Multiple imputation using multivariate gh transformations |
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Authors: | Yulei He Trivellore E Raghunathan |
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Institution: | 1. Department of Health Care Policy , Harvard Medical School , 180 Longwood Avenue, Boston , MA , 02115 , USA;2. Department of Biostatistics , University of Michigan School of Public Health , 1420 Washington Heights, Ann Arbor , MI , 48109 , USA |
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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. |
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Keywords: | bootstrap hospital quality imputation diagnostics latent variable multivariate missingness quantiles |
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