Bayesian Log Linear Estimates for Three-Way Contingency Tables
提出一种贝叶斯方法估计三维列联表的期望比例，适用于对主效应和交互效应有先验知识的情况，并通过皮肤癌调查和英国选举投票转换数据示例。
This paper presents a Bayesian method to estimate the expected proportions in a three-way contingency table appropriate when prior knowledge about the main, first and second-order interaction effects can be described by a particular kind of exchange ability assumption. The proposed Bayes estimates are calculated by finding those values of the effects which maximize the resulting posterior distribution and can be used to explore the possibility that a nonsaturated submodel, such as independence or conditional independence, fits the data. This extends the work of Leonard (1975) for two-dimensional tables. We discuss numerical strategies to solve the estimating equations and point out how an incorrect choice of values for the ‘indifference’ case, as made by previous authors, can have serious effects on the convergence of the algorithms. The method is exemplified by a survey on skin cancer and data on voting transitions in British elections.