On Partitioning χ2 and Detecting Partial Association in Three-Way Contingency Tables

作者：Leo A. Goodman · 发表于：Journal of the Royal Statistical Society Series B (Statistical Methodology) · 年份：1969 · DOI：10.1111/j.2517-6161.1969.tb00808.x · 被引用次数：99 · 研究领域：Bayesian Modeling and Causal Inference、Advanced Statistical Methods and Models、Statistical Methods and Bayesian Inference

Summary This paper presents a method of partitioning a χ2 statistic for the I × J × K contingency table (viz. the χ2 statistic that is based upon the likelihood-ratio criterion for testing the null hypothesis that the three variables pertaining to the three-way table are mutually independent) into additive components that can be used to test (1) the null hypothesis of zero three-factor interaction, (2) the null hypothesis that the partial association between two of the variables in the three-way table is zero, and (3) some null hypotheses concerning the two-way marginal distributions. This paper also discusses the estimation of the degree of partial association between two of the variables in the I × J × K table both in the case where the observed row and column marginals in each of the K different I × J tables (which form the I × J × K table) are considered given, and also in the case where these marginals are not fixed. Both the conditional maximum-likelihood estimator (given the observed row and column marginals in the K different I × J tables) and the unconditional maximum-likelihood estimator are presented, and for the special case where I = J = 2 various approximations to these estimators are compared.