MCARtest (version 1.2.1)

EMiteration: Perform one step of the EM algorithm for finding the MLE under MCAR in a contingency table.

Description

Perform one step of the EM algorithm for finding the MLE under MCAR in a contingency table.

Usage

EMiteration(pt, p0h, n0, pSh, nS, bS, M)

Value

The updated probability mass function on the joint space.

Arguments

pt

An input probability mass function on the joint space, to be updated.

p0h

An empirical mass function calculated using complete observations.

n0

An integer giving the number of complete observations used to calculate p0h.

pSh

A sequence of empirical mass functions calculated using incomplete observations.

nS

A sequence of integers giving the numbers of incomplete observations used to calculate pSh.

bS

A binary matrix specifying the set of observation patterns. Each row encodes a single pattern.

M

A vector of positive integers giving the alphabet sizes of the discrete variables.

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

EMiteration(p0,p0h,n0,pSh,nS,bS,M)