R/citest-mvn.R

In gRim: Graphical Interaction Models

##########################################################################
#'
#' @title Test for conditional independence in the multivariate normal
#'     distribution
#' @description Test for conditional independence in the multivariate
#'     normal distribution.
#' @name citest-mvn
#'
##########################################################################
#'
#' @param x A list with elements \code{cov} and \code{n.obs} (such as
#'     returned from calling \code{cov.wt()} on a dataframe. See
#'     examples below.)
#' @param set A specification of the test to be made. The tests are of
#'     the form u and v are independent condionally on S where u and v
#'     are variables and S is a set of variables. See 'details' for
#'     details about specification of \code{set}.
#' @param statistic The test statistic to be used, valid choices are
#'     \code{"DEV"} and \code{"F"}.
#' @param \dots Additional arguments
#'
#' @details
#' 
#' \code{set} can be 1) a vector or 2) a right-hand sided formula in
#' which variables are separated by '+'. In either case, it is tested
#' if the first two variables in the \code{set} are conditionally
#' independent given the remaining variables in \code{set}.  (Notice
#' an abuse of the '+' operator in the right-hand sided formula: The
#' order of the variables does matter.)
#' 
#' If \code{set} is \code{NULL} then it is tested whether the first
#' two variables are conditionally independent given the remaining
#' variables.
#' 
#' \code{x} must be a list with components \code{cov} and \code{n.obs}
#' such as returned by calling \code{cov.wt( , method='ML')} on a
#' dataframe.
#' 
#' @return An object of class `citest` (which is a list).
#' @author Søren Højsgaard, \email{sorenh@@math.aau.dk}
#' @seealso \code{\link{ciTest}}, \code{\link{ciTest_table}},
#'     \code{\link{ciTest_df}}, \code{\link{ciTest_mvn}},
#'     \code{\link{chisq.test}}
#' @keywords htest
#' @examples
#' 
#' data(carcass)
#' ciTest(cov.wt(carcass, method='ML'), set=~Fat11 + Meat11 + Fat12)
#' ciTest_mvn(cov.wt(carcass, method='ML'), set=~Fat11 + Meat11 + Fat12)
#' 
#' @export 
ciTest_mvn <- function(x, set=NULL, statistic="DEV", ...){

    if(any(is.na(match(c("cov", "n.obs"), names(x))))){
        stop("Expecting a list with components 'cov' and 'n.obs'\n")
    }
    
    if (is.null(set)){
        set   <- colnames(x$cov)
        x$cov <- x$cov[set, set]
    } else {
        if (inherits(set, c("formula", "character"))){
            set <- unlist(rhsFormula2list(set))
            set <- colnames(x$cov)[pmatch(set, colnames(x$cov))]
            x$cov <- x$cov[set, set]
        }
    }
    .ciTest_mvn_internal(x, statistic=statistic, ...) ## Should <set> go here...
}

### This is the workhorse.
###
.ciTest_mvn_internal <- function(x, statistic="DEV", ...){

    statistic <- match.arg(toupper(statistic), c("DEV", "F"))
    method <- if (identical(statistic, "DEV")) "CHISQ" else "F"

    S     <- x$cov
    n.obs <- x$n.obs
    
    vn <- colnames(S)
    K  <- length(vn)
    
    R   <- vn[-(1:2)]
    v1R <- c(vn[1],R)
    v2R <- c(vn[2],R)
    
    v1R.idx <- match(v1R, vn)
    v2R.idx <- match(v2R, vn)
    R.idx   <- match(R,   vn)
    
    d <- n.obs * (log(det(S[v1R.idx, v1R.idx, drop=FALSE])) +
                  log(det(S[v2R.idx, v2R.idx, drop=FALSE])) -
                  log(det(S[R.idx, R.idx, drop=FALSE])) - log(det(S))
    )
    
    num.df <- 1
    switch(statistic,
           "DEV"={
               tobs     <- d
               denom.df <- NULL
               p        <- 1 - pchisq(tobs, df=num.df)
           },
           "F"={
               tobs     <- (exp(d / n.obs) - 1) * (n.obs - K)
               denom.df <- n.obs - K
               p        <- 1 - pf(tobs, num.df, denom.df)
           })
    
    ans <- list(statistic=tobs, p.value=p, df=num.df, denom.df=denom.df,
                statname=statistic, method=method, varNames=vn)
    class(ans) <- "citest"
    ans
}