Evaluation of missing data mechanisms in two and three dimensional incomplete tables

TL;DR

This paper characterizes missing data mechanisms in incomplete contingency tables using odds, discusses log-linear models, and proposes simple procedures for testing MAR, MCAR, and NMAR assumptions, with real data applications.

Contribution

It introduces verifiable methods to assess missing data mechanisms in multi-dimensional tables based on odds, enhancing analysis of incomplete categorical data.

Findings

Methods effectively distinguish MAR, MCAR, and NMAR mechanisms.

Procedures rely on joint and marginal odds from observed counts.

Real datasets confirm the proposed methods' utility.

Abstract

The analysis of incomplete contingency tables is a practical and an interesting problem. In this paper, we provide characterizations for the various missing mechanisms of a variable in terms of response and non-response odds for two and three dimensional incomplete tables. Log-linear parametrization and some distinctive properties of the missing data models for the above tables are discussed. All possible cases in which data on one, two or all variables may be missing are considered. We study the missingness of each variable in a model, which is more insightful for analyzing cross-classified data than the missingness of the outcome vector. For sensitivity analysis of the incomplete tables, we propose easily verifiable procedures to evaluate the missing at random (MAR), missing completely at random (MCAR) and not missing at random (NMAR) assumptions of the missing data models. These methods depend only on joint and marginal odds computed from fully and partially observed counts in the tables, respectively. Finally, some real-life datasets are analyzed to illustrate our results, which are confirmed based on simulation studies.