\name{corFA}
\alias{corFA}

\title{ Insert Communalities in the Diagonal of a Correlation or a Covariance Matrix}

\description{
  This function inserts communalities in the diagonal of a correlation/covariance matrix.
 }

\usage{
 corFA(R, method="ginv")
 }

\arguments{
  \item{R}{      numeric:   correlation matrix.}
  \item{method}{ character: actually only \code{"giv"} is supplied to compute the
                 approximation of the communalities by maximum correlation.}
 }
 
\value{
  \item{values}{ numeric: matrix of correlation/covariance with communalities
                 in the diagonal. }
 }
 
\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/}
 }

\seealso{
 \code{\link{plotuScree}},
 \code{\link{nScree}},
 \code{\link{plotnScree}},
 \code{\link{plotParallel}}
 }

\examples{
## LOWER CORRELATION MATRIX WITH ZEROS ON UPPER PART
## From Gorsuch (table 1.3.1)
 gorsuch <- c(
 1,0,0,0,0,0,0,0,0,0,
 .6283, 1,0,0,0,0,0,0,0,0,
 .5631, .7353, 1,0,0,0,0,0,0,0,
 .8689, .7055, .8444, 1,0,0,0,0,0,0,
 .9030, .8626, .6890, .8874, 1,0,0,0,0,0,
 .6908, .9028, .9155, .8841, .8816, 1,0,0,0,0,
 .8633, .7495, .7378, .9164, .9109, .8572, 1,0,0,0,
 .7694, .7902, .7872, .8857, .8835, .8884, .7872, 1,0,0,
 .8945, .7929, .7656, .9494, .9546, .8942, .9434, .9000, 1,0,
 .5615, .6850, .8153, .7004, .6583, .7720, .6201, .6141, .6378, 1)
 
## UPPER CORRELATION MATRIX FILLS WITH UPPER CORRELATION MATRIX
 gorsuch <- makeCor(gorsuch)
 
## REPLACE DIAGONAL WITH COMMUNALITIES
 gorsuchCfa <- corFA(gorsuch)
 gorsuchCfa
 }

\keyword{ multivariate }