Testing Quasi-Independence in Stratified Triangular Contingency Tables

A special class of incomplete contingency tables has structural zeroes in one or more cells. Some of these tables have a triangular appearance in the sense that they are square and their cells are known a priori to contain zeroes above (or below) their main diagonals. We propose methods of analyzing log-linear models and testing quasi-independence in these triangular tables. We also offer a method for combining such tables that are stratified by a concomitant categorical variable. This strategy follows the same approach used in a Cochran-Mantel-Haenszel test.