Methodology to develop crash modification functions for road safety treatments with fully specified and hierarchical models

• We investigate fully specified and hierarchical models with crash modification functions (CM-Functions).
• Both formulations yield reasonable CM-Functions but hierarchical model is better.
• Hierarchical models provide efficient estimates with conformity and correlations.
• We fill a methodological void about crash modification factors in the Highway Safety Manual.

Crash modification factors (CMFs) for road safety treatments are developed as multiplicative factors that are used to reflect the expected changes in safety performance associated with changes in highway design and/or the traffic control features. However, current CMFs have methodological drawbacks. For example, variability with application circumstance is not well understood, and, as important, correlation is not addressed when several CMFs are applied multiplicatively. These issues can be addressed by developing safety performance functions (SPFs) with components of crash modification functions (CM-Functions), an approach that includes all CMF related variables, along with others, while capturing quantitative and other effects of factors and accounting for cross-factor correlations. CM-Functions can capture the safety impact of factors through a continuous and quantitative approach, avoiding the problematic categorical analysis that is often used to capture CMF variability. There are two formulations to develop such SPFs with CM-Function components – fully specified models and hierarchical models. Based on sample datasets from two Canadian cities, both approaches are investigated in this paper. While both model formulations yielded promising results and reasonable CM-Functions, the hierarchical model was found to be more suitable in retaining homogeneity of first-level SPFs, while addressing CM-Functions in sub-level modeling. In addition, hierarchical models better capture the correlations between different impact factors.