Selecting among Missingness Models for Sequential Outcomes with Nonignorable Nonresponse

2026-08-09

AI Summary

This study addresses the nonignorable nonrandom missingness arising from self-censoring in longitudinal studies, particularly when later responses depend on prior observations. It introduces, for the first time, two classes of graphical-model-based missing mechanisms that enable identification of the full-data distribution under rank or completeness conditions. A two-stage Vuong-type selection procedure is proposed: first testing for observable distinguishability between candidate models, then selecting the preferred model based on Kullback–Leibler divergence to ensure asymptotic validity of Wald inference under the chosen model. The framework jointly guarantees model distinguishability and selection consistency, demonstrates robust performance in simulations, and is successfully applied to Job Corps data, yielding a principled choice of missing mechanism and reliable estimation of functional parameters.

Abstract

Sequential outcomes in longitudinal studies and multi-wave surveys may be missing not at random at both earlier and later occasions. We study graphical models in which at least one outcome is self-censoring and the response indicator for a later outcome may depend on either the earlier response indicator or the realized earlier outcome. These restrictions define two candidate families under which the relevant full-data distributions are identifiable and whose observed-data models overlap; graphs containing both dependencies form a broader class outside the prespecified comparison. For each candidate family, we establish identification of the full-data distribution under rank or completeness conditions and develop likelihood-based estimation. We then propose a two-stage Vuong-type procedure. The first stage determines whether the candidate models are observationally distinguishable; only after distinguishability is established does the second stage compare their Kullback--Leibler divergences from the true observed-data distribution. We also show that ordinary Wald inference remains asymptotically valid for the selected model-specific functional when the selected model has a fixed positive expected log-likelihood advantage. Simulations evaluate the two-stage procedure across graph classes. We finally apply the procedure to compare candidate missingness models in the Job Corps data and perform downstream functional estimation under the selected model.

Problem

• nonignorable nonresponse
• missingness models
• sequential outcomes
• model selection
• identifiability

Innovation

• nonignorable nonresponse
• graphical models
• identifiability
• Vuong test
• likelihood-based estimation