Diagnosing missing always at random in multivariate data

TL;DR

This paper introduces diagnostic tests to assess the validity of the missing always at random assumption in multivariate data analysis, aiding researchers in identifying potential violations and guiding sensitivity analyses.

Contribution

It proposes three novel diagnostic tests for detecting violations of the missing always at random assumption in multivariate data with missing values.

Findings

The tests can identify when the missing always at random assumption is violated.

They help pinpoint which variables are likely causing the violation.

The approach facilitates targeted sensitivity analyses.

Abstract

Models for analyzing multivariate data sets with missing values require strong, often unassessable, assumptions. The most common of these is that the mechanism that created the missing data is ignorable - a twofold assumption dependent on the mode of inference. The first part, which is the focus here, under the Bayesian and direct-likelihood paradigms, requires that the missing data are missing at random; in contrast, the frequentist-likelihood paradigm demands that the missing data mechanism always produces missing at random data, a condition known as missing always at random. Under certain regularity conditions, assuming missing always at random leads to an assumption that can be tested using the observed data alone namely, the missing data indicators only depend on fully observed variables. Here, we propose three different diagnostic tests that not only indicate when this assumption is incorrect but also suggest which variables are the most likely culprits. Although missing always at random is not a necessary condition to ensure validity under the Bayesian and direct-likelihood paradigms, it is sufficient, and evidence for its violation should encourage the careful statistician to conduct targeted sensitivity analyses.