Laudy Olav, Hoijtink Herbert
Department of Methodology and Statistics, Utrecht University, The Netherlands.
Stat Methods Med Res. 2007 Apr;16(2):123-38. doi: 10.1177/0962280206071925.
A Bayesian methodology for the analysis of inequality constrained models for contingency tables is presented. The problem of interest lies in obtaining the estimates of functions of cell probabilities subject to inequality constraints, testing hypotheses and selection of the best model. Constraints on conditional cell probabilities and on local, global, continuation and cumulative odds ratios are discussed. A Gibbs sampler to obtain a discrete representation of the posterior distribution of the inequality constrained parameters is used. Using this discrete representation, the credibility regions of functions of cell probabilities can be constructed. Posterior model probabilities are used for model selection and hypotheses are tested using posterior predictive checks. The Bayesian methodology proposed is illustrated in two examples.
提出了一种用于分析列联表不等式约束模型的贝叶斯方法。感兴趣的问题在于获得受不等式约束的单元格概率函数的估计值、检验假设以及选择最佳模型。讨论了对条件单元格概率以及局部、全局、连续和累积优势比的约束。使用吉布斯采样器来获得不等式约束参数后验分布的离散表示。利用这种离散表示，可以构建单元格概率函数的可信区间。后验模型概率用于模型选择，假设通过后验预测检验进行检验。通过两个例子说明了所提出的贝叶斯方法。
