Marginal Log‐linear Parameters and their Collapsibility for Categorical Data

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-13 DOI:10.1111/stan.12332

S. Ghosh, P. Vellaisamy

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引用次数: 1

Abstract

Collapsibility is a practical and useful technique for dimension reduction in multidimensional contingency tables. In this paper, we consider marginal log‐linear models for studying collapsibility and related aspects in such tables. These models generalize ordinary log‐linear and multivariate logistic models, besides several others. First, we obtain some characteristic properties of marginal log‐linear parameters. Then we define collapsibility and strict collapsibility of these parameters in a general sense. Several necessary and sufficient conditions for collapsibility and strict collapsibility are derived based on simple functions of only the cell probabilities, which are easily verifiable. These include results for an arbitrary set of marginal log‐linear parameters having some common effects. The connections of strict collapsibility to various forms of independence of the variables are explored. We analyze some real‐life datasets to illustrate the above results on collapsibility and strict collapsibility. Finally, we obtain a result relating parameters with the same effect, but different margins for an arbitrary table, and demonstrate smoothness of marginal log‐linear models under collapsibility conditions. This article is protected by copyright. All rights reserved.

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分类数据的边际对数线性参数及其可折叠性

折叠性是一种实用的多维列联表降维技术。在本文中，我们考虑边际对数线性模型来研究这种表的可折叠性和相关方面。这些模型推广了普通的对数线性和多元逻辑模型，以及其他一些模型。首先，我们得到了边际对数线性参数的一些特征性质。然后在一般意义上定义了这些参数的可折叠性和严格可折叠性。从单元概率的简单函数出发，导出了可折叠性和严格可折叠性的几个充分必要条件，这些条件易于验证。这些结果包括具有一些共同效应的任意一组边际对数线性参数的结果。探讨了严格可折叠性与各种形式的变量独立性之间的联系。我们分析了一些实际数据集来说明上述关于可折叠性和严格可折叠性的结果。最后，我们得到了一个关于任意表的参数具有相同效果，但边界不同的结果，并证明了边际对数线性模型在可折叠性条件下的平滑性。这篇文章受版权保护。版权所有。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.