Poisson. By relaxing the condition that the mean is equal to the variance, NB regression
models are more suitable for describing discrete and nonnegative events.
An additional problem is unobserved heterogeneity which can occur with cross-
sectional analyses. One way to overcome this limitation is to use panel data and to consider
separate persistent individual effects in the NB models as suggested by Hausman, et al.
(1984) in their study of patent applications. Hausman et al. (1984) considered both the fixed
and random definitions of the individual effects; the former does not allow group-specific
variations. In employing the model in what may be its first application in traffic accident
studies, Shankar et al (1998) have indicated that the random effect negative binomial (RENB)
model may be more appropriate because geometric and traffic variables are likely to have
location-specific effects. With his study, it appears that the RENB models can significantly
improve the explanatory power of accident models. Chin and Quddus (2002) applied the
random effects version of Hausman et al.’s model to examine traffic accident occurrence at
signalized intersections.
Noland (2001a, 2001b) used the fixed effects NB model to overcome the
heterogeneity in cross-sectional time-series data. Olmstead (2001) also used the fixed effects
version of Hausman et al.’s model to measure the impact of a freeway management system
on the incidence of reported motor-vehicle crashes in Phoenix. These studies both suggested
found the Hausman specification test (Hausman, 1978) rejected the random effects model in
favor of fixed effects models in the vast majority of cases. The approach taken here is to use
the fixed effects negative binomial model to examine the factors influencing vehicle
casualties in the UK.
Methodology
The data in our analyses form a cross-sectional time-series consisting of repeated
observations on the same UK regions. We utilize the method derived by Hausman et al.
10
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