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Estimation of logistic regression with covariates missing separately or simultaneously via multiple imputation methods

Author

Listed:
  • Shen-Ming Lee

    (Feng Chia University)

  • Truong-Nhat Le

    (Feng Chia University
    Ton Duc Thang University)

  • Phuoc-Loc Tran

    (Can Tho University)

  • Chin-Shang Li

    (University at Buffalo)

Abstract

Logistic regression is a standard model in many studies of binary outcome data, and the analysis of missing data in this model is a fascinating topic. Based on the idea of Wang D, Chen SX (2009) Empirical likelihood for estimating equations with missing values. Ann Stat, 37:490–517, proposed are two different types of multiple imputation (MI) estimation methods, which each use three empirical conditional distribution functions to generate random values to impute missing data, to estimate the parameters of logistic regression with covariates missing at random (MAR) separately or simultaneously by using the estimating equations of Fay RE (1996) Alternative paradigms for the analysis of imputed survey data. J Am Stat Assoc, 91:490–498. The derivation of the two proposed MI estimation methods is under the assumption of MAR separately or simultaneously and exclusively for categorical/discrete data. The two proposed methods are computationally effective, as evidenced by simulation studies. They have a quite similar efficiency and outperform the complete-case, semiparametric inverse probability weighting, validation likelihood, and random forest MI by chained equations methods. Although the two proposed methods are comparable with the joint conditional likelihood (JCL) method, they have more straightforward calculations and shorter computing times compared to the JCL and MICE methods. Two real data examples are used to illustrate the applicability of the proposed methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01250-3
    DOI: 10.1007/s00180-022-01250-3
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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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    Cited by:

    1. Truong-Nhat Le & Shen-Ming Lee & Phuoc-Loc Tran & Chin-Shang Li, 2023. "Randomized Response Techniques: A Systematic Review from the Pioneering Work of Warner (1965) to the Present," Mathematics, MDPI, vol. 11(7), pages 1-26, April.
    2. 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.

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