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Multiple Imputation Under Power Polynomials

2008; Taylor & Francis; Volume: 37; Issue: 8 Linguagem: Inglês

10.1080/03610910802101531

1532-4141

Hakan Demirtaş, Donald Hedeker,

Statistical Distribution Estimation and Applications

Abstract Although the normality assumption has been regarded as a mathematical convenience for inferential purposes due to its nice distributional properties, there has been a growing interest regarding generalized classes of distributions that span a much broader spectrum in terms of symmetry and peakedness behavior. In this respect, Fleishman's power polynomial method seems to have been gaining popularity in statistical theory and practice because of its flexibility and ease of execution. In this article, we conduct multiple imputation for univariate continuous data under Fleishman polynomials to explore the extent to which this procedure works properly. We also make comparisons with normal imputation models via widely accepted accuracy and precision measures using simulated data that exhibit different distributional features as characterized by competing specifications of the third and fourth moments. Finally, we discuss generalizations to the multivariate case. Multiple imputation under power polynomials that cover most of the feasible area in the skewness-elongation plane appears to have substantial potential of capturing real missing-data trends. Keywords: KurtosisMultiple imputationNormalitySymmetrySkewnessMathematics Subject Classification: 62F4062P10 Notes 1It is trivial to prove this by Cauchy–Schwarz inequality. Furthermore, one can show that equality condition is impossible to reach, but this is immaterial for the purposes of this work. 2There is nothing magical about the Newton–Raphson method, one can use any other plausible root-finding algorithm.