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2.2.2.2 Bayesian hierarchical binary logit

In another study, Huang et al. (2008) developed a hierarchical binomial logistic model to

investigate the main associated factors between driver injury severity and vehicle damage.
The model can address within-crash correlation, which has two-level specifications to

examine the effect of independent variables on injury severity.

2.2.2.3 Bivariate and multivariate binary outcome models
Lee et al. (2008) used a bivariate binary probit model to investigate the existence of

correlations between passengers, drivers and collision risk. Instead of using two logistic

models to examine the correlation between the presence and non-presence of passengers on
collision risk, a bivariate model was developed. In a logistic regression, a dependent variable

cannot be used in another regression model as an independent variable due to the

heterogeneity issue. The advantage of this model is that it can generate efficient and unbiased
coefficient estimation to address the possible correlation of unobserved impacts between

interrelated responses (e.g. presence of passengers) and crash risk.

On the other hand, Winston et al. (2006) developed a multivariate model which

simultaneously uses four series of binary outputs to examine the willingness of drivers to

have airbags or antilock brakes in the vehicle and the influence of these binary outputs on
collisions, and the resulting injury severity level of crashes.

2.2.2.4 A copula-based multivariate ordered probit model

Eluru et al. (2010) developed a model to enhance safety and reduce the injury severity of all

occupants in vehicles involved in road collisions. The method used in this research was a
copula-based approach. A copula is a method which produces stochastic dependence

connections between random variables and pre-specified marginal distribution. The strength
of this copula-based approach is that it considers the unobserved factors in modelling severity

injury of all vehicle occupants in collisions.

2.2.2.5 Bivariate ordered probit models

Bivariate ordered probit is appropriate to simultaneously model two dependent variables to
address the possibility of endogeneity issue in crash injury severity (Savolainen, 2011).

Lapparent (2008) developed a bivariate model to investigate the influence of wearing safety

belts in cars and injury severity levels in crashes.

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