Selecting among Missingness Models for Sequential Outcomes with Nonignorable Nonresponse

Yingying Wang; Yuan Liu; Shanshan Luo

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arXiv · 2608.09026

Selecting among Missingness Models for Sequential Outcomes with Nonignorable Nonresponse

Yingying Wang·Yuan Liu·Shanshan Luo

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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.

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BibTeX RIS

Yingying Wang, Yuan Liu, Shanshan Luo. 2026-08-10. Selecting among Missingness Models for Sequential Outcomes with Nonignorable Nonresponse. https://arxiv.org/abs/2608.09026

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