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On familial longitudinal Poisson mixed models with gamma random effects

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  • Sutradhar, Brajendra C.
  • Jowaheer, Vandna

Abstract

Poisson mixed models are used to analyze a wide variety of cluster count data. These models are commonly developed based on the assumption that the random effects have either the log-normal or the gamma distribution. Obtaining consistent as well as efficient estimates for the parameters involved in such Poisson mixed models has, however, proven to be difficult. Further problem gets mounted when the data are collected repeatedly from the individuals of the same cluster or family. In this paper, we introduce a generalized quasilikelihood approach to analyze the repeated familial data based on the familial structure caused by gamma random effects. This approach provides estimates of the regression parameters and the variance component of the random effects after taking the longitudinal correlations of the data into account. The estimators are consistent as well as highly efficient.

Suggested Citation

  • Sutradhar, Brajendra C. & Jowaheer, Vandna, 2003. "On familial longitudinal Poisson mixed models with gamma random effects," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 398-412, November.
    • Handle: RePEc:eee:jmvana:v:87:y:2003:i:2:p:398-412
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    References listed on IDEAS

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    1. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    2. Sutradhar, Brajendra C. & Rao, R. Prabhakar, 2001. "On Marginal Quasi-Likelihood Inference in Generalized Linear Mixed Models," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 1-34, January.
    3. C. Sutradhar, Brajendra & Das, Kalyan, 2001. "A higher-order approximation to likelihood inference in the Poisson mixed model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 59-67, March.
    4. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
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    1. Brajendra C. Sutradhar & Vandna Jowaheer & Gary Sneddon, 2008. "On a Unified Generalized Quasi–likelihood Approach for Familial–Longitudinal Non‐Stationary Count Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 597-612, December.
    2. Youn Ahn, Jae & Jeong, Himchan & Lu, Yang, 2021. "On the ordering of credibility factors," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 626-638.

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