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Large-sample properties of multiple imputation estimators for parameters of logistic regression with covariates missing at random separately or simultaneously

Author

Listed:
  • Phuoc-Loc Tran

    (Can Tho University)

  • Shen-Ming Lee

    (Feng Chia University)

  • Truong-Nhat Le

    (Ton Duc Thang University)

  • Chin-Shang Li

    (University of Rochester Medical Center)

Abstract

We examine the asymptotic properties of two multiple imputation (MI) estimators, given in the study of Lee et al. (Computational Statistics, 38, 899–934, 2023) for the parameters of logistic regression with both sets of discrete or categorical covariates that are missing at random separately or simultaneously. The proposed estimated asymptotic variances of the two MI estimators address a limitation observed with Rubin’s estimated variances, which lead to underestimate the variances of the two MI estimators (Rubin, 1987, Statistical Analysis with Missing Data, New York:Wiley). Simulation results demonstrate that our two proposed MI methods outperform the complete-case, semiparametric inverse probability weighting, random forest MI using chained equations, and stochastic approximation of expectation-maximization methods. To illustrate the methodology’s practical application, we provide a real data example from a survey conducted at the Feng Chia night market in Taichung City, Taiwan.

Suggested Citation

  • Phuoc-Loc Tran & Shen-Ming Lee & Truong-Nhat Le & Chin-Shang Li, 2025. "Large-sample properties of multiple imputation estimators for parameters of logistic regression with covariates missing at random separately or simultaneously," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(2), pages 251-287, April.
    • Handle: RePEc:spr:aistmt:v:77:y:2025:i:2:d:10.1007_s10463-024-00914-9
    DOI: 10.1007/s10463-024-00914-9
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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. Jiang, Wei & Josse, Julie & Lavielle, Marc, 2020. "Logistic regression with missing covariates—Parameter estimation, model selection and prediction within a joint-modeling framework," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    3. Paolo Righi & Stefano Falorsi & Andrea Fasulo, 2014. "Methods for variance estimation under random hot deck imputation in business surveys," Rivista di statistica ufficiale, ISTAT - Italian National Institute of Statistics - (Rome, ITALY), vol. 16(1-2), pages 45-64.
    4. Shen-Ming Lee & Chin-Shang Li & Shu-Hui Hsieh & Li-Hui Huang, 2012. "Semiparametric estimation of logistic regression model with missing covariates and outcome," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 621-653, July.
    5. T. Martin Lukusa & Shen-Ming Lee & Chin-Shang Li, 2016. "Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(4), pages 457-483, May.
    6. Shen-Ming Lee & T. Martin Lukusa & Chin-Shang Li, 2020. "Estimation of a zero-inflated Poisson regression model with missing covariates via nonparametric multiple imputation methods," Computational Statistics, Springer, vol. 35(2), pages 725-754, June.
    7. Josse, Julie & Husson, François, 2016. "missMDA: A Package for Handling Missing Values in Multivariate Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 70(i01).
    8. Shen‐Ming Lee & Wen‐Han Hwang & Jean de Dieu Tapsoba, 2016. "Estimation in closed capture–recapture models when covariates are missing at random," Biometrics, The International Biometric Society, vol. 72(4), pages 1294-1304, December.
    9. Wang, Suojin & Wang, C. Y., 2001. "A note on kernel assisted estimators in missing covariate regression," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 439-449, December.
    10. Shen-Ming Lee & Mei-Jih Gee & Shu-Hui Hsieh, 2011. "Semiparametric Methods in the Proportional Odds Model for Ordinal Response Data with Missing Covariates," Biometrics, The International Biometric Society, vol. 67(3), pages 788-798, September.
    11. Hsieh, Shu-Hui & Li, Chin-Shang & Lee, Shen-Ming, 2013. "Logistic regression with outcome and covariates missing separately or simultaneously," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 32-54.
    12. Shen-Ming Lee & Truong-Nhat Le & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Estimation of logistic regression with covariates missing separately or simultaneously via multiple imputation methods," Computational Statistics, Springer, vol. 38(2), pages 899-934, June.
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