On the Partitioning of Goodness-of-Fit Statistics for Multivariate Categorical Response Models
研究了一类多元分类响应模型中拟合优度统计量的分解方法，通过将联合假设拆分为联合分布和边际分布两个子假设，并证明在特定条件下两个分量统计量渐近独立，为模型检验提供了更细致的工具。
Abstract Numerical and asymptotic stochastic partitioning of goodness-of-fit statistics are considered for a broad class of simultaneous multivariate categorical response models. These simultaneous models impose constraints on the joint and marginal distributions of categorical response variables. Under certain conditions, the tenability of the corresponding simultaneous hypothesis can be assessed by separately testing the two subhypotheses: one regarding the joint distributions and the other regarding the marginal distributions. Specifically, easily verifiable sufficient conditions are introduced that allow us to partition the overall goodness-of-fit statistic into two interesting goodness-of-fit statistics: one for testing whether the joint distribution model holds and the other for testing whether the marginal distribution model holds. Moreover, it is proven that when the sufficient conditions hold and the simultaneous hypothesis is true, the two component goodness-of-fit statistics are asymptotically independent. These results are illustrated through several examples.