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Multiple Imputation for Bounded Variables

Published online by Cambridge University Press:  01 January 2025

Marco Geraci Open the ORCID record for Marco Geraci [Opens in a new window]  and
Alexander McLain
Marco Geraci*
Affiliation:
University of South Carolina
Alexander McLain
Affiliation:
University of South Carolina
*
Correspondence should be made to Marco Geraci, Department of Epidemiology and Biostatistics, Arnold School of Public Health, University of South Carolina, 915 Greene Street, Columbia, SC 29208, USA. Email: [email protected]
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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.

Keywords

ceiling effectseducationfloor effectsgradingnonlinear associationspsychometric scores
Type
Original Paper
Information
Psychometrika , Volume 83 , Issue 4 , December 2018 , pp. 919 - 940
Copyright
Copyright © The 2018 Psychometric Society

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Footnotes

Electronic supplementary materialThe online version of this article (https://doi.org/10.1007/s11336-018-9616-y) contains supplementary material, which is available to authorized users.

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