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where,
is a vector of measurable characteristics,

is a vector of coefficients to be estimated.

is an error term accounting for unobserved effects influencing the injury severity.

If the error terms are assumed to be type 1 extreme value distribution (McFadden, 1981),
then:

( )
( ) ∑ ( ) (2.5)

is a vector of measurable characteristics that determine outcome i,

is a vector of estimable parameters.

The model is more likely to violate the independence of irrelevant alternatives since the

correlation of unobserved effects with one injury severity level may be similar to another
injury severity level (Savolainen et al., 2011).

2.2.1.4 Heteroskedastic ordered probit and ordered logit models

This model was developed to address the heteroskedasticity in crash severity data which may

produce biassed estimation results (Savolainen, 2011). Lemp et al. (2011), developed
heteroskedastistic ordered probit models to examine the effect of environmental, driver and

vehicle characteristics on severity of injury in collisions. Their findings show that this model
significantly out-performs ordered probit models because it relaxes the assumptions of

constant variation. On the other hand, Lee and Li (2014) developed a heteroscedastic ordered

logit model which focuses on identifying the variables influencing drivers’ injury severity in
crashes.

2.2.1.5 Mixed logit (Random parameter logit) models

Random parameter logit or mixed logit models have been applied to allow the possibility that

the parameters may vary across observations (Washington et al., 2010). Some researchers
have chosen to use the random coefficient logit model to allow for heterogeneous effects and

correlations in unobserved factors, to address the limitations of multinomial logit models

(Milton et al., 2008; Anastasopoulos & Mannering, 2011; Tay, 2015). Islam and Hernandez
(2013) developed a model to identify the variables associated with injury severity in crashes
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