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Semiparametric estimation of a zero-inflated Poisson regression model with missing covariates

Author

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  • T. Martin Lukusa

    (Feng Chia University)

  • Shen-Ming Lee

    (Feng Chia University)

  • Chin-Shang Li

    (University of California)

Abstract

Zero-inflated Poisson (ZIP) regression models have been widely used to study the effects of covariates in count data sets that have many zeros. However, often some covariates involved in ZIP regression modeling have missing values. Assuming that the selection probability is known or unknown and estimated via a non-parametric method, we propose the inverse probability weighting (IPW) method to estimate the parameters of the ZIP regression model with covariates missing at random. The asymptotic properties of the proposed estimators are studied in detail under certain regularity conditions. Both theoretical analysis and simulation results show that the semiparametric IPW estimator is more efficient than the true weight IPW estimator. The practical use of the proposed methodology is illustrated with data from a motorcycle survey of traffic regulations conducted in 2007 in Taiwan by the Ministry of Transportation and Communication.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:79:y:2016:i:4:d:10.1007_s00184-015-0563-7
    DOI: 10.1007/s00184-015-0563-7
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    References listed on IDEAS

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    1. Chen, Xue-Dong & Fu, Ying-Zi, 2011. "Model selection for zero-inflated regression with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 765-773, January.
    2. Daniel B. Hall & Jing Shen, 2010. "Robust Estimation for Zero‐Inflated Poisson Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 237-252, June.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    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. Jansakul, N. & Hinde, J. P., 2002. "Score Tests for Zero-Inflated Poisson Models," Computational Statistics & Data Analysis, Elsevier, vol. 40(1), pages 75-96, July.
    6. 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.
    7. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    8. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    9. Creemers, An & Aerts, Marc & Hens, Niel & Molenberghs, Geert, 2012. "A nonparametric approach to weighted estimating equations for regression analysis with missing covariates," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 100-113, January.
    10. C. Y. Wang & Hua Yun Chen, 2001. "Augmented Inverse Probability Weighted Estimator for Cox Missing Covariate Regression," Biometrics, The International Biometric Society, vol. 57(2), pages 414-419, June.
    11. Hsieh, S.H. & Lee, S.M. & Shen, P.S., 2009. "Semiparametric analysis of randomized response data with missing covariates in logistic regression," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2673-2692, May.
    12. Shou-En Lu & Yong Lin & Wei-Chung Joe Shih, 2004. "Analyzing Excessive No Changes in Clinical Trials with Clustered Data," Biometrics, The International Biometric Society, vol. 60(1), pages 257-267, March.
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    Cited by:

    1. 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.
    2. Lukusa, Martin T. & Phoa, Frederick Kin Hing, 2020. "A note on the weighting-type estimations of the zero-inflated Poisson regression model with missing data in covariates," Statistics & Probability Letters, Elsevier, vol. 158(C).
    3. Eric Han & Majid Mojirsheibani, 2021. "On histogram-based regression and classification with incomplete data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 635-662, July.
    4. Buu-Chau Truong & Nguyen Van Thuan & Nguyen Huu Hau & Michael McAleer, 2019. "Applications of the Newton-Raphson Method in Decision Sciences and Education," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(4), pages 52-80, December.
    5. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    6. 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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