Conditional Symmetry Models for Three-Way Contingency Tables
نویسندگان
چکیده
We generalize the conditional symmetry model for an I×I×I contingency table with commensurable ordinal classification variables. The new family of models is constructed in such a way so that possesses the usual desirable properties that appear in the similar generalizations of symmetry and marginal homogeneity models, that is connections between the models above obey a coherent structure.
منابع مشابه
Analysis of data in square contingency tables with ordered categories using the conditional symmetry model and its decomposed models.
For the analysis of square contingency tables with ordered categories, three kinds of decompositions for the conditional symmetry model derived by Tomizawa are simply described. Using the conditional symmetry model and its decomposed models, this paper analyzes the data of unaided distance vision of women in Britain first analyzed by Stuart, the data of unaided distance vision of students in a ...
متن کاملMarkov bases for typical block effect models of two-way contingency tables
Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via Markov chain Monte Carlo method. In this paper we derive explicit forms of Markov bases for change point models and block diagonal effect models, which are typical block-wise effect models of two-way contingency tables, and perform conditional tests with some real da...
متن کاملPartial Association Components in Multi-way Contingency Tables and Their Statistiical Analysis
In analyses of contingency tables made up of categorical variables, the study of relationship between the variables is usually the major objective. So far, many association measures and association models have been used to measure the association structure present in the table. Although the association measures merely determine the degree of strength of association between the study varia...
متن کاملDecompositions for Extended Double Symmetry Models in Square Contingency Tables with Ordered Categories
For square contingency tables with ordered categories, Tomizawa (1992) proposed three kinds of double symmetry models, whose each has a structure of both symmetry about the main diagonal and asymmetry about the reverse diagonal of the table. This paper proposes the extensions of those models and gives the decompositions for three kinds of double symmetry models into the extended quasi double sy...
متن کاملAdditive and Multiplicative Models for Three-Way Contingency Tables: Darroch (1974) Revisited
In an only occasionally referenced paper, Darroch (1974) discussed the relative merits of additive and multiplicative definitions of interaction for higher-order contingency tables. In particular, he compared the following aspects: partitioning properties, closeness to independence, conditional independence as a special case, distributional equivalence, subtable invariance, and constraints on t...
متن کامل