A note on estimating safety performance functions with a flexible specification of traffic volume

In this note, a flexible approach to allow for variation in the impact of traffic volume in the estimation of Safety Performance Functions (SPFs) is proposed. The approach generalizes a recently proposed approach by Gayah and Donnell (2021) (GD) titled "Estimating safety performance functions for two-lane rural roads using an alternative functional form for traffic volume". GD approach proposes a multiple regime structure for AADT impact while explicitly constraining the impact at the regime threshold to be the same. While the GD approach provides a flexible structure, the framework as proposed calls for careful judgement for threshold selection and additional model estimation complexity for the AADT constraint. The current note establishes the equivalence of the proposed approach with the GD approach and subsequently presents a more flexible model structure that improves on the GD approach. Subsequently, we document the advantages of our proposed approach in terms of model estimation, parameter significance testing, flexibility to consider multiple traffic volume ranges and ease of accommodating random parameters for analysis. Finally, we present potential directions for future research.