Statistical Science

Mitigating Bias in Generalized Linear Mixed Models: The Case for Bayesian Nonparametrics

Joseph Antonelli, Lorenzo Trippa, and Sebastien Haneuse

Full-text: Open access

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.

Article information

Source
Statist. Sci., Volume 31, Number 1 (2016), 80-95.

Dates
First available in Project Euclid: 10 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ss/1455115915

Digital Object Identifier
doi:10.1214/15-STS533

Mathematical Reviews number (MathSciNet)
MR3458594

Zentralblatt MATH identifier
06946213

Keywords
Dirichlet process prior generalized linear mixed models model misspecification random effects

Citation

Antonelli, Joseph; Trippa, Lorenzo; Haneuse, Sebastien. Mitigating Bias in Generalized Linear Mixed Models: The Case for Bayesian Nonparametrics. Statist. Sci. 31 (2016), no. 1, 80--95. doi:10.1214/15-STS533. https://projecteuclid.org/euclid.ss/1455115915


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Supplemental materials

  • Supplement to “Mitigating bias in generalized linear mixed models: The case for Bayesian nonparametrics”. We include in the supplementary files a detailed description of both the model and prior specification for the Logistic-DP model. We also include extended simulation results that include all parameters from the model and an additional simulation that looks at a larger sample size. Finally, we include convergence diagnostics for all Bayesian models in the Medicare application.