Statistical Inference with Different Missing-data Mechanisms

TL;DR

This paper extends statistical inference methods to handle data missing due to multiple causes by modeling various missing-data mechanisms, including mixtures of MAR and NMAR, and investigates their ignorability.

Contribution

It introduces a framework for analyzing data with multiple missing-data causes by extending the missing-data indicator to discrete vectors and studying the ignorability of mixed mechanisms.

Findings

Mixture of MAR and NMAR mechanisms generally cannot be ignored.

Special cases exist where MAR components in mixtures can be ignored.

New methods enable inference with complex missing-data causes.

Abstract

When data are missing due to at most one cause from some time to next time, we can make sampling distribution inferences about the parameter of the data by modeling the missing-data mechanism correctly. Proverbially, in case its mechanism is missing at random (MAR), it can be ignored, but in case not missing at random (NMAR), it can not be. There are no methods, however, to analyze when missing of the data can occur because of several causes despite of there being many such data in practice. Hence the aim of this paper is to propose how to inference on such data. Concretely, we extend the missing-data indicator from usual binary random vectors to discrete random vectors, define missing-data mechanism for every causes and research ignorability of a mixture of missing-data mechanisms such as "MAR & MAR" and "MAR & NMAR". In particular, when the combination of mechanisms is "MAR & NMAR", generally the component of MAR can not be ignored, but in special case, it can be.