A Pseudo-Marginal Metropolis-Hastings Algorithm for Estimating Generalized Linear Models in the Presence of Missing Data

2019/07/22 by Taylor R. Brown, Timothy L. McMurry, Brown, Taylor R. +3
Mathematics · #FOS: Computer and information sciences #Markov Chains and Monte Carlo Methods #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1907.09090

openalex publication_date 2019/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The missing data issue often complicates the task of estimating generalized linear models (GLMs). We describe why the pseudo-marginal Metropolis-Hastings algorithm, used in this setting, is an effective strategy for parameter estimation. This approach requires fewer assumptions, it provides joint inferences on the parameters in the likelihood, the covariate model, and the parameters of the missingness-mechanism, and there is no logical inconsistency of assuming that there are multiple posterior distributions. Moreover, this approach is asymptotically exact, just like most other Markov chain Monte Carlo techniques. We discuss computing strategies, conduct a simulation study demonstrating how standard errors change as a function of percent missingness, and we use our approach on a "real-world" data set to describe how a collection of variables influences the car crash outcomes.

Citations

• mice: Multivariate Imputation by Chained Equations inR
• Monte Carlo sampling methods using Markov chains and their applications

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