# Discrete Choice Models for Nonmonotone Nonignorable Missing Data: Identification and Inference

arXiv: https://arxiv.org/abs/1607.02631 · HTML: https://mlsanity.com/paper/1607.02631/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2016.

## Built on by (most cited first, 5 of 5)

- [What Makes A Good Fisherman? Linear Regression under Self-Selection Bias](https://mlsanity.com/paper/2205.03246/) (2022)
- [Learning High-dimensional Gaussians from Censored Data](https://mlsanity.com/paper/2504.19446/) (2025)
- [Identification and Estimation for Nonignorable Missing Data: A Data Fusion Approach](https://mlsanity.com/paper/2311.09015/) (2023)
- [Markov Missing Graph: A Graphical Approach for Missing Data Imputation](https://mlsanity.com/paper/2509.03410/) (2025)
- [Identifiable Deep Latent Variable Models for MNAR Data](https://mlsanity.com/paper/2603.24771/) (2026)

## Abstract (arXiv)

Nonmonotone missing data arise routinely in empirical studies of social and health sciences, and when ignored, can induce selection bias and loss of efficiency. In practice, it is common to account for nonresponse under a missing-at-random assumption which although convenient, is rarely appropriate when nonresponse is nonmonotone. Likelihood and Bayesian missing data methodologies often require specification of a parametric model for the full data law, thus a priori ruling out any prospect for semiparametric inference. In this paper, we propose an all-purpose approach which delivers semiparametric inferences when missing data are nonmonotone and not at random. The approach is based on a discrete choice model (DCM) as a means to generate a large class of nonmonotone nonresponse mechanisms that are nonignorable. Sufficient conditions for nonparametric identification are given, and a general framework for fully parametric and semiparametric inference under an arbitrary DCM is proposed. Special consideration is given to the case of logit discrete choice nonresponse model (LDCM) for which we describe generalizations of inverse-probability weighting, pattern-mixture estimation, doubly robust estimation and multiply robust estimation.