Open Access
August 2012 Generalized fiducial inference for normal linear mixed models
Jessi Cisewski, Jan Hannig
Ann. Statist. 40(4): 2102-2127 (August 2012). DOI: 10.1214/12-AOS1030


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.


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Jessi Cisewski. Jan Hannig. "Generalized fiducial inference for normal linear mixed models." Ann. Statist. 40 (4) 2102 - 2127, August 2012.


Published: August 2012
First available in Project Euclid: 30 October 2012

zbMATH: 1257.62075
MathSciNet: MR3059078
Digital Object Identifier: 10.1214/12-AOS1030

Primary: 62J99
Secondary: 62F10 , 62F25

Keywords: hierarchical model , multilevel model , random-effects model , sequential Monte Carlo , variance component

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 4 • August 2012
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