From the past to the future: Modeling the temporal instability of safety performance functions

In roadway safety management, safety performance functions (SPFs) are widely used by state and local agencies to predict crashes for base site conditions. SPFs are developed based on historical traffic safety data and are used to make predictions for anticipated site characteristics in the future. An underlying assumption in SPF development is that the relationships between crash frequency and site conditions are stationary from the past (when the model data were collected) to the future (for which SPFs are applied). The assumption using the past to represent the future could be fundamentally problematic. This study proposes a modeling framework that can relax this assumption. Specifically, this framework integrates temporal modeling with time-series analysis to strengthen the current SPF estimation methods. The temporal modeling approach is Temporally Weighted Negative Binomial Regression (TWNBW), and the time-series analysis is tried by employing the Seasonal Autoregressive Integrated Moving Average (SARIMA) and Artificial Neural Networks (ANN) methods. The temporal modeling is to uncover the temporal variations of SPFs and the time-series analysis explains and predicts the relationship between the SPF's temporal variation and time. The outcome of the framework is a set of Future SPFs that capture the temporal unobserved heterogeneity in safety data and describe the predicted relationships between safety performance and site characteristics in the future. A case study using six-year safety datasets from Georgia was conducted to illustrate the key components of the modeling framework. The temporal modeling results showed significant variations in SPFs across time. The parameters for traffic volume, i.e., Average Annual Daily Traffic (AADT), and segment length are associated with an increasing trend with time, and for access point density there is a descending trend. The SPF parameters are found to have a strong seasonality. Both time-series modeling methods appear to be appropriate to explain the temporal variations of SPF parameters, and the models are able to predict SPF parameters with acceptable errors smaller than 1% on average. Future SPFs can be used to support the roadway safety management that affects future traffic safety performance.