Econometric approaches to examine the onset and duration of temporal variations in pedestrian and bicyclist injury severity analysis

• A flexible econometric structure is proposed to examine time-varying effects. • Onset and duration of temporal variations are examined in injury severity model. • Piecewise linear function is used in capturing temporal variations. • Active traveler injury severity outcomes in examined. • Onset of time-varying effects could be different than the start of a year. There is considerable evidence in existing safety literature that the exogenous variable effects are likely to be time-varying in the injury severity analysis. The majority of these earlier studies tested time-varying effects of exogenous variables by crash year. However, there might be variability in the variable effects within a year, while the same effect might carry over in some or all parts of the preceding years. Towards that end, in this study, we propose a flexible framework to identify when the time-varying effect is likely to occur (the onset of temporal variation) and how long such time-varying effect lasts (duration of temporal variation) in the model estimates. In the study design, we assume that the onset of temporal variation can be any quarter of a year under consideration, while the time-varying effect can continue over different quarters after the onset of temporal variation in a variable effect. The injury severity model is estimated by using Correlated Random Parameter Generalized Ordered Logit formulation with piecewise linear functions. The empirical analysis is demonstrated by employing active traveler (pedestrian and bicyclist) crash data from Queensland, Australia for the years 2015 through 2020. The estimation results are further augmented by computing elasticity effects. The results indicate that the time-varying effects are likely to be different across years for several variables, while for other variables, the onset of time-varying effects could be different than the start of a year. Such flexibility in model specification is likely to have significant implications for devising and implementing effective countermeasures since it allows us to understand how road traffic injuries are evolving over time and when a new road safety issue might be arising.