Lattice Conditional Independence Models for Contingency Tables with Non Monotone Missing Data Patterns

In the analysis of non monotone missing data patterns in multinomial distri butions for contingency tables it is known that explicit MLEs of the unknown parameters cannot be obtained Iterative procedures such as the EM algorithm are therefore required to obtain the MLEs These iterative procedures however may o er several potential di culties Andersson and Perlman intro duced lattice conditional independence LCI models for multivariate normal distributions which can be applied to the analysis of non monotone missing observations in continuous data Andersson and Perlman In this paper we consider LCI models for categorical data and show that LCI modelsmay also be applied to the analysis of categorical data with non monotone missing data patterns Under a parsimonious set of LCI assumptions naturally determined by the observed data pattern the likelihood function for the observed data can be factored as in the monotone case and explicit MLEs can be obtained for the unknown parameters Furthermore the LCI assumptions can be tested by explicit likelihood ratio tests