loglik0 {MCARtest}

Compute the log likelihood of a probability mass function, under MCAR, given complete and incomplete data

Description

Compute the log likelihood of a probability mass function, under MCAR, given complete and incomplete data

Usage

loglik0(p, p0h, n0, pSh, nS, bS, M)

Arguments

p

A probability mass function whose log likelihood is to be calculated.

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.

Value

The value of the log likelihood.

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

loglik0(p0,p0h,n0,pSh,nS,bS,M)