Obtaining the maximum likelihood estimates in incomplete R x C contingency tables using a Poisson generalized linear model

Abstract

This article describes estimation of the cell probabilities in an R x C contingency table with ignorable missing data. Popular methods for maximizing the incomplete data likelihood are the EM-algorithm and the Newton--Raphson algorithm. Both of these methods require some modification of existing statistical software to get the MLEs of the cell probabilities as well as the variance estimates. We make the connection between the multinomial and Poisson likelihoods to show that the MLEs can be obtained in any generalized linear models program without additional programming or iteration loops.