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A hierarchical Bayesian approach for the analysis of longitudinal count data with overdispersion: A simulation study

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  • Aregay, Mehreteab
  • Shkedy, Ziv
  • Molenberghs, Geert

Abstract

In sets of count data, the sample variance is often considerably larger or smaller than the sample mean, known as a problem of over- or underdispersion. The focus is on hierarchical Bayesian modeling of such longitudinal count data. Two different models are considered. The first one assumes a Poisson distribution for the count data and includes a subject-specific intercept, which is assumed to follow a normal distribution, to account for subject heterogeneity. However, such a model does not fully address the potential problem of extra-Poisson dispersion. The second model, therefore, includes also random subject and time dependent parameters, assumed to be gamma distributed for reasons of conjugacy. To compare the performance of the two models, a simulation study is conducted in which the mean squared error, relative bias, and variance of the posterior means are compared.

Suggested Citation

  • Aregay, Mehreteab & Shkedy, Ziv & Molenberghs, Geert, 2013. "A hierarchical Bayesian approach for the analysis of longitudinal count data with overdispersion: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 233-245.
    • Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:233-245
    DOI: 10.1016/j.csda.2012.06.020
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    References listed on IDEAS

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    1. Pryseley, Assam & Tchonlafi, Clotaire & Verbeke, Geert & Molenberghs, Geert, 2011. "Estimating negative variance components from Gaussian and non-Gaussian data: A mixed models approach," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1071-1085, February.
    2. Iddi, Samuel & Molenberghs, Geert, 2012. "A combined overdispersed and marginalized multilevel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1944-1951.
    3. Hinde, John & Demetrio, Clarice G. B., 1998. "Overdispersion: Models and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 27(2), pages 151-170, April.
    4. Stuart J. Pocock & Derek G. Cook & Shirley A. A. Beresford, 1981. "Regression of Area Mortality Rates on Expalanatory Variables: What Weighting is Appropriate?," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(3), pages 286-295, November.
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    1. Oludare Ariyo & Emmanuel Lesaffre & Geert Verbeke & Adrian Quintero, 2022. "Bayesian Model Selection for Longitudinal Count Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 516-547, November.

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