标题： 通过多向分组的交叉随机效应模型的可扩展估计 显示英文标题

标题： Scalable Estimation of Crossed Random Effects Models via Multi-way Grouping

摘要： 跨层次数据在教育、医疗保健和社会科学等科学领域中经常出现。 一种常见的建模策略是在回归框架内引入交叉随机效应。 然而，这种方法在非高斯结果的情况下常常遇到严重的计算瓶颈。 在本文中，我们提出了一种可扩展且灵活的方法，通过将每个随机效应的分布近似为离散分布，有效地将随机效应划分为有限数量的代表性组。 这种近似使我们可以将模型表示为多维分组结构，可以使用简单快速的迭代算法进行高效估计。 所提出的方法适用于广泛的结果模型，并且在超过两维交叉分类的设置中仍然适用。 我们在一般的分类水平设置下理论证明了估计量的一致性和渐近正态性。 通过模拟研究和实际数据应用，我们展示了该方法在涉及交叉分类结构的逻辑回归、泊松回归和有序概率回归模型中的实际性能。 显示英文摘要

摘要： Cross-classified data frequently arise in scientific fields such as education, healthcare, and social sciences. A common modeling strategy is to introduce crossed random effects within a regression framework. However, this approach often encounters serious computational bottlenecks, particularly for non-Gaussian outcomes. In this paper, we propose a scalable and flexible method that approximates the distribution of each random effect by a discrete distribution, effectively partitioning the random effects into a finite number of representative groups. This approximation allows us to express the model as a multi-way grouped structure, which can be efficiently estimated using a simple and fast iterative algorithm. The proposed method accommodates a wide range of outcome models and remains applicable even in settings with more than two-way cross-classification. We theoretically establish the consistency and asymptotic normality of the estimator under general settings of classification levels. Through simulation studies and real data applications, we demonstrate the practical performance of the proposed method in logistic, Poisson, and ordered probit regression models involving cross-classified structures.