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2.2.1 Crash severity models focusing on heavy vehicle crashes

2.2.1.1 Ordered logit and ordered probit models

Duncan et al. (1998) developed an ordered probit model to investigate the injury severity of

passenger vehicle occupants in rear-end collisions. This model is an appropriate model for
analysing categorical injury data which are in order, either from low injury to higher severity

injury or non-injury to fatal injury. The developed model has a linear function as below:

(2.1)
where,

is assuming the injury severity (dependent variable),

is the vector of estimated parameters,

is the vector of the explanatory variables, and is an error term.

The observed ordinal injury outcome, for each observed crash is defined as:

(2.2)

{

where, is estimable threshold parameter between categorical responses .

The is a parameter that is estimated jointly with the model parameter . Therefore, the
model outcome probabilities are as below:

( ) ( ) ( ) (2.3)

where, and are the upper and lower bound of injury severity n.

The disadvantage of this model is that it may produce biassed estimation results for under-

reported crash data (Yamamoto et al., 2008; Ye, 2011). The other drawback of this model is
that it is difficult to interpret how the independent variables influence the likelihood of the

outcome (Savolainen et al., 2011). A further weakness of this model is that it neglects the
effect of injury severity level with a small percentage of observations (Li et al., 2012).

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