Generalized fiducial inference for normal linear mixed models

TL;DR

This paper introduces a generalized fiducial inference approach combined with sequential Monte Carlo methods for interval estimation in Gaussian linear mixed models, especially effective in unbalanced and small sample scenarios.

Contribution

It develops a novel generalized fiducial inference framework for linear mixed models that handles unbalanced data and multiple variance components, outperforming classical and Bayesian methods.

Findings

Competitive or superior coverage probabilities

Shorter average confidence intervals in simulations

Effective in small sample and unbalanced settings

Abstract

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.