R/FuchsTest.R

In MCARtest: Optimal Nonparametric Testing of Missing Completely at Random

#' Carry out Fuchs's test of MCAR in a contingency table, given complete and incomplete observations.
#'
#' @param p0h An empirical mass function calculated using complete observations.
#' @param n0 An integer giving the number of complete observations used to calculate \code{p0h}.
#' @param pSh A sequence of empirical mass functions calculated using incomplete observations.
#' @param nS A sequence of integers giving the numbers of incomplete observations used to calculate \code{pSh}.
#' @param bS A binary matrix specifying the set of observation patterns. Each row encodes a single pattern.
#' @param M A vector of positive integers giving the alphabet sizes of the discrete variables.
#' @param Niter An integer giving the number of iterations to be used in the EM algorithm for calculating the null MLE.
#'
#' @return The p-value of Fuchs's test, found by comparing the log likelihood ratio statistic to the chi-squared distribution
#' with the appropriate number of degrees of freedom. Described in \insertCite{Fuchs1982;textual}{MCARtest}.
#' @export
#'
#' @references \insertRef{Fuchs1982}{MCARtest}
#'
#' @importFrom stats pchisq
#'
#' @examples
#' bS=matrix(c(1,1,0, 1,0,1, 0,1,1),byrow=TRUE,ncol=3) # Our canonical 3d example
#' M=c(2,2,2)
#' n0=200
#' nS=c(200,200,200)
#'
#' pS=c(0.125,0.375,0.375,0.125,0.250,0.250,0.250,0.250,0.100,0.400,0.400,0.100)
#' P12=pS[1:4]; P13=pS[5:8]; P23=pS[9:12]
#' X12=t(rmultinom(1,size=nS[1],prob=P12)/nS[1])
#' X13=t(rmultinom(1,size=nS[2],prob=P13)/nS[2])
#' X23=t(rmultinom(1,size=nS[3],prob=P23)/nS[3])
#' pSh=cbind(X12,X13,X23)
#'
#' p0=array(0.125,dim=c(2,2,2))
#' p0h=array(rmultinom(1,n0,p0),dim=M)/n0
#'
#' FuchsTest(p0h,n0,pSh,nS,bS,M,50)


FuchsTest=function(p0h,n0,pSh,nS,bS,M,Niter){
  ll1=loglik1(p0h,pSh,p0h,n0,pSh,nS,bS,M)

  nullMLE=MLE(p0h,n0,pSh,nS,bS,M,Niter)
  ll0=loglik0(nullMLE,p0h,n0,pSh,nS,bS,M)
  TestStat=2*(ll1-ll0)

  A=Amatrix(bS,M)
  df=nrow(A)-nrow(bS)
  pval=1-pchisq(TestStat,df)
  return(pval)
}