https://github.com/cran/nFactors
Tip revision: 0d077e574bae60fadd67bd0683ad4277c58f593a authored by Gilles Raiche on 10 October 2022, 11:20:07 UTC
version 2.4.1.1
version 2.4.1.1
Tip revision: 0d077e5
iterativePrincipalAxis.Rd
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/iterativePrincipalAxis.r
\name{iterativePrincipalAxis}
\alias{iterativePrincipalAxis}
\title{Iterative Principal Axis Analysis}
\usage{
iterativePrincipalAxis(R, nFactors = 2, communalities = "component",
iterations = 20, tolerance = 0.001)
}
\arguments{
\item{R}{numeric: correlation or covariance matrix}
\item{nFactors}{numeric: number of factors to retain}
\item{communalities}{character: initial values for communalities (\code{"component", "maxr", "ginv" or "multiple"})}
\item{iterations}{numeric: maximum number of iterations to obtain a solution}
\item{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
}
\description{
The \code{iterativePrincipalAxis} function returns a principal axis analysis with
iterated communality estimates. Four different choices of initial communality
estimates are given: maximum correlation, multiple correlation (usual and
generalized inverse) or estimates based
on the sum of the squared principal component analysis loadings. Generally, statistical
packages initialize the communalities at the multiple correlation value.
Unfortunately, this strategy cannot always deal with singular correlation or
covariance matrices.
If a generalized inverse, the maximum correlation or the estimated communalities
based on the sum of loadings
are used instead, then a solution can be computed.
}
\examples{
## ................................................
# Example 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 with lower diagonal
RU <- diagReplace(R, upper=TRUE)
nFactors <- 2
fComponent <- iterativePrincipalAxis(RU, nFactors=nFactors,
communalities="component")
fComponent
rRecovery(RU,fComponent$loadings, diagCommunalities=FALSE)
fMaxr <- iterativePrincipalAxis(RU, nFactors=nFactors,
communalities="maxr")
fMaxr
rRecovery(RU,fMaxr$loadings, diagCommunalities=FALSE)
fMultiple <- iterativePrincipalAxis(RU, nFactors=nFactors,
communalities="multiple")
fMultiple
rRecovery(RU,fMultiple$loadings, diagCommunalities=FALSE)
# .......................................................
}
\references{
Kim, J.-O. and Mueller, C. W. (1978). \emph{Introduction to factor analysis. What it
is and how to do it}. Beverly Hills, CA: Sage.
Kim, J.-O. and Mueller, C. W. (1987). \emph{Factor analysis. Statistical methods and
practical issues}. Beverly Hills, CA: Sage.
}
\seealso{
\code{\link{componentAxis}}, \code{\link{principalAxis}}, \code{\link{rRecovery}}
}
\author{
Gilles Raiche \cr Centre sur les Applications des Modeles de
Reponses aux Items (CAMRI) \cr Universite du Quebec a Montreal\cr
\email{raiche.gilles@uqam.ca}
\cr \cr David Magis \cr Departement de mathematiques \cr Universite de Liege
\cr \email{David.Magis@ulg.ac.be}
}
\keyword{multivariate}