Abstract
Missing data are a common issue in statistical analyses. Multiple imputation is a technique that has been applied in countless research studies and has a strong theoretical basis. Most of the statistical literature on multiple imputation has focused on unbounded continuous variables, with mostly ad hoc remedies for variables with bounded support. These approaches can be unsatisfactory when applied to bounded variables as they can produce misleading inferences. In this paper, we propose a flexible quantile-based imputation model suitable for distributions defined over singly or doubly bounded intervals. Proper support of the imputed values is ensured by applying a family of transformations with singly or doubly bounded range. Simulation studies demonstrate that our method is able to deal with skewness, bimodality, and heteroscedasticity and has superior properties as compared to competing approaches, such as log-normal imputation and predictive mean matching. We demonstrate the application of the proposed imputation procedure by analysing data on mathematical development scores in children from the Millennium Cohort Study, UK. We also show a specific advantage of our methods using a small psychiatric dataset. Our methods are relevant in a number of fields, including education and psychology.
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Acknowledgements
Marco Geraci was funded by an ASPIRE grant from the Office of the Vice President for Research at the University of South Carolina and by the National Institutes of Health–National Institute of Child Health and Human Development (Grant Number: 1R03HD084807-01A1). The authors wish to thank four anonymous referees for helpful comments and suggestions that substantially improved the paper.
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Geraci, M., McLain, A. Multiple Imputation for Bounded Variables. Psychometrika 83, 919–940 (2018). https://doi.org/10.1007/s11336-018-9616-y
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DOI: https://doi.org/10.1007/s11336-018-9616-y