Diagnosing global case influence on MAR versus MNAR model comparisons

Abstract

When missingness is suspected to be not at random (MNAR) in longitudinal studies, researchers sometimes compare the fit of a target model that assumes missingness at random (here termed a MAR model) and a model that accommodates a hypothesized MNAR missingness mechanism (here termed a MNAR model). It is well known that such comparisons are only interpretable conditional on the validity of the chosen MNAR model's assumptions about the missingness mechanism. For that reason, researchers often perform a sensitivity analysis comparing the MAR model to not one, but several, plausible alternative MNAR models. In the social sciences, it is not widely known that such model comparisons can be particularly sensitive to case influence, such that conclusions drawn could depend on a single case. This article describes two convenient diagnostics suited for detecting case influence on MAR-MNAR model comparisons. Both diagnostics require much less computational burden than global influence diagnostics that have been used in other disciplines for MNAR sensitivity analyses. We illustrate the interpretation and implementation of these diagnostics with simulated and empirical latent growth modeling examples. It is hoped that this article increases awareness of the potential for case influence on MAR-MNAR model comparisons and how it could be detected in longitudinal social science applications.