On the Analysis of Special Incomplete Three‐dimensional Contingency Tables

Abstract

Incomplete contingency tables, i.e. tables with structurally caused cmptp cclls, arc analpeed by means of so-called quasilog-linear models. I n general the expected values can be calculated by means of iterative cyclic adaption to corresponding marginals of the empirical contingencytables (in the same way as in complete tables) under different hierarchical hypotheses concerning the parameters of the models.For important cases of %dimensional contingency tables it is possible to demonstrate that expected values and teat statistics are to find in a closed form.If all 2-dimensional sub or partial tablea of a %dimensional table can be assigned to such cases thcn the hypotheses of cleeees ( A B X C ) (m). ( B X C ) / A ( W ) , ( A X B ) / . (W) etc. are testable inclosed form. But the expected values to (A X B X C ) (W) have to be calculated iteratively.An cxample shows that some definite additive decompositions of the test statistic 2 I are no longer valid while some others remain valid in spite of incompleteness of the tables.Key words : Three-dimensional contingency tables, structurally caused i n m p kteness, quasi-independence, closed form expected values and test statistics.