\name{drawObs}
\alias{drawObs}
\alias{llikeObs}
\title{Draws observable values or calculates their likelihood
}
\description{

  The function \code{drawObs} takes an evidence model, an
  associated parameter object, and a matrix of latent profiles and
  generates an observed response vector for each profile.

  The function \code{llObs} takes an evidence model, its
  associated parameter, and a matrix of latent profiles, and a matrix of
  observation vectors and calculates
  the log priors for those observations.
  
}
\usage{
drawObs(em, latent, background = NA, QQ=Q(em), param=parameters(em))
llikeObs(em, obs, latent, background = NA, QQ=Q(em), param=parameters(em))
}
\arguments{
  \item{em}{
    An object of class \code{\link{EvidenceModel}}.
  }
  \item{obs}{
    A matrix of observation vectors corresponding whose likelihood
    should be evaluated.  It should be true that either
    \code{nrow(latent) == nrow(obs)} or \code{nrow(latent)==1}.  It
    should also be true that \code{ncol(obs) == nobserved(em)}.
  }
  \item{latent}{
    A matrix of latent vectors corresponding to the individuals
    represented in the observations.  It should be true that
    \code{ncol(latent) == ncol(QQ)}.
  }
  \item{background}{
    An optional set of background (demographic) variables.  Some
    proficiency model types ignore background variables.
  }
  \item{QQ}{A Q-matrix to use (only needed if different from the one
    stored with the evidence model).}
  \item{param}{
    An object representing the parameters of \code{em}.  The type
    required is determined by the class of \code{em}.
  }
}
\details{

  The function \code{drawObs} draws an observation vector for each
  latent profile in \code{latent}.

  The function \code{llObs} evaluates the prior distribution at
  each row of the \code{obs} matrix.  A log prior value is generated
  for each row of \code{obs}.

  Each concrete subclass of \code{EvidenceModel} has a corresponding
  parameter class.  The class of the \code{param} argument should be the
  appropriate parameter class for the \code{em} argument.
}
\value{

  The function \code{drawObs} returns a matrix with
  \code{nrow(latent)} rows and \code{nobserved(em)} columns.

  The function \code{llObs} returns a vector log prior values
  with a number of elements equal to \code{nrow(obs)}.
  
}
\references{
%% ~put references to the literature/web site here ~
}
\author{Russell Almond}
\seealso{
  \code{\link{ProficiencyModel}}
  
}
\examples{
pm1 <-
  TimelessNormalPM(muMean=c(Mechanics=2,Fluency=2),  varWeight=3,
                   precScale=solve(matrix(c(.7,.3,.3,.7),2,2)), Sdf=3)
parameters(pm1) <- drawPMParam(pm1)

pm1.stud10 <- drawInitialLatent(pm1,10)

Q <- matrix(c(1,0,1,1),2,2)
em1 <- new("FixedQNormalEM", Q=Q,
           zMean=c(Mechanics=0,Fluency=0),  zStd=diag(c(1,1)),
           Rmean=matrix(c(.7,.3,.3,.7),2,2), Rdf=3,
           hMean=c(1,1,.5), hStd=rep(.25,3))
parameters(em1) <- drawEMParam(em1)


em1.obs10 <- drawObs(em1,pm1.stud10)
llikeObs(em1,em1.obs10,pm1.stud10)


}
\keyword{ distribution }
\keyword{ random }