Analysis of contingency tables with structural zeros and ordered categories

Abstract

In this dissertation, procedures were presented for developing estimators of cell probabilities in contingency tables in the presence of structural zeros. Also, procedures were developed to analyze contingency tables using correspondence analysis in the presence of ordered categories. The development of estimators in the first situation consisted of extending the Hocking and Oxspring (1971) procedure, developing and simplifying the likelihood equations, obtaining an expression for the asymptotic variance and bias, and identifying the procedure to test the quasi-independence hypothesis. In the case of ordered categories, procedures were developed which incorporated the ordering in the categories classifying the contingency table. Distinction was made between the following two cases: (i) Strong Structure defining cases in which the differences between the optimal scores were specified and (ii) Weak Structure when the differences between the optimal scores were not specified. The development of the optimal scores in case (i) consisted of using correspondence analysis and for case (ii) three approaches were identified to solve the problem. Further, it was shown that the solution required solving a quadratic programming problem.