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Analysis of count data with covariate dependence in both mean and variance

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  • M. J. Faddy
  • D. M. Smith

Abstract

Extended Poisson process modelling is generalised to allow for covariate-dependent dispersion as well as a covariate-dependent mean response. This is done by a re-parameterisation that uses approximate expressions for the mean and variance. Such modelling allows under- and over-dispersion, or a combination of both, in the same data set to be accommodated within the same modelling framework. All the necessary calculations can be done numerically, enabling maximum likelihood estimation of all model parameters to be carried out. The modelling is applied to re-analyse two published data sets, where there is evidence of covariate-dependent dispersion, with the modelling leading to more informative analyses of these data and more appropriate measures of the precision of any estimates.

Suggested Citation

  • M. J. Faddy & D. M. Smith, 2011. "Analysis of count data with covariate dependence in both mean and variance," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(12), pages 2683-2694, February.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:12:p:2683-2694
    DOI: 10.1080/02664763.2011.567250
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    Cited by:

    1. Bao-Linh Tran & Wei-Chun Tseng & Chi-Chung Chen & Shu-Yi Liao, 2020. "Estimating the Threshold Effects of Climate on Dengue: A Case Study of Taiwan," IJERPH, MDPI, vol. 17(4), pages 1-17, February.
    2. Smith, David M. & Faddy, Malcolm J., 2016. "Mean and Variance Modeling of Under- and Overdispersed Count Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 69(i06).
    3. Sáez-Castillo, A.J. & Conde-Sánchez, A., 2013. "A hyper-Poisson regression model for overdispersed and underdispersed count data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 148-157.

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