\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}(data, i=1, j=2, Q=c(), R.code.only=FALSE)
\S4method{qpCItest}{data.frame}(data, i=1, j=2, Q=c(),
                                long.dim.are.variables=TRUE, R.code.only=FALSE)
\S4method{qpCItest}{matrix}(data, N=NULL, i=1, j=2, Q=c(),
                            long.dim.are.variables=TRUE, R.code.only=FALSE)
}
\arguments{
  \item{data}{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 is the
       sample covariance matrix of the data and the sample size parameter
       \code{N} should be provided.}
  \item{N}{number of observations in the data set. Only necessary when the
       sample covariance matrix is provided through the \code{data} parameter.}
  \item{i}{index or name of one of the two variables.}
  \item{j}{index or name of the other variable.}
  \item{Q}{indexes or names of the variables forming the conditioning set.}
  \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{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}.
}
\value{
A list with two members, the t-statistic value and the p-value on rejecting
the null hypothesis of 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.
}
\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=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}