# On Testability and Goodness of Fit Tests in Missing Data Models

arXiv: https://arxiv.org/abs/2203.00132 · HTML: https://mlsanity.com/paper/2203.00132/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 11 of 11)

- [Graphical Models for Processing Missing Data](https://mlsanity.com/paper/1801.03583/) (2018)
- [Causal Discovery in the Presence of Missing Data](https://mlsanity.com/paper/1807.04010/) (2018)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Full Law Identification In Graphical Models Of Missing Data: Completeness Results](https://mlsanity.com/paper/2004.04872/) (2020)
- [Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables](https://mlsanity.com/paper/2003.12659/) (2020)
- [Identification In Missing Data Models Represented By Directed Acyclic Graphs](https://mlsanity.com/paper/1907.00241/) (2019)
- [Semiparametric Inference for Non-monotone Missing-Not-at-Random Data: the No Self-Censoring Model](https://mlsanity.com/paper/1909.01848/) (2019)
- [Estimation of Effects of Sequential Treatments by Reparameterizing Directed Acyclic Graphs](https://mlsanity.com/paper/1302.1566/) (2013)
- [Itemwise conditionally independent nonresponse modeling for incomplete multivariate data](https://mlsanity.com/paper/1609.00656/) (2016)
- [Adjustment Criteria for Recovering Causal Effects from Missing Data](https://mlsanity.com/paper/1907.01654/) (2019)
- [Markov-Restricted Analysis of Randomized Trials with Non-Monotone Missing Binary Outcomes](https://mlsanity.com/paper/2105.08868/) (2021)

## Built on by (most cited first, 4 of 4)

- [Sufficient Identification Conditions and Semiparametric Estimation under Missing Not at Random Mechanisms](https://mlsanity.com/paper/2306.06443/) (2023)
- [MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data](https://mlsanity.com/paper/2410.18918/) (2024)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)
- [Response to Discussions of "Causal and Counterfactual Views of Missing Data Models"](https://mlsanity.com/paper/2510.14694/) (2025)

## Abstract (arXiv)

Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely on the assumptions encoded by the graph holding true; however, verification of these assumptions has not received sufficient attention in prior work. In this paper, we provide new insights on the testable implications of three broad classes of missing data graphical models, and design goodness-of-fit tests for them. The classes of models explored are: sequential missing-at-random and missing-not-at-random models which can be used for modeling longitudinal studies with dropout/censoring, and a no self-censoring model which can be applied to cross-sectional studies and surveys.