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A note on imputing squares via polynomial combination approach

Author

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  • Mingyang Cai

    (Utrecht University)

  • Gerko Vink

    (Utrecht University)

Abstract

The polynomial combination (PC) method, proposed by Vink and Van Buuren, is a hot-deck multiple imputation method for imputation models containing squared terms. The method yields unbiased regression estimates and preserves the quadratic relationships in the imputed data for both MCAR and MAR mechanisms. However, Vink and Van Buuren never studied the coverage rate of the PC method. This paper investigates the coverage of the nominal 95% confidence intervals for the polynomial combination method and improves the algorithm to avoid the perfect prediction issue. We also compare the original and the improved PC method to the substantive model compatible fully conditional specification method proposed by Bartlett et al. and elucidate the two imputation methods’ characters.

Suggested Citation

  • Mingyang Cai & Gerko Vink, 2022. "A note on imputing squares via polynomial combination approach," Computational Statistics, Springer, vol. 37(5), pages 2185-2201, November.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:5:d:10.1007_s00180-022-01194-8
    DOI: 10.1007/s00180-022-01194-8
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    References listed on IDEAS

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    1. van Buuren, Stef & Groothuis-Oudshoorn, Karin, 2011. "mice: Multivariate Imputation by Chained Equations in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i03).
    2. White, Ian R. & Daniel, Rhian & Royston, Patrick, 2010. "Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2267-2275, October.
    3. Little, Roderick J A, 1988. "Missing-Data Adjustments in Large Surveys: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 300-301, July.
    4. Rubin, Donald B, 1986. "Statistical Matching Using File Concatenation with Adjusted Weights and Multiple Imputations," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 87-94, January.
    5. Little, Roderick J A, 1988. "Missing-Data Adjustments in Large Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 287-296, July.
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