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2.2.1.2 Nested logit models

Nested logit models have been used in crash severity analysis since they can overcome the

independency of irrelevant alternatives, which is an assumption in the multinomial models. In
nested logit models, injury severity is partially nested with some unobserved factors, which

have correlations with specific severity outcomes within the same nest (Ye, 2011).

Many researchers have applied nested logit models to analyse crash injury severity in road
collisions (Chang and Mannering, 1999; Haleem and Abdel-Aty, 2010; Hu and Donnell,

2010). For road collisions involving heavy vehicles, Chang and Mannering (1999) developed
a nested logit model to investigate the relationship between severity of injury and vehicle

occupancy.

2.2.1.2 Simultaneous logit model

Ouyang et al. (2002), used a simultaneous logit model to investigate the main factors
contributing to crash injury severity in two-vehicle collisions. This model was developed to

address the limitations of the probit and logit models, which allow analysis of one dependent
variable only.

2.2.1.3 Multinomial Logit

Previous researchers in road safety have widely applied injury severity to model the

dependent ordered variables with more than two outcomes. However, in multinomial logit
models, ordered injury severity has no impact on model development. In road crashes, the

dependent variable of road-user injury severity is generally classified as fatal, incapacitating

injury, non-incapacitating injury, possible injury, and property damage only. Khorashadi et
al. (2005) developed a multinomial logit model to investigate the severity injury of drivers in

collisions involving heavy vehicles. In the development of a multinomial logit model, the
probability of a crash ending in a specific injury severity level is considered. Let ( ) be the

probability of collision n ending in injury severity category i, then

( ) ( ) (2.4)

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