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A Poisson mixed model with nonnormal random effect distribution

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  • Fabio, Lizandra C.
  • Paula, Gilberto A.
  • Castro, Mário de

Abstract

In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration.

Suggested Citation

  • Fabio, Lizandra C. & Paula, Gilberto A. & Castro, Mário de, 2012. "A Poisson mixed model with nonnormal random effect distribution," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1499-1510.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1499-1510
    DOI: 10.1016/j.csda.2011.12.002
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    References listed on IDEAS

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    1. Ortega, Edwin M. M. & Bolfarine, Heleno & Paula, Gilberto A., 2003. "Influence diagnostics in generalized log-gamma regression models," Computational Statistics & Data Analysis, Elsevier, vol. 42(1-2), pages 165-186, February.
    2. Peng Zhang & Peter X.-K. Song & Annie Qu & Tom Greene, 2008. "Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models," Biometrics, The International Biometric Society, vol. 64(1), pages 29-38, March.
    3. Alonso, A. & Litière, S. & Molenberghs, G., 2008. "A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4474-4486, May.
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    Cited by:

    1. Lizandra C. Fabio & Francisco J. A. Cysneiros & Gilberto A. Paula & Jalmar M. F. Carrasco, 2022. "Hierarchical and multivariate regression models to fit correlated asymmetric positive continuous outcomes," Computational Statistics, Springer, vol. 37(3), pages 1435-1459, July.
    2. Carlos A. Cardozo & Gilberto A. Paula & Luiz H. Vanegas, 2022. "Generalized log-gamma additive partial linear models with P-spline smoothing," Statistical Papers, Springer, vol. 63(6), pages 1953-1978, December.
    3. Tang, Niansheng & Wu, Ying & Chen, Dan, 2018. "Semiparametric Bayesian analysis of transformation linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 225-240.

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