\name{polychor.matrix}
\alias{polychor.matrix}
\alias{Yule2poly.matrix}
\alias{phi2poly.matrix}
\alias{Yule2phi.matrix}
\title{Phi or Yule coefficient matrix  to polychoric coefficient matrix}
\description{Given a matrix of phi or Yule correlation coefficients and a vector of marginals, use the polychoric function to convert these to polychoric correlations.   

Some older correlation matrices were reported as matrices of Phi or of Yule correlations.  That is, correlations were found from the two by two table of counts:
 \cr
\tabular{lll}{
\tab a \tab b \cr
\tab c \tab d  \cr
}
Yule Q is (ad - bc)/(ad+bc). \cr

With marginal frequencies of a+b, c+d, a+c, b+d.

Given a square matrix of such correlations, and the proportions for each variable that are in the a + b cells, it is possible to reconvert each correlation into a two by two table and then estimate the corresponding polychoric correlation (using John Fox's polychor function. 
}
\usage{
Yule2poly.matrix(x, v)
phi2poly.matrix(x, v)
Yule2phi.matrix(x, v)
}
%- maybe also 'usage' for other objects documented here.
\arguments{
  \item{x}{a matrix of phi or Yule  coefficients }
  \item{v}{A vector of marginal frequencies  }
}
\details{These functions call \code{\link{Yule2poly}},  \code{\link{Yule2phi}} or \code{\link{phi2poly}} for each cell of the matrix. See those functions for more details.  See \code{\link{phi.demo}} for an example.

}
\value{A matrix of correlations
}

\author{ William Revelle}

\examples{
demo <- phi.demo() #compare the phi (lower off diagonal and polychoric correlations (upper off diagonal)
#show the result from poly.mat
round(demo$tetrachoric$rho,2)
#show the result from phi2poly
#tetrachorics above the diagonal, phi below the diagonal 
round(demo$phis,2) 


}
\keyword{ models }% at least one, from doc/KEYWORDS
\keyword{ multivariate }% __ONLY ONE__ keyword per line