Graphical Models of Entangled Missingness

TL;DR

This paper introduces a graphical modeling framework for causal inference with entangled missing data, addressing data dependence in missingness patterns that traditional methods cannot handle.

Contribution

It develops a comprehensive framework for entangled missingness, extending existing models and providing identification results for complex data dependence scenarios.

Findings

Extended missing data models to cover target law and missingness process dependence.

Provided complete identification results for three types of entangled missingness.

Demonstrated framework effectiveness on synthetic data.

Abstract

Despite the growing interest in causal and statistical inference for settings with data dependence, few methods currently exist to account for missing data in dependent data settings; most classical missing data methods in statistics and causal inference treat data units as independent and identically distributed (i.i.d.). We develop a graphical modeling based framework for causal inference in the presence of entangled missingness, defined as missingness with data dependence. We distinguish three different types of entanglements that can occur, supported by real-world examples. We give sound and complete identification results for all three settings. We show that existing missing data models may be extended to cover entanglements arising from (1) target law dependence and (2) missingness process dependence, while those arising from (3) missingness interference require a novel approach. We demonstrate the use of our entangled missingness framework on synthetic data. Finally, we discuss how, subject to a certain reinterpretation of the variables in the model, our model for missingness interference extends missing data methods to novel missing data patterns in i.i.d. settings.