Positive Quadrant Dependence and Marginal Modeling in Two-Way Tables With Ordered Margins
有序边际二维列联表中的正象限依赖与边际建模AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要聚焦有序列联表的关联结构与约束似然推断，未明确涉及个体选择模型或经济分布效应。
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有序边际二维列联表中的正象限依赖与边际建模
- 研究问题
- 对于按有序变量交叉分类的二维列联表，如何结合边际模型和正依赖等不等式约束，统一开展似然估计与检验？
- 方法与思路
- 作者以全局 logit 和全局对数优势比参数化条件联合分布，用 Fisher 评分算法求最大似然估计，并处理等式及不等式约束。
- 材料陈述的贡献
- 摘要称，不等式约束下似然比检验具有卡方混合型渐近分布，并给出不依赖边际 logit 的紧界及条件于观测边际的扩展。
- 阅读关注点
- 应核对正象限依赖等约束的参数表达、卡方混合分布的权重与边界情形，以及固定边际抽样下算法和推断如何调整。
- 阅读边界
- 仅据版本未注明的 OpenAlex 摘要，无法确定算法收敛、混合权重或紧界公式；三项真实数据应用的来源和结果未提供。
原文摘要
For a collection of two-way tables, where subjects are cross-classified according to the same pair of ordinal categorical variables conditionally on the value of one or more discrete explanatory variables, we propose a general approach to likelihood inference that combines marginal modeling with fitting and testing of inequality constraints such as those implied by the assumption that one marginal distribution is stochastically larger than the other, positive dependence and stronger positive dependence. The approach is based on parameterizing bivariate conditional distributions with global logits and global log-odds ratios, and we provide a general framework for handling models defined by equality and inequality constraints on these parameters. In this way, such models as marginal homogeneity, proportional odds among row or columns margins, and Plackett distribution may be treated together with various models defined by inequality constraints on the same parameters, such as, for instance, those implied by the positive quadrant dependence. For this class of models, we define a Fisher scoring algorithm for computing maximum likelihood estimates and derive the asymptotic distribution of the likelihood ratio tests that turn out to be of the chi-bar squared type when inequalities are involved. When the main interest is on positive dependence, we derive tight bounds on the asymptotic distribution of these statistics that are independent of the marginal logits. These also may be removed by conditioning on one or both observed margins in each table, and we describe in detail how the approach may be adapted to these sampling schemes. Three applications to real datasets are discussed.