\name{rRecovery} \alias{rRecovery} \title{ Test of Recovery of a Correlation or a Covariance matrix from a Factor Analysis Solution } \description{ The \code{rRecovery} function returns a verification of the quality of the recovery of the initial correlation or covariance matrix by the factor solution. } \usage{ rRecovery(R, loadings, diagCommunalities=FALSE) } \arguments{ \item{R}{ numeric: initial correlation or covariance matrix} \item{loadings}{ numeric: loadings from a factor analysis solution} \item{diagCommunalities}{ logical: if \code{TRUE}, the correlation between the initial solution and the estimated one will use a correlation of one in the diagonal. If \code{FALSE} (default) the diagonal is not used in the computation of this correlation.} } \value{ \item{R}{ numeric: initial correlation or covariance matrix } \item{recoveredR}{ numeric: recovered estimated correlation or covariance matrix } \item{difference}{ numeric: difference between initial and recovered estimated correlation or covariance matrix} \item{cor}{ numeric: Pearson correlation between initial and recovered estimated correlation or covariance matrix. Computations depend on the logical value of the \code{communalities} argument. } } \seealso{ \code{\link{componentAxis}}, \code{\link{iterativePrincipalAxis}}, \code{\link{principalAxis}} } \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) # Replace upper diagonal with lower diagonal RU <- diagReplace(R, upper=TRUE) nFactors <- 2 loadings <- principalAxis(RU, nFactors=nFactors, communalities="component")$loadings rComponent <- rRecovery(RU,loadings, diagCommunalities=FALSE)$cor loadings <- principalAxis(RU, nFactors=nFactors, communalities="maxr")$loadings rMaxr <- rRecovery(RU,loadings, diagCommunalities=FALSE)$cor loadings <- principalAxis(RU, nFactors=nFactors, communalities="multiple")$loadings rMultiple <- rRecovery(RU,loadings, diagCommunalities=FALSE)$cor round(c(rComponent = rComponent, rmaxr = rMaxr, rMultiple = rMultiple), 3) # ....................................................... } \keyword{ utilities }