Page 25 - tmp_Neat

2.2.2.6 Generalized ordered logit models

The generalized logit model is a model which generalises the standard ordered logit model.

Quddus et al. (2009) developed models to discover the relationship between crash injury
severity and traffic congestion conditions. The generalized ordered logit model was used

because of it does not impose a constraint on parallel regression (Fu, 1998).

2.2.2.7 Bayesian ordered probit, mixed generalized ordered logit and mixed ordered
The Bayesian ordered probit model and the mixed generalized ordered logit and mixed

ordered logit models are an extension to conventional ordered probability models. Xie et al.

(2009) developed a Bayesian ordered probit model to investigate the crash injury severity of
drivers in vehicle collisions. The Bayesian inference was extended into existing ordered

probit to develop this model. The model produces more accurate predictions than ordered

probit with a smaller size of crash data.

On the other hand, Eluru et al. (2008) developed mixed generalized ordered logit to

investigate pedestrian and bicyclist injury severity level in road crashes. This model allows
the parameters to vary across observations and allows for heterogeneous effects in

unobserved factors. It is also a generalized form of the standard ordered logit model. In

another version, the mixed ordered logit model produces non–biassed estimation results and
superior fit to the observed data than traditional ordered logit models (Srinivisan, 2002).

2.2.2.8 Markov switching multinomial logit

Malyshkina and Mannering (2009) developed a two-state Markov switching multinomial

logit model to examine injury severity. This model assumes that there are two unobserved
states of road safety related to injury severity, such as roadway entities which can switch

between states over time. These two states consider possible unobserved heterogeneity
factors of roadway effects which may influence injury severity.

2.2.2.9 Sequential logit and probit models

Sequential logit and probit models are generalized models of ordered logit and probit models

which relax the restriction applied to standard ordered probability models (Eluru et al., 2008).
Jung et al. (2010) developed a sequential logit model and compared it with an ordered probit

to investigate the effect of rainfall in single vehicle collisions. The sequential logit not only

retains the dependent variable in order but also allows different regression variables for the
injury severity levels. On the other hand, Yamamoto et al. (2008) developed a sequential

14