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33 CHAPTER 4 SAFETY IMPACT ANALYSIS OF PRPM INSTALLATIONS Two sets of analyses were undertaken to investigate the negative binomial generalized linear modeling. SPFs safety impact of snowplowable PRPMs on non-intersection- for disaggregate crash types were obtained by applying related crashes. First, composite analyses based on the empir- a multiplier to the SPF for total crashes. This multiplier ical Bayes before-and-after procedure were used to assess the is the ratio for the reference group and consists of the overall impact of PRPMs on different crash types. The same number of crashes of a specific type divided by the total procedure was also applied to a sample of adjacent nontreat- number of crashes. To account for the effect of trends in ment sites to assess whether there were any spillover (i.e., safety not related to traffic volumes, annual factors were crash migration) effects associated with PRPM implementa- estimated using a procedure documented by Harwood tion for two-lane roadways in Pennsylvania. Second, a dis- et al. (40). The resulting SPFs, multipliers ( f), and aggregate analysis, applying univariate analysis and multi- annual factors are presented in Appendix A. variate regression techniques, was performed on the results Step 2: Determine SPF predictions for each year in the of the nighttime composite analysis for individual sites. The before and after period at each PRPM location [i.e., disaggregate analysis aimed to determine the circumstances E(K1) ... E(Kn - 1), E(Kn + 1) ... E(KY)], where n is the under which PRPMs were beneficial to safety. The results of PRPM implementation year. these analyses were used to support the development of PRPM Step 3: Determine Cy , the ratio of the SPF estimate for implementation guidelines. Year y relative to Year 1 This chapter first describes the two methodologies (com- posite and disaggregate) used to evaluate the safety perfor- E( K y ) mance of PRPMs. It then presents the results of these analy- Cy = (4-1) E( K1 ) ses for two-lane roadways, four-lane freeways, and four-lane divided expressways, respectively. A more in-depth discus- Step 4: Determine Cb and Ca , the sum of the ratios dur- sion of the results is presented in Chapter 5. Appendix A con- ing the before period and the after period, respectively: tains tables with the individual safety performance functions and annual factors developed during the analysis. n -1 Cb = Cy (4-2) 1 4.1 COMPOSITE ANALYSIS METHODOLOGY Y An empirical Bayes before-and-after procedure (39) is Ca = Cy (4-3) n +1 presented in this section. The procedure was used to account for RTM while normalizing, where possible, for differences Step 5: Calculate K ^ 1, the expected nonintersection crash between the before periods and after periods. Overcoming frequency for the base year, Year 1: these differences, as described in Section 2.2, is key to achieving a statistically defensible analysis. The empirical ^1 = Xb + k Bayes procedure accommodates temporal differences K (4-4) k E( K1 ) + Cb between before and after periods, such as traffic volumes, weather, traffic reporting practices, driving demographics, Where and vehicle technology. The steps followed by the empirical Bayes approach are as Xb = Number of recorded nonintersection crashes dur- follows: ing the before period and k = Constant for a given model. k is estimated from Step 1: Calibrate SPFs for total nonintersection crashes the SPF calibration process with the use of a using data from the reference groups without PRPMs, as maximum likelihood procedure. In the calibra- described in Chapter 3. The calibration of SPFs applies tion process, a negative binomial distributed