Safety Evaluation of Cable Median Barriers in Combination With Rumble Strips on Divided Roads

CHAPTER 6. DEVELOPMENT OF SPFS

This chapter presents the SPFs developed for each State. The EB methodology uses SPFs to estimate the safety effectiveness of this strategy.⁽¹⁰⁾ The research team used generalized linear modeling to estimate model coefficients assuming a negative binomial error distribution, which was consistent with the state of research in developing these models. Most previous studies had used the traditional power function as the default for AADT. In this effort, the team used the hoerl function to provide more flexibility in the functional form for AADT.⁽¹⁷⁾ With the hoerl function for AADT, the dependent variable (Y) is related to AADT as shown in figure 8.

Where a₁, a₂, and a₃ are parameters to be estimated. This allows the function for AADT to have a convex/concave shape with inflection points. The other variables were included in a log-linear/exponential form as shown in figure 9:

Where X₄ through X_n represent the other independent variables and a₄ through a_n are parameters to be estimated. The equation included segment length as an offset. In specifying a negative binomial error structure, the dispersion parameter k was estimated iteratively from the model and the data. For a given dataset, smaller values of k indicate relatively better models. As discussed earlier, k was estimated as a function of the segment length, and k₁ (overdispersion for a 1-mi section) is shown in the tables in the following sections.

Illinois and Kentucky SPFs

The research team calibrated SPFs for each State separately using the reference sites from that State. As discussed in chapter 5, the team developed the Missouri SPFs separately for the before and after periods at the treated sites. Table 12 and table 13 present the SPFs developed for Illinois and Kentucky, respectively.

Missouri SPFs

As discussed earlier, reference groups were not available in Missouri because the State implemented the treatment systemwide. Therefore, the research team used the before-period data for the treated sites to estimate the SPFs, which are shown in table 14. In Missouri, because the team could not reliably estimate SPFs for cross-median crashes, they based the predictions for cross-median crashes on the product of the SPFs for total crashes with the proportion of cross-median crashes.