MCARtest (version 1.2.1)

FuchsTest: Carry out Fuchs's test of MCAR in a contingency table, given complete and incomplete observations.

Description

Carry out Fuchs's test of MCAR in a contingency table, given complete and incomplete observations.

Usage

FuchsTest(p0h, n0, pSh, nS, bS, M, Niter)

Value

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 Fuchs1982;textualMCARtest.

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 for calculating the null MLE.

References

Fuchs1982MCARtest

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)