A Modeler's Choices for Missing Not at Random Scenario

Missing data are a common problem in longitudinal studies. For example, respondents may refuse to participate after the first wave of data collection was completed.  It is well known that restricting analysis to complete cases may produce biased and less efficient estimates. Generally, there are three main approaches for accounting missing data in longitudinal studies which include, weighting, imputation , and likelihood.

As a modeler, the key concern is whether the estimated parameters using any of the three approaches are different from their true values. If the missing cases do not have strong effect on the estimation, then it can be ignored. If the missing cases are not at random; however, modeling the missing and the responses as a joint distribution must be considered. However, testing the ignobility of missing data is difficult and complex. Therefore, the choice between using a missing-at-random (MAR) model and a missing-not-at-random (MNAR) model should be based on results of sensitivity analysis.  Although over the last decade a variety of joint models and methods to test sensitivity have been proposed, applications of such models in social science research are still uncommon, partially due to the computational complexity and technical difficulties of implementation in regular commercial packages such as SAS, and STATA. 

In this study, taking advantage of newly updated procedure PROC MCMC in SAS, we implement two MNAR models-- the selection model and the shared-parameter model with various indicators for sensitivity analysis. In addition, we also extend the two above models to nonlinear outcomes, such as Binary, Poisson, and zero-inflated Poisson. To evaluate the performance of our model, simulation studies are conducted with various setups. We also reanalyze the result published by Guo et.al on delinquency. The example provides a comprehensive modeling strategy for dealing with missing in longitudinal studies.