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In this study, the binary response variable, , is defined as:

{ (5.1)

Let P n (i) and 1- P n (i) denote the probability of crash n being a severe injury and minor injury

crash, respectively. McFadden (1981) shows that under the standard logistic distribution, the
closed form solution of the probabilities are:

( )
( ) ( ) (5.2)

where,
is a vector of measurable characteristics that determine outcome i,

is a vector of estimable parameters.

The best estimate of β can be obtained by maximising the log-likelihood function:

( ) ∑ { ( ( )) ( ) ( ( ))} (5.3)

5.2.3 Skewed Logistic (Scobit) Models

The skewed logistic model has been applied by a previous researcher in road safety for
modelling a dependent variable when the assumption of symmetry is violated (Tay, 2016).

Let be the latent injury level of person n that is unobserved and continuous and can be

specified as:

(5.4)

where,
= a vector of coefficients for explanatory variables,
= a vector of explanatory variables associated with person n ,

= a random disturbance term.

Although the latent injury category could be assumed to be continuous in theory, in practice,

the injury severity level of road users tends to be recorded using fairly general and ordinal

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