| Abstract: | Incomplete contingency tables, i.e. tables with structurally caused empty cells, are analysed by means of so-called quasilog-linear models. In general the expected values can be calculated by means of iterative cyclic adaption to corresponding marginals of the empirical contingency tables (in the same way as in complete tables) under different hierarchical hypotheses concerning the parameters of the models. For important cases of 2-dimensional contingency tables it is possible to demonstrate that expected values and test statistics are to find in a closed form. If all 2-dimensional sub or partial tables of a 3-dimensional table can be assigned to such cases then the hypotheses of classes (AB×C) (??), (B×C)/A(??), (A??B)/A(??) etc. are testable in closed form. But the expected values to (A×B×C) (×) have to be calculated iteratively. An example shows that some definite additive decompositions of the test statistic 2 I are no longer valid while some others remain valid in spite of incompleteness of the tables. |
