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Robust Estimation for Zero‐Inflated Poisson Regression

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  • DANIEL B. HALL
  • JING SHEN

Abstract

. The zero‐inflated Poisson regression model is a special case of finite mixture models that is useful for count data containing many zeros. Typically, maximum likelihood (ML) estimation is used for fitting such models. However, it is well known that the ML estimator is highly sensitive to the presence of outliers and can become unstable when mixture components are poorly separated. In this paper, we propose an alternative robust estimation approach, robust expectation‐solution (RES) estimation. We compare the RES approach with an existing robust approach, minimum Hellinger distance (MHD) estimation. Simulation results indicate that both methods improve on ML when outliers are present and/or when the mixture components are poorly separated. However, the RES approach is more efficient in all the scenarios we considered. In addition, the RES method is shown to yield consistent and asymptotically normal estimators and, in contrast to MHD, can be applied quite generally.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:2:p:237-252
    DOI: 10.1111/j.1467-9469.2009.00657.x
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    References listed on IDEAS

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    1. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
    2. Zudi Lu & Yer Van Hui & Andy H. Lee, 2003. "Minimum Hellinger Distance Estimation for Finite Mixtures of Poisson Regression Models and Its Applications," Biometrics, The International Biometric Society, vol. 59(4), pages 1016-1026, December.
    3. A. M. C. Vieira & J. P. Hinde & C. G. B. Demetrio, 2000. "Zero-inflated proportion data models applied to a biological control assay," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(3), pages 373-389.
    4. Adimari, Gianfranco & Ventura, Laura, 2001. "Robust inference for generalized linear models with application to logistic regression," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 413-419, December.
    5. John S. Preisser & Bahjat F. Qaqish, 1999. "Robust Regression for Clustered Data with Application to Binary Responses," Biometrics, The International Biometric Society, vol. 55(2), pages 574-579, June.
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    Cited by:

    1. 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.
    2. 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.
    3. Dalei Yu, 2016. "Conditional Akaike Information Criteria for a Class of Poisson Mixture Models with Random Effects," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1214-1235, December.

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