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Negative Binomial Regression Models and Estimation …

D 1 Appendix D: Negative Binomial Regression Models and Estimation Methods By Dominique Lord Texas A&M University Byung-Jung Park Korea Transport Institute This appendix presents the characteristics of Negative Binomial Regression Models and discusses their estimating methods. Probability Density and Likelihood Functions The properties of the Negative Binomial Models with and without spatial intersection are described in the next two sections. Poisson-Gamma model The Poisson-Gamma model has properties that are very similar to the Poisson model discussed in Appendix C, in which the dependent variable iy is modeled as a Poisson variable with a mean i where the model error is assumed to follow a Gamma distribution.

where, exp 0 i is defined as a random intercept; 0 1 exp K iijj j x is the log-link between the Poisson mean and the covariates or independent variables xs; and s are the regression coefficients. As discussed in Appendix C, the relationship can also be formulated using vectors, such that exp(x'β) i i.

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