On Quasi-Independence and Quasi-Dependence in Contingency Tables, with Special Reference to Ordinal Triangular Contingency Tables
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列联表的拟独立与拟依赖：特别关注有序三角列联表
- 研究问题
- 当列联表部分单元格因缺失、不可靠或限制而不纳入分析时，如何定义和检验拟独立，以及正向或负向的拟依赖？
- 方法与思路
- 作者引入似然比意义下的拟依赖，研究其零依赖与拟独立的关系，并构造针对正负方向备择的检验，重点讨论三角表。
- 材料陈述的贡献
- 摘要称该框架简化既有拟独立公式并提供解释，提出方向性备择检验，且其中一些检验在某些情形下具有更高功效。
- 阅读关注点
- 应核对可用单元格的结构、拟独立与零拟依赖的区别、正负依赖的定义，以及三角表结论推广到一般列联表的条件。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；更高功效仅为特定情形下的摘要陈述，未说明缺失机制，也不能据此识别因果关系。
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.