The Annals of Statistics

Generalized fiducial inference for normal linear mixed models

Jessi Cisewski and Jan Hannig

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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.

Article information

Ann. Statist., Volume 40, Number 4 (2012), 2102-2127.

First available in Project Euclid: 30 October 2012

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J99: None of the above, but in this section
Secondary: 62F25: Tolerance and confidence regions 62F10: Point estimation

Variance component random-effects model sequential Monte Carlo hierarchical model multilevel model


Cisewski, Jessi; Hannig, Jan. Generalized fiducial inference for normal linear mixed models. Ann. Statist. 40 (2012), no. 4, 2102--2127. doi:10.1214/12-AOS1030.

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Supplemental materials

  • Supplementary material: Additional simulation results. The asymptotic stability of the algorithm, with respect to the sample size and the particle sample size, was tested, and the simulation results are included in this document. The raw results for the simulation study in Section 3 are also displayed, along with additional summary figures.