Page 87 - tmp_Neat

5.2.4 Random Parameter (Mixed Logit) Models

A summary of existing studies on random parameter logit model is presented in Section
2.2.1.5 of Chapter 2. Mixed logit (random parameters) has 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 or probit model to allow for
heterogeneous effects and correlations in unobserved factors (Anastasopoulos & Mannering,

2011; Kim et al., 2010; Milton et al., 2008; Tay, 2015). The mixed logit model was
developed by Milton et al., (2008) and starts with the severity function as below:

(5.9)

Where,

= is a linear function for determining the injury severity category i to occupants n

= a vector of estimated coefficients

= a vector of explanatory variables

= an error term

If are assumed to be extreme value distributions, we have the standard multinomial logit

model (McFadden, 1981). Let ( ) be the probability of injury severity category i for

observation n. Then

( )
( ) ∑ ( ) (5.10)

In the random parameter model, to let parameter ( ) vary across observations, a mixing

distribution is introduced in this model (Train, 2003) and the resulting injury severity

probalities are given by:

∫ [ ] ( | ) (5.11)

∑ [ ]

70