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Estimation of a zero-inflated Poisson regression model with missing covariates via nonparametric multiple imputation methods

Author

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  • Shen-Ming Lee

    (Feng Chia University
    Academia Sinica)

  • T. Martin Lukusa

    (Academia Sinica)

  • Chin-Shang Li

    (The State University of New York, University at Buffalo)

Abstract

Zero-inflated Poisson (ZIP) regression is widely applied to model effects of covariates on an outcome count with excess zeros. In some applications, covariates in a ZIP regression model are partially observed. Based on the imputed data generated by applying the multiple imputation (MI) schemes developed by Wang and Chen (Ann Stat 37:490–517, 2009), two methods are proposed to estimate the parameters of a ZIP regression model with covariates missing at random. One, proposed by Rubin (in: Proceedings of the survey research methods section of the American Statistical Association, 1978), consists of obtaining a unified estimate as the average of estimates from all imputed datasets. The other, proposed by Fay (J Am Stat Assoc 91:490–498, 1996), consists of averaging the estimating scores from all imputed data sets to solve the imputed estimating equation. Moreover, it is shown that the two proposed estimation methods are asymptotically equivalent to the semiparametric inverse probability weighting method. A modified formula is proposed to estimate the variances of the MI estimators. An extensive simulation study is conducted to investigate the performance of the estimation methods. The practicality of the methodology is illustrated with a dataset of motorcycle survey of traffic regulations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00930-x
    DOI: 10.1007/s00180-019-00930-x
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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, January.
    2. 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.
    3. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    4. 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.
    5. David Clayton & David Spiegelhalter & Graham Dunn & Andrew Pickles, 1998. "Analysis of longitudinal binary data from multiphase sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 71-87.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
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