Multiple imputation using multivariate gh transformations

Abstract

Multiple imputation has emerged as a popular approach to handling data sets with missing values. For incomplete continuous variables, imputations are usually produced using multivariate normal models. However, this approach might be problematic for variables with a strong non-normal shape, as it would generate imputations incoherent with actual distributions and thus lead to incorrect inferences. For non-normal data, we consider a multivariate extension of Tukey's gh distribution/transformation [38] to accommodate skewness and/or kurtosis and capture the correlation among the variables. We propose an algorithm to fit the incomplete data with the model and generate imputations. We apply the method to a national data set for hospital performance on several standard quality measures, which are highly skewed to the left and substantially correlated with each other. We use Monte Carlo studies to assess the performance of the proposed approach. We discuss possible generalizations and give some advices to practitioners on how to handle non-normal incomplete data.

Keywords:

• bootstrap
• hospital quality
• imputation diagnostics
• latent variable
• multivariate missingness
• quantiles

Acknowledgements

We thank the Editor and reviewers for their helpful comments which have greatly improved the manuscript.