On Quasi-Independence and Quasi-Dependence in Contingency Tables, with Special Reference to Ordinal Triangular Contingency Tables
列联表中的拟独立与拟依赖：兼论有序三角列联表AI 解读 ↓
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列联表中的拟独立与拟依赖：兼论有序三角列联表
- 研究问题
- 当部分列联表单元因缺失、不可靠或结构限制而不参与分析时，如何定义并检验剩余单元间的拟独立与方向性依赖？
- 方法与思路
- 作者引入似然比意义的拟依赖，研究其零依赖与拟独立的关系，并构造针对正、负拟依赖的检验，重点分析三角表。
- 材料陈述的贡献
- 摘要称该视角简化了既有拟独立模型的部分公式，并提供方向性备择检验；某些情形下检验功效高于既有程序。
- 阅读关注点
- 应核对可用单元集合、有序性和拟依赖的定义，确认零拟依赖与拟独立的关系，以及三角表结果推广的具体范围。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，不能推断刊本变化；遗漏单元的处理不等于解决任意缺失机制，摘要未说明功效优势的完整条件。
原文摘要
In the usual statistical analysis of the entries (frequencies) in a contingency table having I rows and J columns (I ≥ 2, J ≥ 2), an important role is often played by the usual null hypothesis of independence (i.e., the hypothesis that the row variable and the column variable are statistically independent of each other). In the situation considered in this article, the entries in some of the I × J cells of the contingency table are omitted from the analysis (because these entries are either missing, unreliable, void, or restricted in certain ways); and in this situation, the usual null hypothesis of independence cannot be applied in a meaningful way. The concept of “quasi-independence” was introduced for this situation; and an important role can often be played in this situation by the null hypothesis of quasi-independence (a generalization of the usual null hypothesis of independence). For this situation, we introduce also the concept of likelihood-ratio “quasi-dependence” (a generalization of the usual concept of likelihood-ratio dependence in the I × J table), and we consider the null hypothesis of null quasi-dependence and the alternative hypotheses of positive quasi-dependence and negative quasi-dependence. The relationship between quasi-independence and null quasi-dependence is considered, and methods are introduced for testing these null hypotheses against the aforementioned alternative hypotheses. Special attention is given to the triangular contingency table; and some of the results presented for this special case can also be applied more generally to the I × J contingency table. With the approach presented in this article, we are able to simplify and gain further insight into some formulas appearing in the earlier literature on the quasi-independence model applied to contingency tables. This approach has certain other advantages as well. For example, with this approach we are able to introduce various tests of the quasi-independence model against alternative hypotheses of positive or negative quasi-dependence, and these tests will in some cases be more powerful than other tests proposed in the earlier literature.