MLE {MCARtest}

Compute the MLE under MCAR in a contingency table using the EM algorithm, given complete and incomplete observations.

Description

Compute the MLE under MCAR in a contingency table using the EM algorithm, given complete and incomplete observations.

Usage

MLE(p0h, n0, pSh, nS, bS, M, Niter, loglik = FALSE)

Arguments

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.

Niter

An integer giving the number of iterations to be used in the EM algorithm.

loglik

A logical value indicating whether or not the log likelihoods at each step of the EM algorithm should be an output. Defaults to FALSE.

Value

The output of the EM algorithm, approximating the MLE for the probability mass function on the joint space.

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

MLE(p0h,n0,pSh,nS,bS,M,50)

trace=MLE(p0h,n0,pSh,nS,bS,M,50,loglik=TRUE)[[2]]
plot(1:50,trace,type="l")