\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 } \item{loadings}{ numeric: loadings of each variable on 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{ \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}, \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 }