R/gaussCItwd.R

In micd: Multiple Imputation in Causal Graph Discovery

#' Fisher's z-Test for (Conditional) Independence between Gaussian Variables with Missings
#' 
#' A wrapper for \code{pcalg::\link[pcalg:condIndFisherZ]{gaussCItest}}, 
#' to be used within \code{pcalg::\link[pcalg]{skeleton}}, \code{pcalg::\link[pcalg]{pc}} or 
#' \code{pcalg::\link[pcalg]{fci}} when the data contain missing values. Observations 
#' where at least one of the variables involved in the test is missing are 
#' deleted prior to performing the test (test-wise deletion).
#'
#' @param x,y,S (integer) position of variable X, Y and set of variables S, 
#' respectively, in each correlation matrix in \code{suffStat}. It is tested 
#' whether X and Y are conditionally independent given the subset S of the 
#' remaining variables.
#' @param suffStat \code{data.frame} containing the raw data.
#'
#' @return See \code{pcalg::\link[pcalg:condIndFisherZ]{gaussCItest}} for details on 
#' Fisher's z-test. Test-wise deletion is valid if missingness does not jointly 
#' depend on X and Y.
#' 
#' @return A p-value.
#' 
#' @importFrom stats cor pnorm
#' 
#' @seealso [pcalg::condIndFisherZ()] for complete data, [gaussCItestMI()] for multiply imputed data
#' 
#' @examples
#' 
#' ## load data (numeric variables)
#' dat <- as.matrix(windspeed)
#' 
#' ## delete some observations
#' set.seed(123)
#' dat[sample(1:length(dat), 260)] <- NA
#' 
#' ## analyse data
#' # complete data:
#' suffcomplete <- getSuff(windspeed, test="gaussCItest")
#' gaussCItest(1, 2, c(4,5), suffStat = suffcomplete)
#' 
#' # test-wise deletion: ==========
#' gaussCItwd(1, 2, c(4,5), suffStat = dat)
#' 
#' # list-wise deletion: ==========
#' sufflwd <- getSuff(dat[complete.cases(dat), ], test="gaussCItest")
#' gaussCItest(1, 2, c(4,5), suffStat = sufflwd)
#' 
#' ## use gaussCItwd within pcalg::pc
#' pc.fit <- pc(suffStat = dat, indepTest = gaussCItwd, alpha = 0.01, p = 6)
#' pc.fit
#' 
#' @export
gaussCItwd <- function(x, y, S=NULL, suffStat) {
  
  miss <- apply(suffStat[ ,c(x,y,S)], 1, anyNA)
  C <- stats::cor(suffStat[!miss, c(x,y,S)])
  
  if (anyNA(C)) { return(NA) }
  
  n <- sum(!miss)
  
  if (length(S)==0) {
    z <- pcalg::zStat(1, 2, NULL, C=C, n=n)
  } else {
    z <- pcalg::zStat(1, 2, 3:(2+length(S)), C=C, n=n)
  }
  2 * stats::pnorm(abs(z), lower.tail = FALSE)
}