Examination of the reliability of the crash modification factors using empirical Bayes method with resampling...

There have been plenty of studies intended to use different methods, for example, empirical Bayes before-after methods, to get accurate estimation of CMFs. All of them have different assumptions toward crash count if there was no treatment. Additionally, another major assumption is that multiple sites share the same true CMF. Under this assumption, the CMF at an individual intersection is randomly drawn from a normally distributed population of CMFs at all intersections. Since CMFs are non-zero values, the population of all CMFs might not follow normal distributions, and even if it does, the true mean of CMFs at some intersections may be different from that at others. Therefore, a bootstrap method based on before-after empirical Bayes theory was proposed to estimate CMFs, but it did not make distributional assumptions. This bootstrap procedure has the added benefit of producing a measure of CMF stability. Furthermore, based on the bootstrapped CMF, a new CMF precision rating method was proposed to evaluate the reliability of CMFs. This study chose 29 urban four-legged intersections as treated sites, and their controls were changed from stop-controlled to signal-controlled. Meanwhile, 124 urban four-legged stop-controlled intersections were selected as reference sites. At first, different safety performance functions (SPFs) were applied to five crash categories, and it was found that each crash category had different optimal SPF form. Then, the CMFs of these five crash categories were estimated using the bootstrap empirical Bayes method. The results of the bootstrapped method showed that signalization significantly decreased Angle+Left-Turn crashes, and its CMF had the highest precision. While, the CMF for Rear-End crashes was unreliable. For KABCO, KABC, and KAB crashes, their CMFs were proved to be reliable for the majority of intersections, but the estimated effect of signalization may be not accurate at some sites.