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Bivariate Negative Binomial Generalized Linear Models for Environmental Count Data

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  • Masakazu Iwasaki
  • Hiroe Tsubaki

Abstract

We propose a new bivariate negative binomial model with constant correlation structure, which was derived from a contagious bivariate distribution of two independent Poisson mass functions, by mixing the proposed bivariate gamma type density with constantly correlated covariance structure (Iwasaki & Tsubaki, 2005), which satisfies the integrability condition of McCullagh & Nelder (1989, p. 334). The proposed bivariate gamma type density comes from a natural exponential family. Joe (1997) points out the necessity of a multivariate gamma distribution to derive a multivariate distribution with negative binomial margins, and the luck of a convenient form of multivariate gamma distribution to get a model with greater flexibility in a dependent structure with indices of dispersion. In this paper we first derive a new bivariate negative binomial distribution as well as the first two cumulants, and, secondly, formulate bivariate generalized linear models with a constantly correlated negative binomial covariance structure in addition to the moment estimator of the components of the matrix. We finally fit the bivariate negative binomial models to two correlated environmental data sets.

Suggested Citation

  • Masakazu Iwasaki & Hiroe Tsubaki, 2006. "Bivariate Negative Binomial Generalized Linear Models for Environmental Count Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 909-923.
    • Handle: RePEc:taf:japsta:v:33:y:2006:i:9:p:909-923
    DOI: 10.1080/02664760600744157
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    References listed on IDEAS

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    1. Masakazu Iwasaki & Hiroe Tsubaki, 2005. "A new bivariate distribution in natural exponential family," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(3), pages 323-336, June.
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