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( | ) is the density function of β and refers to a vector of parameters of the

density function (mean and variance) and other terms are as previously defined.

Equation (5.11) shows the mixed logit model. In the mixed logit model estimation, β can now

account for observation-specific variations of the effect of on injury severity probabilities,
with the density functions ( | ) used to determine β.

The random parameter model uses a weighted average for different values of β across

observations where some elements of the parameter vector β may be fixed and some are
randomly distributed. If any parameters are found to be random, then the mixed logit weight

is determined by the density function. For the functional form of the density function,

numerous distributions have been considered, such as normal, uniform and lognormal. Mixed
logit models are usually estimated using the simulation of maximum likelihood with Halton

draws (Bhat 2003; Train 1999).

In this study, normal and uniform distributions were used as a density function in the mixed

logit model. Although the normal distribution had been widely used in road safety research,
Hensher and Greene (2003) and Train (2003) suggest that the normal distribution should be

used for continuous variables, while the uniform distribution should be used for dummy or
binary variables. However, neither study provided any examples or empirical evidence to

support this recommendation. Hence, the present study provides an example to explore this

recommendation.

It should be noted that although the mixed logit was formulated for multinomial responses, it
can also be used for binary responses. The binary logit, skewed logit and mixed logit models

were estimated using NLogit version 5.

5.3 Results and Discussion

The estimation results of the four models are summarized in Table 2. In terms of the models'

goodness-of-fit, the lower Akaike information criterion (AIC) value for the scobit model
implies that it fits the data better than the standard binary logit and mixed logit models. This

result was expected, partly because of the potential violation of the symmetry assumption due

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