On Testability and Goodness of Fit Tests in Missing Data Models
This work addresses a critical gap in missing data analysis for researchers and practitioners in fields like longitudinal studies and surveys, offering tools to test model assumptions, though it is incremental as it builds on existing graphical model frameworks.
The paper tackles the problem of verifying modeling assumptions in missing data graphical models, which are crucial for valid results but often overlooked, by providing new insights on testable implications and designing goodness-of-fit tests for three classes of models, including sequential missing-at-random and missing-not-at-random models for longitudinal studies and a no self-censoring model for cross-sectional studies.
Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely on the assumptions encoded by the graph holding true; however, verification of these assumptions has not received sufficient attention in prior work. In this paper, we provide new insights on the testable implications of three broad classes of missing data graphical models, and design goodness-of-fit tests for them. The classes of models explored are: sequential missing-at-random and missing-not-at-random models which can be used for modeling longitudinal studies with dropout/censoring, and a no self-censoring model which can be applied to cross-sectional studies and surveys.