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Combining rules for F- and Beta-statistics from multiply-imputed data

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  • Chaurasia, Ashok

Abstract

Missing values in data impede the task of inference for population parameters of interest. Multiple Imputation (MI) is a popular method for handling missing data since it accounts for the uncertainty of missing values. Inference in MI involves combining point and variance estimates from each imputed dataset via Rubin’s rules. A sufficient condition for these rules is that the estimator is approximately (multivariate) normally distributed. However, these traditional combining rules get computationally cumbersome for multicomponent parameters of interest, and unreliable at high rates of missingness (due to an unstable variance matrix). New combining rules for univariate F- and Beta-statistics from multiply-imputed data are proposed for decisions about multicomponent parameters. The proposed combining rules have the advantage of being computationally convenient since they only involve univariate F- and Beta-statistics, while providing the same inferential reliability as the traditional multivariate combining rules. Simulation study is conducted to demonstrate that the proposed method has good statistical properties of maintaining low type I and type II error rates at relatively large proportions of missingness. The general applicability of the proposed method is demonstrated within a lead exposure study to assess the association between lead exposure and neurological motor function.

Suggested Citation

  • Chaurasia, Ashok, 2023. "Combining rules for F- and Beta-statistics from multiply-imputed data," Econometrics and Statistics, Elsevier, vol. 25(C), pages 51-65.
    • Handle: RePEc:eee:ecosta:v:25:y:2023:i:c:p:51-65
    DOI: 10.1016/j.ecosta.2021.08.013
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    References listed on IDEAS

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    1. Jerome P. Reiter, 2007. "Small-sample degrees of freedom for multi-component significance tests with multiple imputation for missing data," Biometrika, Biometrika Trust, vol. 94(2), pages 502-508.
    2. Ofer Harel, 2009. "The estimation of R2 and adjusted R2 in incomplete data sets using multiple imputation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(10), pages 1109-1118.
    3. Paul T. von Hippel, 2020. "How Many Imputations Do You Need? A Two-stage Calculation Using a Quadratic Rule," Sociological Methods & Research, , vol. 49(3), pages 699-718, August.
    4. Horton N. J. & Lipsitz S. R., 2001. "Multiple Imputation in Practice: Comparison of Software Packages for Regression Models With Missing Variables," The American Statistician, American Statistical Association, vol. 55, pages 244-254, August.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    combining F- and Beta-statistics; combining R2; F-tests; missing data; multiple imputation; linear models;
    All these keywords.

    JEL classification:

    • R2 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Household Analysis

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