##### https://github.com/cran/nFactors
Tip revision: b6fe861
rRecovery.rd
\name{rRecovery}
\alias{rRecovery}
\title{ Test of Recovery of a Correlation or a Covariance matrix from a Facor Analysis Solution }

\description{
The \emph{rRecovery} function return a verification of the quality of the recovery
of the initial correlation or covariance matrix by the factor solution.
}

\usage{
}

\arguments{
\item{R}{             numeric: initial correlation or covariance matrix}
\item{communalities}{ logical: if \emph{TRUE}, the correlation between the initail
solution and the estimated one will use a correlation
of one in the diagonal. If \emph{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. Computions depend on the
logical value of the \emph{communalities} argument. }
}

\seealso{
}

\author{
Gilles Raiche, Universite du Quebec a Montreal
\email{raiche.gilles@uqam.ca}, \url{http://www.er.uqam.ca/nobel/r17165/}
}

\examples{
# .......................................................
# Exemple 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 by lower diagonal
RU         <- diagReplace(R, upper=TRUE)
nFactors   <- 2
loadings   <- principalAxis(RU, nFactors=nFactors, communalities="component")$loadings rComponent <- rRecovery(RU,loadings, communalities=FALSE)$cor

loadings   <- principalAxis(RU, nFactors=nFactors, communalities="maxr")$loadings rMaxr <- rRecovery(RU,loadings, communalities=FALSE)$cor

loadings   <- principalAxis(RU, nFactors=nFactors, communalities="multiple")$loadings rMultiple <- rRecovery(RU,loadings, communalities=FALSE)$cor

round(c(rComponent = rComponent,
rmaxr      = rMaxr,
rMultiple  = rMultiple), 3)
# .......................................................

}

\keyword{ multivariate }