GENERALIZED FIDUCIAL INFERENCE FOR NORMAL LINEAR MIXED MODELS

• 成果类型: Article
• 署名作者: Cisewski, Jessi; Hannig, Jan
• 署名单位: Carnegie Mellon University; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1030
• 发表日期: 2012
• 页码: 2102-2127
• 关键词: monte-carlo methods; confidence-intervals; variance-components; limited resolution; uncertainty; distributions; probability; hypotheses; simulation

摘要

While linear mixed modeling methods are foundational concepts introduced in any statistical education, adequate general methods for interval estimation involving models with more than a few variance components are lacking, especially in the unbalanced setting. Generalized fiducial inference provides a possible framework that accommodates this absence of methodology. Under the fabric of generalized fiducial inference along with sequential Monte Carlo methods, we present an approach for interval estimation for both balanced and unbalanced Gaussian linear mixed models. We compare the proposed method to classical and Bayesian results in the literature in a simulation study of two-fold nested models and two-factor crossed designs with an interaction term. The proposed method is found to be competitive or better when evaluated based on frequentist criteria of empirical coverage and average length of confidence intervals for small sample sizes. A MATLAB implementation of the proposed algorithm is available from the authors.