Models for three-dimensional contingency tables with completely and partially cross-classified data

We develop models for three-dimensional contingency tables containing both completely and partially cross-classified data for which one of the variables is regarded as dependent and the other two variables are regarded as independent variables. Parameters of interest include the cell probabilities and the probabilities that the observations on one or both independent variables are missing. The models allow inferences on these two sets of probabilities to be made independently. Maximum likelihood methods for estimating and testing hypotheses regarding these parameters are described, along with conditional goodness-of-fit test statistics, which display a convenient additivity property. The methodology is applied to cervical cancer data from a case-control study performed in Atlanta, Georgia, 1985-1988.