% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/principalComponents.r
\name{principalComponents}
\alias{principalComponents}
\title{Principal Component Analysis}
\usage{
principalComponents(R)
}
\arguments{
\item{R}{numeric: correlation or covariance matrix}
}
\value{
\item{values}{ numeric: variance of each component }
\item{varExplained}{ numeric: variance explained by each component }
\item{varExplained}{ numeric: cumulative variance explained by each
component } \item{loadings}{ numeric: loadings of each variable on each
component }
}
\description{
The \code{principalComponents} function returns a principal component
analysis.  Other R functions give the same results, but
\code{principalComponents} is customized mainly for the other factor
analysis functions available in the \pkg{nfactors} package. In order to
retain only a small number of components the \code{componentAxis} function
has to be used.
}
\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 component -
# Kim et Mueller (1978, p. 21)
# Replace upper diagonal with lower diagonal
 RU <- diagReplace(R, upper=TRUE)
 principalComponents(RU)

# Replace lower diagonal with upper diagonal
 RL <- diagReplace(R, upper=FALSE)
 principalComponents(RL)
# .......................................................

}
\references{
Joliffe, I. T. (2002). \emph{Principal components analysis} (2th
Edition).  New York, NJ: Springer-Verlag.

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{iterativePrincipalAxis}},
\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}
}
\keyword{multivariate}