principalComponents.rd
\name{principalComponents}
\alias{principalComponents}
\title{ Principal Component Analysis }

\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.
}

\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 }
}

\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{
}

\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}, \url{http://www.er.uqam.ca/nobel/r17165/}
}

\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)
# .......................................................
}

\keyword{ multivariate }