Research Institute of Child Development and Education, University of Amsterdam, P.O. Box 15776, 1001, NG, Amsterdam, The Netherlands.
THE London School of Economics AND POLITICAL SCIENCE, London, UK.
Psychometrika. 2023 Dec;88(4):1228-1248. doi: 10.1007/s11336-023-09932-7. Epub 2023 Sep 26.
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.
类别边缘模型（CMM）是一种灵活的工具，可用于对相关或聚类的类别数据进行建模，而无需关注相关性本身。最大似然（ML）估计 CMM 的一个主要限制是，列联表的大小随变量数量呈指数级增长，因此，即使对于中等数量的变量（例如 10 到 20 个变量），ML 估计也可能在计算上不可行。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，我们表明，MEL 往往会在大型稀疏列联表中失效。作为一种解决方案，我们提出了一种新方法，称为最大扩充经验似然（MAEL）估计，它涉及用一些精心选择的单元格来扩充经验似然支持。模拟结果表明，对于非常大的列联表，MAEL 在有限样本中的性能良好。
