Misspecifying the Shape of a Random Effects Distribution: Why Getting It Wrong May Not Matter

TL;DR

This paper investigates whether incorrect assumptions about the distribution of random effects in statistical models significantly impact inference, finding that maximum likelihood methods are often robust to such misspecifications.

Contribution

It provides theoretical, simulation, and example analyses showing that misspecifying random effects distributions often does not severely affect results in generalized linear mixed models.

Findings

Maximum likelihood estimates are robust to distribution misspecification.

Inferences about covariate effects remain accurate despite misspecification.

Prediction of random effects is generally unaffected by distribution assumptions.

Abstract

Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature as to whether such parametric assumptions are important or innocuous. In the context of generalized linear mixed models used to analyze clustered or longitudinal data, we examine the impact of random effects distribution misspecification on a variety of inferences, including prediction, inference about covariate effects, prediction of random effects and estimation of random effects variances. We describe examples, theoretical calculations and simulations to elucidate situations in which the specification is and is not important. A key conclusion is the large degree of robustness of maximum likelihood for a wide variety of commonly encountered situations.