Usable and precise asymptotics for generalized linear mixed model analysis and design

• 成果类型: Article
• 署名作者: Jiang, Jiming; Wand, Matt P.; Bhaskaran, Aishwarya
• 署名单位: University of California System; University of California Davis; University of Technology Sydney
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12473
• 发表日期: 2022
• 页码: 55-82
• 关键词: exponential laplace approximations; matrix

摘要

We derive precise asymptotic results that are directly usable for confidence intervals and Wald hypothesis tests for likelihood-based generalized linear mixed model analysis. The essence of our approach is to derive the exact leading term behaviour of the Fisher information matrix when both the number of groups and number of observations within each group diverge. This leads to asymptotic normality results with simple studentizable forms. Similar analyses result in tractable leading term forms for the determination of approximate locally Doptimal designs.