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Random effects regression models for count data with excess zeros in caries research

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  • D. Todem
  • Y. Zhang
  • A. Ismail
  • W. Sohn

Abstract

We extend the family of Poisson and negative binomial models to derive the joint distribution of clustered count outcomes with extra zeros. Two random effects models are formulated. The first model assumes a shared random effects term between the conditional probability of perfect zeros and the conditional mean of the imperfect state. The second formulation relaxes the shared random effects assumption by relating the conditional probability of perfect zeros and the conditional mean of the imperfect state to two different but correlated random effects variables. Under the conditional independence and the missing data at random assumption, a direct optimization of the marginal likelihood and an EM algorithm are proposed to fit the proposed models. Our proposed models are fitted to dental caries counts of children under the age of six in the city of Detroit.

Suggested Citation

  • D. Todem & Y. Zhang & A. Ismail & W. Sohn, 2010. "Random effects regression models for count data with excess zeros in caries research," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(10), pages 1661-1679.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:10:p:1661-1679
    DOI: 10.1080/02664760903127605
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    References listed on IDEAS

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    1. Thomas R. Ten Have & Alfredo Morabia, 1999. "Mixed Effects Models with Bivariate and Univariate Association Parameters for Longitudinal Bivariate Binary Response Data," Biometrics, The International Biometric Society, vol. 55(1), pages 85-93, March.
    2. 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.
    3. S. Rabe-Hesketh & A. Skrondal, 2001. "Parameterization of Multivariate Random Effects Models for Categorical Data," Biometrics, The International Biometric Society, vol. 57(4), pages 1256-1263, December.
    4. Martin Ridout & John Hinde & Clarice G. B. Demétrio, 2001. "A Score Test for Testing a Zero‐Inflated Poisson Regression Model Against Zero‐Inflated Negative Binomial Alternatives," Biometrics, The International Biometric Society, vol. 57(1), pages 219-223, March.
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    Cited by:

    1. Ping Zeng & Yongyue Wei & Yang Zhao & Jin Liu & Liya Liu & Ruyang Zhang & Jianwei Gou & Shuiping Huang & Feng Chen, 2014. "Variable selection approach for zero-inflated count data via adaptive lasso," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(4), pages 879-894, April.

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