大型稀疏列联表范畴边际模型的最大增广经验似然估计。

IF 2.9 2区 心理学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Psychometrika Pub Date : 2023-12-01 Epub Date: 2023-09-26 DOI:10.1007/s11336-023-09932-7
L Andries van der Ark, Wicher P Bergsma, Letty Koopman
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引用次数: 0

摘要

分类边际模型(CMM)是一种灵活的工具,用于在不关心依赖关系本身时对依赖或聚类的分类数据进行建模。CMM的最大似然(ML)估计的一个主要限制是列联表的大小随着变量的数量呈指数级增加,因此即使对于中等数量的变量,例如10到20之间,ML估计在计算上也可能变得不可行。另一种方法是最大经验似然(MEL)估计,它保留了ML的最优渐近效率。然而,我们展示了MEL倾向于分解大型稀疏列联表。作为一种解决方案,我们提出了一种新的方法,我们称之为最大增强经验似然(MAEL)估计,该方法涉及用许多精心选择的单元来增强经验似然支持。仿真结果表明,对于非常大的列联表,有限样本具有良好的性能。
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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Maximum Augmented Empirical Likelihood Estimation of Categorical Marginal Models for Large Sparse Contingency Tables.

Categorical marginal models (CMMs) are flexible tools for modelling dependent or clustered categorical data, when the dependencies themselves are not of interest. A major limitation of maximum likelihood (ML) estimation of CMMs is that the size of the contingency table increases exponentially with the number of variables, so even for a moderate number of variables, say between 10 and 20, ML estimation can become computationally infeasible. An alternative method, which retains the optimal asymptotic efficiency of ML, is maximum empirical likelihood (MEL) estimation. However, we show that MEL tends to break down for large, sparse contingency tables. As a solution, we propose a new method, which we call maximum augmented empirical likelihood (MAEL) estimation and which involves augmentation of the empirical likelihood support with a number of well-chosen cells. Simulation results show good finite sample performance for very large contingency tables.

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来源期刊
Psychometrika
Psychometrika 数学-数学跨学科应用
CiteScore
4.40
自引率
10.00%
发文量
72
审稿时长
>12 weeks
期刊介绍: The journal Psychometrika is devoted to the advancement of theory and methodology for behavioral data in psychology, education and the social and behavioral sciences generally. Its coverage is offered in two sections: Theory and Methods (T& M), and Application Reviews and Case Studies (ARCS). T&M articles present original research and reviews on the development of quantitative models, statistical methods, and mathematical techniques for evaluating data from psychology, the social and behavioral sciences and related fields. Application Reviews can be integrative, drawing together disparate methodologies for applications, or comparative and evaluative, discussing advantages and disadvantages of one or more methodologies in applications. Case Studies highlight methodology that deepens understanding of substantive phenomena through more informative data analysis, or more elegant data description.
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