Abstract

Today, generalized linear mixed models (GLMM) are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under GLMM. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools.

摘要

今天，广义线性混合模型（GLMM）被广泛应用于许多领域。然而，在这个领域中，用于执行同步推理的工具的开发在很大程度上被忽视了。联合推理的框架对于在所有或几个集群之间对感兴趣的参数进行统计上有效的多重比较是必不可少的。因此，我们为 GLMM 下的经验最佳预测因子开发了同时置信区间和多个测试程序。此外，我们实施我们的方法来研究广泛使用的混合模型示例，即单位级二项式、区域级泊松伽玛和区域级泊松对数正态混合模型。渐近结果伴随着广泛的模拟。