\name{qpCItest}
\alias{qpCItest}
\alias{qpCItest,ExpressionSet-method}
\alias{qpCItest,data.frame-method}
\alias{qpCItest,matrix-method}

\title{
Conditional independence test
}
\description{
Performs a conditional independence test between two variables given
a conditioning set.
}
\usage{
\S4method{qpCItest}{ExpressionSet}(X, i=1, j=2, Q=c(), I=NULL, R.code.only=FALSE)
\S4method{qpCItest}{data.frame}(X, i=1, j=2, Q=c(), I=NULL, long.dim.are.variables=TRUE,
                                exact.test=TRUE, R.code.only=FALSE)
\S4method{qpCItest}{matrix}(X, i=1, j=2, Q=c(), I=NULL, n=NULL, long.dim.are.variables=TRUE,
                            exact.test=TRUE, R.code.only=FALSE)
}
\arguments{
  \item{X}{data set where the test should be performed. It can be either an
       \code{ExpressionSet} object, a data frame, or a matrix. If it is a matrix
       and the matrix is squared then this function assumes the matrix corresponds
       to the sample covariance matrix of the data and the sample size parameter
       \code{n} should be provided.}
  \item{i}{index or name of one of the two variables in \code{X} to test.}
  \item{j}{index or name of the other variable in \code{X} to test.}
  \item{Q}{indexes or names of the variables in \code{X} forming the conditioning set.}
  \item{I}{indexes or names of the variables in \code{X} that are discrete. See details
       below regarding this argument.}
  \item{n}{number of observations in the data set. Only necessary when the
       sample covariance matrix is provided through the \code{X} parameter.}
  \item{long.dim.are.variables}{logical; if TRUE it is assumed
       that when data are in a data frame or in a matrix, the longer dimension
       is the one defining the random variables (default); if FALSE, then random
       variables are assumed to be at the columns of the data frame or matrix.}
  \item{exact.test}{logical; if \code{FALSE} an asymptotic conditional independence
       test is employed with mixed (i.e., continuous and discrete) data;
       if \code{TRUE} (default) then an exact conditional independence test with
       mixed data is employed. See details below regarding this argument.}
  \item{R.code.only}{logical; if FALSE then the faster C implementation is used
       (default); if TRUE then only R code is executed.}
}
\details{
Note that the size of possible \code{Q} sets should be in the range 1 to
\code{min(p,n-3)}, where \code{p} is the number of variables and \code{n}
the number of observations. The computational cost increases linearly with
the number of variables in \code{Q}.

When \code{I} is set different to \code{NULL} then mixed graphical model theory
is employed and, concretely, it is assumed that the data comes from an homogeneous
conditional Gaussian distribution. In this setting further restrictions to the
maximum value of \code{q} apply, concretely, it cannot be smaller than
\code{p} plus the number of levels of the discrete variables involved in the
marginal distributions employed by the algorithm. By default, with
\code{exact.test=TRUE}, an exact test for conditional independence is employed,
otherwise an asymptotic one will be used. Full details on these features can
be found in Tur and Castelo (2011).
}
\value{
A list with two members, the value of the statistic and its corresponding
P-value of rejecting the null hypothesis of conditional independence.
}
\references{
Castelo, R. and Roverato, A. A robust procedure for
Gaussian graphical model search from microarray data with p larger than n,
\emph{J. Mach. Learn. Res.}, 7:2621-2650, 2006.

Tur, I. and Castelo, R. Learning mixed grpahical models from data with p larger than n,
In \emph{Proc. 27th Conference on Uncertainty in Artificial Intelligence}, Barcelona, 2011.
}
\author{R. Castelo and A. Roverato}
\seealso{
  \code{\link{qpNrr}}
  \code{\link{qpEdgeNrr}}
}
\examples{
require(mvtnorm)

nObs <- 100 ## number of observations to simulate

## the following adjacency matrix describes an undirected graph
## where vertex 3 is conditionally independent of 4 given 1 AND 2
A <- matrix(c(FALSE,  TRUE,  TRUE,  TRUE,
              TRUE,  FALSE,  TRUE,  TRUE,
              TRUE,   TRUE, FALSE, FALSE,
              TRUE,   TRUE, FALSE, FALSE), nrow=4, ncol=4, byrow=TRUE)
Sigma <- qpG2Sigma(A, rho=0.5)

X <- rmvnorm(nObs, sigma=as.matrix(Sigma))

qpCItest(X, i=3, j=4, Q=1, long.dim.are.variables=FALSE)

qpCItest(X, i=3, j=4, Q=c(1,2), long.dim.are.variables=FALSE)
}
\keyword{models}
\keyword{multivariate}