The Multivariate Analysis of Qualitative Data: Interactions among Multiple Classifications

Abstract For the m-way contingency table, we discuss both the direct estimation of the multiplicative interactions among the m variables, and the indirect testing of hypotheses pertaining to these interactions. We consider, among other things, hierarchical hypotheses pertaining to the interactions among the m variables, including hypotheses that can be expressed in terms of one or more of the following kinds of concepts: (a) the usual concepts of independence and equiprobability; (b) concepts describing conditional properties (e.g., conditional independence) pertaining to a subset of the m variables, given the level of some of the remaining variables; (c) concepts related to the usual logit-analysis or to a generalized form of logit-analysis; and (d) concepts related to a more general log-linear model. Methods of partitioning these hypotheses are introduced which provide, among other things, insight into the relationship between tests applied to the m-way table and tests applied to marginal tables formed ...

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