% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/rRecovery.r
\name{rRecovery}
\alias{rRecovery}
\title{Test of Recovery of a Correlation or a Covariance matrix from a Factor
Analysis 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. }
}
\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.
}
\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)
# .......................................................


}
\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}
}
\keyword{utilities}