Diagnosing missing always at random in multivariate data
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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 (MAR); in contrast, the frequentist-likelihood paradigm demands that the missing data mechanism always produces MAR data, a condition known as missing always at random (MAAR). Under certain regularity conditions, assuming MAAR 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 diagnostics procedures that not only indicate when this assumption is invalid but also suggest which variables are the most likely culprits. Although MAAR 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 statistician to conduct a targeted sensitivity analysis.
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