Modeling the Safety Performance of Freeway Horizontal and Crest Vertical Curve Combinations Using Hierarchical Negative Binomial Approaches with Temporal Correlation

The safety performance of horizontal and crest vertical curve combinations (also named as crest combinations or crest combined curves) is substantially associated with their geometric design. To evaluate their safety performance accurately, three Bayesian hierarchical negative binomial (NB) models with various structures of temporal correlation (including linear time trend, quadratic time trend, and autoregressive-1) are proposed for building a relationship between crash frequency and the separated and combined geometric design attributes of crest combination on freeways. An 8 year (2011–2018) crash dataset of 124 crest combination sections on four freeways in Washington state is collected and used for the model development and comparison. The results of model assessment indicate that the hierarchical NB model with autoregressive-1 is clearly superior to other alternatives. The parameter estimation results in the model reveal that in addition to the crash exposure variables (i.e., section length and annual average daily traffic), four geometric design attributes (vertical curvature, horizontal curvature, approach grade, and overlapping proportion) and two roadway configuration characteristics (lane width and left shoulder width) have significant effects on the safety performance. Considerable over-dispersion, cross-group heterogeneity, and temporal correlation are also found in the best-performing model. According to the results, some strategies for highway design are proposed to improve the safety performance of freeway crest combinations.