Convergence Properties of a Sequential Regression Multiple Imputation Algorithm

A sequential regression or chained equations imputation approach uses a Gibbs sampling-type iterative algorithm that imputes the missing values using a sequence of conditional regression models. It is a flexible approach for handling different types of variables and complex data structures. Many simulation studies have shown that the multiple imputation inferences based on this procedure have desirable repeated sampling properties. However, a theoretical weakness of this approach is that the specification of a set of conditional regression models may not be compatible with a joint distribution of the variables being imputed. Hence, the convergence properties of the iterative algorithm are not well understood. This article develops conditions for convergence and assesses the properties of inferences from both compatible and incompatible sequence of regression models. The results are established for the missing data pattern where each subject may be missing a value on at most one variable. The sequence of regression models are assumed to be empirically good fit for the data chosen by the imputer based on appropriate model diagnostics. The results are used to develop criteria for the choice of regression models. Supplementary materials for this article are available online.