Plausibility of multivariate normality assumption when multiply imputing non-Gaussian continuous outcomes: a simulation assessment

Abstract Multiple imputation under the assumption of multivariate normality has emerged as a frequently used model-based approach in dealing with incomplete continuous data in recent years. Despite its simplicity and popularity, however, its plausibility has not been thoroughly evaluated via simulation. In this work, the performance of multiple imputation under a multivariate Gaussian model with unstructured covariances was examined on a broad range of simulated incomplete data sets that exhibit varying distributional characteristics such as skewness and multimodality that are not accommodated by a Gaussian model. Behavior of efficiency and accuracy measures was explored to determine the extent to which the procedure works properly. The conclusion drawn is that although the real data rarely conform with multivariate normality, imputation under the assumption of normality is a fairly reasonable tool, even when the assumption of normality is clearly violated; the fraction of missing information is high, especially when the sample size is relatively large. Although we discourage its uncritical, automatic and, possibly, inappropriate use, we report that its performance is better than we expected, leading us to believe that it is probably an underrated approach. Keywords: Multivariate normalityMultiple imputationSymmetrySkewnessMultimodality Notes †The parameter values used in figure 1 are different from the ones used in simulations. This graph is created for the purpose of exposition of different tail behaviors.