Bayesian estimation of hourly exposure functions by crash type and time of day

The study describes an investigation of the relationship between crash occurrence and hourly volume counts for small samples of highway segments from two states: Michigan and Connecticut. We used a hierarchical Bayesian framework to fit binary regression models for predicting crash occurrence for each of four crash types: (1) single-vehicle, (2) multi-vehicle same direction, (3) multi-vehicle opposite direction, and (4) multi-vehicle intersecting direction, as a function of the hourly volume, segment length, speed limit and pavement width. The results reveal how the relationship between crashes and hourly volume varies by time of day, thus improving the accuracy of crash occurrence predictions. The results show that even accounting for time of day, the disaggregate exposure measure - hourly volume - is indeed non-linear for each of the four crash types. This implies that at any time of day, the crash occurrence is not proportional to the hourly volume. These findings help us to further understand the relationship between crash occurrence and hourly volume, segment length and other risk factors, and facilitate more meaningful comparisons of the safety record of seemingly similar highway locations.