Estimating generalized linear models with the pseudo-marginal Metropolis-Hastings algorithm

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. The flexibility of this approach allows for general priors to be put on both the missing covariates and the parameters, uses all of the available data, can easily be extended to handle a nonignorable missing-data mechanism, and is still asymptotically exact 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 influence the car crash outcomes.