Abstract:
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Imputation is arguably the most popular approach to statistical analysis with missing data. The focus of the past research has been on the development and application of imputation models under various settings. Yet the corresponding model diagnostic approaches have been lacking, and some ad-hoc checking procedures can be misleading. We propose a principled approach and consider the problem in which the missingness occurs to a single variable Y and covariates X are fully observed. Assuming that the missingness is at random, we aim to check whether the distribution of imputed Y is consistent with that of the observed Y conditional on X. Instead of checking this directly, which might be hard to implement in practice, we propose to decompose the task into two parts. First, we compare the distribution of observed and imputed Y conditional on the estimated propensity scores for the missingness. Second, we compare the distributions of covariates conditional on the observed and imputed Y and the propensity scores. We provide both theoretical justifications and recommendations for practical implementations. Simulation study and real examples are used for illustration.
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