\name{TimelessNormalPM}
\alias{TimelessNormalPM}
\title{A multivariate normal proficiency model at a single time point
}
\description{

  This class represents a proficiency model as a multivariate normal
  distribution.  In particular, the latent variable is considered to be
  a multivariate normal variable.  The parameter associated with this
  model is a \code{\link{TimelessNormalParam}}.  The prior distributions
  of the two parameter components are independent:  the mean vector has
  a normal prior and the covariance matrix has an inverse Wishert prior.
  
}
\usage{
TimelessNormalPM(...)
}
\arguments{
  \item{\dots}{
    The hyperparameters of the normal model.  See details.
  }
}
\details{

  This is an extension of \code{ProficiencyModel} for cases where the
  latent variable follows a multivariate normal distribution.  It is
  called \sQuote{Timeless} because it is at a single time point.  The
  parameter is a \code{TimelessNormalParam}.

  The prior distribution for the parameters is \code{mu ~
  dnorm(muMean,muStd)} and \code{Sigma ~ diwish(Smean,Sdf)}.  The four
  hyperparameters should be specified in the \ldots argument to the
  constructor function: 

  \describe{
    \item{muMean}{Mean of prior distribution for mean vector.}
    \item{varWeight}{Scale factor for covariance matrix.}
    \item{precMean}{Mean matrix for precision (inverse covariance) 
      matrix.}
    \item{Sdf}{Degrees of freedom for prior distribution for precision
    (inverse covariance) matrix.} 
  }

  This class ignores \code{background} variables.
  
}
\value{

  An object of class \code{TimelessNormalPM}.
}
\references{

  The following link:
  \url{http://thaines.com/content/misc/gaussian_conjugate_prior_cheat_sheet.pdf}
  is helpful in explaining the parameterization and the optimization
  updating.
  
}
\author{Russell Almond}
\seealso{
  Methods:
  \code{\link{nlatent}}, \code{\link{drawPMParam}},
  \code{\link{drawInitialLatent}}, \code{\link{lpriorLatent}},
  \code{\link{lpriorParam}}

  Superclass: \code{\link{ProficiencyModel}}

  Subclasses:
  
}
\examples{

pm1 <-
  TimelessNormalPM(muMean=c(Mechanics=2,Fluency=2),  varWeight=3,
                   precScale=solve(matrix(c(.7,.3,.3,.7),2,2)), Sdf=3)

stopifnot(nlatent(pm1)==2L)

pm1.p1 <- drawPMParam(pm1)
## Construct an invalid param (singular covariance) to test error
## handling.
pm.pX <- TimelessNormalParam(mu=c(0,0),Sigma=matrix(1,2,2))


lpriorPMParam(pm1,pm1.p1)
stopifnot(!is.finite(lpriorPMParam(pm1,pm.pX))) # -Inf


pm1.stud10 <- drawInitialLatent(pm1,10,param=pm1.p1)
print("Next command should generate an error.")
stopifnot(class(try(drawInitialLatent(pm1,10,param=pm.pX))) == "try-error")

lpriorLatent(pm1,pm1.stud10,param=pm1.p1)
stopifnot(!is.finite(lpriorLatent(pm1,pm1.stud10,param=pm.pX))) # -Inf

## Test again using internal parameter
parameters(pm1) <- drawPMParam(pm1)
pm1.stud5 <- drawInitialLatent(pm1,5)
lpriorLatent(pm1,pm1.stud5)


stud1k <- drawInitialLatent(pm1,1000,param=pm1.p1)

##MLE
pparam1.mle <- optimalPMParams(pm1,stud1k,Bayes=FALSE)$param

##MAP
pparam1.map <- optimalPMParams(pm1,stud1k,Bayes=TRUE)$param


}
\keyword{ class }
\keyword{ distribution }