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Multiple imputation using multivariate gh transformations

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  • Yulei He
  • Trivellore E. Raghunathan

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.

Suggested Citation

  • Yulei He & Trivellore E. Raghunathan, 2012. "Multiple imputation using multivariate gh transformations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(10), pages 2177-2198, June.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:10:p:2177-2198
    DOI: 10.1080/02664763.2012.702268
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    References listed on IDEAS

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    1. Kobi Abayomi & Andrew Gelman & Marc Levy, 2008. "Diagnostics for multivariate imputations," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(3), pages 273-291, June.
    2. Velilla, Santiago, 1993. "A note on the multivariate Box--Cox transformation to normality," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 259-263, July.
    3. He, Yulei & Raghunathan, Trivellore E., 2006. "Tukey's gh Distribution for Multiple Imputation," The American Statistician, American Statistical Association, vol. 60, pages 251-256, August.
    4. Hakan Demirtas & Donald Hedeker, 2008. "Imputing continuous data under some non‐Gaussian distributions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(2), pages 193-205, May.
    5. Andrew Gelman & Iven Van Mechelen & Geert Verbeke & Daniel F. Heitjan & Michel Meulders, 2005. "Multiple Imputation for Model Checking: Completed-Data Plots with Missing and Latent Data," Biometrics, The International Biometric Society, vol. 61(1), pages 74-85, March.
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    Cited by:

    1. Paul T. von Hippel, 2013. "Should a Normal Imputation Model be Modified to Impute Skewed Variables?," Sociological Methods & Research, , vol. 42(1), pages 105-138, February.
    2. Xu, Ganggang & Genton, Marc G., 2015. "Efficient maximum approximated likelihood inference for Tukey’s g-and-h distribution," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 78-91.
    3. Zhixin Lun & Ravindra Khattree, 2021. "Imputation for Skewed Data: Multivariate Lomax Case," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(1), pages 86-113, May.
    4. Ganggang Xu & Marc G. Genton, 2017. "Tukey -and- Random Fields," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1236-1249, July.
    5. Marco Geraci & Alexander McLain, 2018. "Multiple Imputation for Bounded Variables," Psychometrika, Springer;The Psychometric Society, vol. 83(4), pages 919-940, December.

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