Maximum likelihood estimation and model selection in contingency tables with missing data

In many studies the values of one or more variables are missing for subsets of the original sample. This article focuses on the problem of obtaining maximum likelihood estimates (MLE) for the parameters of log-linear models under this type of incomplete data. The appropriate systems of equations are presented and the expectation-maximization (EM) algorithm (Dempster, Laird, and Rubin 1977) is suggested as one of the possible methods for solving them. The algorithm has certain advantages but other alternatives may be computationally more effective. Tests of fit for log-linear models in the presence of incomplete data are considered. The data from the Protective Services Project for Older Persons (Blenkner, Bloom, and Nielsen 1971; Blenkner, Bloom, and Weber 1974) are used to illustrate the procedures discussed in the article.