Exploring the implications of temporal and spatial variability in data for capturing the non-linear safety effects of roadway attributes

The paper builds on earlier research in which a full Bayesian approach was used to derive crash modification factors (CMFs) from regression models that capture the variability in these CMFs. The approach estimates a non-linear function that reflects the logical reality that the CMF for a given change in a feature's value depends not only on the amount of the change but also on the original value. However, in developing the approach, it was necessary to amalgamate panel data over several years by averaging annual traffic volumes and modeling the summation of annual crash counts. Such aggregation could be problematic if there is significant temporal variability in traffic volumes and crash frequencies, as would be the assumption that there is no site-to-site variation in the effects of independent variables on the crash frequency. The research for this paper examined whether these limitations can materially affect the CMF estimates by using simulated data to introduce substantial temporal and spatial variability in expected crash frequencies. A non-linear model with random effects that captures this variability was developed and compared to the non-linear model with fixed effects. The results show that the parameter estimates and CMFs for freeway median width, the feature used for the case study, were almost identical for the two non-linear approaches. This suggests that the aggregation approach in the earlier research may be adequate for capturing the non-linear safety effects of roadway attributes. The finding has practical importance in the sense that the amalgamation is often necessary when traffic data are not available for each year and also in the sense that when such amalgamation is done, the extent of the temporal variability in traffic volumes and expected crash frequencies is usually unknown. Future studies should expand the investigation to datasets that exhibit temporal variations in some features, such as pavement friction.