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February 2016 Mitigating Bias in Generalized Linear Mixed Models: The Case for Bayesian Nonparametrics
Joseph Antonelli, Lorenzo Trippa, Sebastien Haneuse
Statist. Sci. 31(1): 80-95 (February 2016). DOI: 10.1214/15-STS533

Abstract

Generalized linear mixed models are a common statistical tool for the analysis of clustered or longitudinal data where correlation is accounted for through cluster-specific random effects. In practice, the distribution of the random effects is typically taken to be a Normal distribution, although if this does not hold then the model is misspecified and standard estimation/inference may be invalid. An alternative is to perform a so-called nonparametric Bayesian analyses in which one assigns a Dirichlet process (DP) prior to the unknown distribution of the random effects. In this paper we examine operating characteristics for estimation of fixed effects and random effects based on such an analysis under a range of “true” random effects distributions. As part of this we investigate various approaches for selection of the precision parameter of the DP prior. In addition, we illustrate the use of the methods with an analysis of post-operative complications among $n=18{,}643$ female Medicare beneficiaries who underwent a hysterectomy procedure at $N=503$ hospitals in the US. Overall, we conclude that using the DP prior in modeling the random effect distribution results in large reductions of bias with little loss of efficiency. While no single choice for the precision parameter will be optimal in all settings, certain strategies such as importance sampling or empirical Bayes can be used to obtain reasonable results in a broad range of data scenarios.

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Joseph Antonelli. Lorenzo Trippa. Sebastien Haneuse. "Mitigating Bias in Generalized Linear Mixed Models: The Case for Bayesian Nonparametrics." Statist. Sci. 31 (1) 80 - 95, February 2016. https://doi.org/10.1214/15-STS533

Information

Published: February 2016
First available in Project Euclid: 10 February 2016

zbMATH: 06946213
MathSciNet: MR3458594
Digital Object Identifier: 10.1214/15-STS533

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.31 • No. 1 • February 2016
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