A general approach for imputation of non-normal continuous data based on copula transformation

Abstract

Dealing with missing data problems for skewed data is a difficult task especially since most of the imputation and data augmentation methodologies assume multivariate normality. The performance of imputation and hence the accuracy of inference on parameters become questionable when the violation of the above assumption occurs. One approach to solve the normality violation is to apply normalizing transformation prior to the imputation phase. However, this approach may introduce new problems such as altering the dependence structure among random variables. We present a general purpose multiple imputation approach based on Copula transformation. The approach is used to effectively transform any continuous multivariate non-normal data to multivariate normal, thereby allowing the imputation using standard normality-based techniques. The method then allows to conveniently back transform the data into original space. Real data sets are used to illustrate the techniques. We then compare the performance of our Copula-based method with other traditional normality-based multiple imputation approaches through extensive simulated and real non-normal multivariate datasets. We demonstrate that this method significantly mitigates the problem and hence the practice of making the blind assumption of multivariate normality for non-normal multivariate data under the assumption that data are missing at different mechanisms.