\name{OffsetConjunctive}
\alias{OffsetDisjunctive}
\alias{OffsetConjunctive}
\title{
  Conjunctive combination function with one difficulty per parent.
}
\description{
  These functions take a vector of \dQuote{effective theta} values for a
  collection of parent variables and calculates the effective theta value
  for the child variable according to the named rule.  Used in
  calculating DiBello--Samejima and DiBello--Normal probability tables.
  These versions have a single slope parameter (alpha) and one
  difficulty parameter per parent variable.
}
\usage{
OffsetConjunctive(theta, alpha, betas)
OffsetDisjunctive(theta, alpha, betas)
}
\arguments{
  \item{theta}{A matrix of effective theta values whose columns correspond to
    parent variables and whose rows correspond to possible skill profiles.}
  \item{alpha}{A single common discrimination parameter.  (Note these
    function expect discrimination parameters and not log discrimination
    parameters as used in \code{\link{calcDSTable}}.)} 
  \item{betas}{A vector of difficulty (-intercept) parameters.  Its
    length should be the same as the number of columns in \code{theta}.}
}
\details{
  For \code{OffsetConjunctive}, the combination function for each row is:
  \deqn{alpha*min(theta[1]-betas[1], ..., theta[K]-beta[K])}

  For \code{OffsetDisjunctive}, the combination function for each row is:
  \deqn{alpha*max(theta[1]-betas[1], ..., theta[K]-beta[K])}

}
\value{
  A vector of normal deviates corresponding to the effective theta
  value.  Length is the number of rows of \code{thetas}.
}
\references{
  Almond, R.G., Mislevy, R.J., Steinberg, L.S., Yan, D. and Williamson, D.M.
  (2015). \emph{Bayesian Networks in Educational Assessment.}
  Springer.  Chapter 8.

  Almond, R.G., DiBello, L., Jenkins, F., Mislevy, R.J.,  
Senturk, D., Steinberg, L.S. and Yan, D. (2001) Models for Conditional
Probability Tables in Educational Assessment.  \emph{Artificial
Intelligence and Statistics 2001}  Jaakkola and Richardson (eds).,
Morgan Kaufmann, 137--143.  
}
\author{Russell Almond}
\seealso{
  \code{\link{effectiveThetas}},\code{\link{calcDSTable}},
  \code{\link{calcDNTable}},\code{\link{calcDPCTable}},
  \code{\link{Compensatory}},
  \code{\link{eThetaFrame}}
}
\note{
  These functions expect the unlogged discrimination parameters, while
  \code{calcDSTable} expect the log of the discrimination parameters.
  The rationale is that log discrimination is bound away from zero, and
  hence a more natural space for MCMC algorithms.  However, it is poor
  programming design, as it is liable to catch the unwary.

  These functions are meant to be used as structure functions in the
  DiBello--Samejima and DiBello--Normal models.  Other structure
  functions are possible and can be excepted by those functions as long
  as they have the same signature as these functions.

  Note that the offset conjunctive and disjunctive model don't really
  make much sense in the no parent case.  Use \code{\link{Compensatory}}
  instead. 
}
\examples{
  skill <- c("High","Medium","Low")
  thetas <- expand.grid(list(S1=(3:1 -2), S2 = (3:1 -2)))
  OffsetDisjunctive(thetas, 1.0, c(S1=0.25,S2=-0.25))
  OffsetConjunctive(thetas, 1.0, c(S1=0.25,S2=-0.25))
  eThetaFrame(list(S1=skill,S2=skill), 1.0, c(S1=0.25,S2=-0.25),
              "OffsetConjunctive")
  eThetaFrame(list(S1=skill,S2=skill), 1.0, c(S1=0.25,S2=-0.25),
              "OffsetDisjunctive")
}
% R documentation directory.
\keyword{distribution}