\name{EvidenceModel}
\alias{EvidenceModel}
\alias{Q}
\alias{Q<-}
\title{A class encapulated the relationship between observable outcomes
  and proficiencies}
\description{

  A evidence model is essentially a likelihood for observed outcome
  variables given the proficiency profile for the student.  This is an
  abstract class for evidence models.  Specific instances are are always
  associated with an evidence model parameter object.
  
}
\usage{
EvidenceModel(...)
Q(em)
Q(em) <- value
}
\arguments{
  \item{\dots}{
    Parts of the evidence model:  these will depend on the subclass.
    This list should include a term \code{Q} which provides the Q-matrix
    for the evidence model.
  }
  \item{em}{An object of class \code{EvidenceModel}}
  \item{value}{A new Q-matrix for the evidence model (see details).}
}
\details{

  An \code{EvidenceMode} object provides a likelihood, as well as
  drawing methods for a collection of \emph{observable}
  variables.  The the function \code{\link{nobserved}} gives the number
  of observables associated with an evidence model.

  It is a subclass of \code{\link{AbstractModel}} which supplies the
  \code{param} slot and the \code{\link{parameters}} method for
  accessing it.

  The distribution of the observable variables should depend on the
  proficiency profile associated with a given student.  The Q-matrix
  describes which observables depend on which proficiency variables.  In
  the Q-matrix, the rows correspond to the observables and the columns
  corrspond to the proficiency variables.  In the traditional view, the
  entries are 1 if the proficiency is releveant for the observable, and
  0 if it is irrelevant.  This package allows arbitrary values for the
  relevant case.  See the function \code{\link{scaleQ}} which scales the
  Q-matrix so that the sum of squares for each row are 1.

  Generally speaking there will be a set of parameters associated
  with this model.  Often the goal of a calibration exercise is to
  estimate this parameter.  The generic function
  \code{\link{drawEMParam}} samples a value of this parameter.  The
  function \code{\link{optimalParams}} attempts to find a set of values
  for the parameters which maximizes the posterior distribution of the
  observed data.

  Given the parameter and a proficiency profile, it is possible to
  calculate the likelihood of a given set of observables or draw a
  random set of observables.  The functions
  \code{\link{drawObs}} and \code{\link{llikeObs}} perform
  those operations.


}
\value{
  This is an abstract class, and must be extended by other classes.

  The following slots are supplied by the abstract class:
  \item{Q}{A matrix linking the proficiency variables to the observed outcomes.}

  It is an extension of \code{\link{AbstractModel}} which supplies the
  \code{param} and \code{paramType} slots.

}
\references{
%% ~put references to the literature/web site here ~
}
\author{Russell Almond}

\seealso{
  Methods:
  \code{Q}
  \code{\link{nobserved}}, \code{\link{drawEMParam}},
  \code{\link{drawObs}}, \code{\link{llikeObs}},
  \code{\link{optimalParams}}

  Superclasses:
  \code{\link{AbstractModel}}

  Subclasses:
  \code{\link{FixedQNormalEM}}

}
\examples{

## This is not directly executable.  See NormalEM.R for an sample implementation.
}
\keyword{ distribution }
\keyword{ classes }