Multidimensional contingency tables with missing data

This paper is concerned wim ine maximum likelihood estimation and the likelihood ratio test for hierarchical loglinear models of multidimensional contingency tables with missing data. The problems of estimation and test for a high dimensional contingency table can be reduced into those for a class of low dimensional tables. In some cases, the incomplete data in the high dimensional table can become complete in the low dimensional tables through the reduction can indicate how much the incomplete data contribute to the estimation and the test.