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Background on Statistical Models for Accident Analyses

In traffic accident studies, multiple linear regression models have been frequently
used (Jovanis and Chang, 1986; Joshua and Garber, 1990; Miaou and Lum, 1993a). Accident
data consists of counts and the use of regression models that assume a normal distribution can
result in undesirable statistical properties, such as the possibility of negative accident counts
as has been suggested by Zeeger et al. (1990), Miaou and Lum (1993a), and Jovanis and
Chang (1986). Besides being unable to give appropriate statistical inferences about accident
occurrence, linear regression models that assume normality can also result in inaccurate
standard errors.

Accident occurrences are necessarily discrete, often sporadic and more likely random
events. Therefore, Poisson regression models are the appropriate statistical method to use. In
a number of studies in recent years (Miaou and Lim, 1993a, 1993b; Miaou et al., 1992;
Joshua and Garber, 1990; Jones et al., 1991; Kulmala, 1994; Maycock and Hall, 1984),
Poisson regression models have been used to establish statistical relationships between traffic
accidents and factors that contribute to accident occurrence.

The Poisson regression model also has limitations. One important constraint in
Poisson regression models is that the mean must be equal to the variance. If this assumption
is not valid, the standard errors, usually estimated by the maximum likelihood (ML) method,
will be biased and the test statistics derived from the models will be incorrect. In a number of
recent studies (Miaou, 1994; Shankar et al., 1995; Vogt and Bared, 1998), the accident data
were found to be significantly overdispersed, i.e., the variance is much greater than the mean.
This will result in incorrect estimation of the likelihood of accident occurrence.

In overcoming the problem of overdispersion, several researchers, like Miaou (1994),
Kulmala (1995), Shankar et al. (1995), Poch and Mannering (1996) and Abdel-Aty and
Radwan (2000) have employed the negative binomial (NB) distribution instead of the

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