Chapter 9. Adding variables
1. VIEDA for the intersection data.
In problem 2 of Chapter 8 the model equation 𝛽0 × (𝑀𝑎𝑗𝑜𝑟 𝑅𝑜𝑎𝑑 𝐴𝐴𝐷𝑇)𝛽1 ×
(𝑀𝑖𝑛𝑜𝑟 𝑅𝑜𝑎𝑑 𝐴𝐴𝐷𝑇)𝛽2 was fitted to the multivehicle injury crash counts of the Edmonton
intersection data in the ‘Edmonton 4-legged Signalized Intersections.xls’ file. A part of that file
is shown in Figure 1.
Figure 1
The Negative Binomial fit of the model equation to the data is in the ‘Edmonton NB.xls’
file.
Not used in the model equation are the variables ‘Area’ (in column B), ‘Number of
approaches with left-turn lane, lt’ (in column C), and ‘Number of approaches with right-turn
lane, rt’ (in column D). The question is whether the ‘Area’ and ‘lt’ variables are safety related
and, if yes, how might they be represented in the model equation.
2. What was gained by adding the ‘Area’ variable
By maximizing the NB likelihood with 𝛽0 × (𝑀𝑎𝑗𝑜𝑟 𝐴𝐴𝐷𝑇)𝛽1 × (𝑀𝑖𝑛𝑜𝑟 𝐴𝐴𝐷𝑇)𝛽2 as the
model equation the parameter estimates in Figure 2 were obtained.
Figure 2
With separate models for ‘Urban’ and ‘Suburban’ intersections, the parameter
estimates were those in Figure 3.
Figure 3
Was anything gained?
a. Is the change in log-likelihood justified in view of the AIC and BIC?
b. Compare CURE plots
The C-F spreadsheets for ‘All’, ‘Urban’ and ‘Suburban’ intersections are in the
‘Edmonton C-Fs.xls’ file.