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2.2.1.6 Partial proportional odds model

In another study, Qin et al. (2013) developed a partial proportional odds (PPO) model to

examine the factors contributing to crash injury severity in crashes involving a heavy vehicle.
According to their findings, the PPO model is slightly better than the multinomial model and

mixed logit model in terms of the goodness of fit. The ordered logit model estimates the same
coefficient for each level of the response group and this restriction is known as the

proportional odds assumption. The PPO model overcomes the limitation of the ordered logit

model by allowing the coefficient to vary across the outcome levels if the proportional odds
assumption is violated.

2.2.1.7 Classification and Regression Tree model (CART) models

Chang and Chien (2013) developed a CART to examine heavy-vehicle drivers’ injury

severity in road collisions in Taiwan. For variables with categorical value, a classification
tree was developed, while a regression tree was developed for continuous values. The

classification and regression tree has three steps in modelling. The three stages in this model
are: tree growing, tree pruning and optimal tree selection. The first stage is to build a

classification tree, which is tree growing and this process is basically to reduce the variance
in terminal node. In the second stage, known as tree pruning, the structure of the tree is

simplified by removing some branches to increase the predictive value. The final stage is

optimisation to find the right size of tree (minimising the misclassification rate of both
learning and testing samples) and avoiding overfit in original learning samples. The

advantage of this model is that there is no need to specify the independent and dependent
variables. It also has a drawback to examine the effect of critical variables on injury severity

using elasticity analysis.

2.2.2 Crash severity models focusing on non-heavy vehicle crashes

2.2.2.1 Binary logit and probit models

In road safety studies, the binary model has been widely applied by previous researchers for a
dependent variable with the dichotomous output. In the binary model, severity injury

outcome is generally categorized as severe or non-severe injury crashes, or fatal or non-fatal
collisions. Rifaat and Tay (2009) developed a binary logit model to examine the effect of

street patterns on injury risk in two-vehicle collisions.

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