplace(R, upper=TRUE)
 nFactors   <- 2
 fComponent <- iterativePrincipalAxis(RU, nFactors=nFactors, communalities="component")
 fComponent
 rRecovery(RU,fComponent$loadings, communalities=FALSE)

 fMaxr      <- iterativePrincipalAxis(RU, nFactors=nFactors, communalities="maxr")
 fMaxr
 rRecovery(RU,fMaxr$loadings, communalities=FALSE)

 fMultiple  <- iterativePrincipalAxis(RU, nFactors=nFactors, communalities="multiple")
 fMultiple
 rRecovery(RU,fMultiple$loadings, communalities=FALSE)
# .......................................................
 

[Package nFactors version 2.2 Index]