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3.2.2 Binary Logit Model

A summary of existing studies on binary logit model is presented in Chapter Two Section
2.2.2.1 above. Since the dependent variable in this study is the crash location of the heavy

vehicle which is divided into two categories in the present research (intersections and mid-
blocks), the binary logit regression model is appropriate. This model has been widely applied

by previous researchers in road safety for modelling a dependent variable with a dichotomous

outcome (Obeng, 2007; Tay et al., 2008, 2009; Rifaat & Tay, 2009; Haleem & Abdel-Aty,
2010; Johnson et al., 2011; Anowar et al., 2013; Weng & Meng,2014; Tay 2016; Tay & Choi

2016).

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

{ (3.1)

Let, P n (i) and 1- P n (i) denote the probability of crash n occurring at an intersection and mid-

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

( )
( ) ( ) (3.2)

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:

( ) ∑ { ( ( )) ( ) ( ( ))} (3.3)

The estimates of the model can be interpreted as follows: if the coefficient (β i) >0, then the
crash is more likely to occur at an intersection with increasing value for X i; if (β i) <0, then the
crash is more likely to occur at mid-block with increasing value of X i.

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