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Performance of Sequential Imputation Method in Multilevel Applications

In missing-data problems complicated not only by the underlying data-generating mechanism (e.g. multi-stage surveys) but also skip patterns, censored items and a diverse set of variable types, a variable-by-variable imputation strategy has been increasingly popular among practitioners. While this approach offers certain advantages, it does not necessarily follow a conventional joint modeling approach. Our work assesses the performance and compatibility of sequential approach to a joint modeling approach in multilevel settings. This sequential approach uses a set of hierarchical regression models each of which follows the appropriate format for the underlying variable subject to missingness. Computational techniques used to approximate the conditional posterior predictive distributions are based on Markov Chain Monte Carlo and/or numerical integration techniques to overcome the problem of intractability. We present a simulation study assessing the performance of the sequential approach. In most realistic applications, our simulations suggest that the sequential method lead to well-calibrated estimates and in some settings the performance is even better than the more conventional methods with well-defined joint model in some scenarios.