Monotone Missing Data: A Blessing and a Curse

TL;DR

This paper explores the dual nature of monotone missing data, showing it can both aid and hinder the identifiability of the full data distribution depending on the graphical structure.

Contribution

It provides a nuanced analysis of how monotonicity affects the identifiability of the full law in graphical models, highlighting cases where it helps or impedes.

Findings

Monotone missingness can enable identification of the full law in some cases.

Monotonicity can also prevent identification where nonmonotone cases succeed.

Proper treatment of monotone missing data is crucial for accurate analysis.

Abstract

Monotone missingness is commonly encountered in practice when a missing measurement compels another measurement to be missing. Because of the simpler missing data pattern, monotone missing data is often viewed as beneficial from the perspective of practical data analysis. However, in graphical missing data models, monotonicity has implications for the identifiability of the full law, i.e., the joint distribution of actual variables and response indicators. In the general nonmonotone case, the full law is known to be nonparametrically identifiable if and only if specific graphical structures are not present. We show that while monotonicity may enable the identification of the full law despite some of these structures, it also prevents the identification in certain cases that are identifiable without monotonicity. The results emphasize the importance of proper treatment of monotone missingness in the analysis of incomplete data.