Modeling Multivariate Missingness with Tree Graphs and Conjugate Odds

TL;DR

This paper introduces a novel approach for modeling multivariate missing data under MNAR assumptions using tree graphs and conjugate odds, enabling elegant data distribution modeling and simple imputation.

Contribution

It extends pattern graph models by incorporating conjugate odds families within tree graph structures, facilitating full data distribution modeling and missing data imputation.

Findings

Effective modeling of MNAR data with tree graphs and conjugate odds.

Simple imputation models derived from the conjugate odds family.

Validated approach through simulations and real data analysis.

Abstract

In this paper, we analyze a specific class of missing not at random (MNAR) assumptions called tree graphs, extending upon the work of pattern graphs. We build off previous work by introducing the idea of a conjugate odds family in which certain parametric models on the selection odds can preserve the data distribution family across all missing data patterns. Under a conjugate odds family and a tree graph assumption, we are able to model the full data distribution elegantly in the sense that for the observed data, we obtain a model that is conjugate from the complete-data, and for the missing entries, we create a simple imputation model. In addition, we investigate the problem of graph selection, sensitivity analysis, and statistical inference. Using both simulations and real data, we illustrate the applicability of our method.