A correlated random parameters tobit model to analyze the safety effects and temporal instability of factors affecting crash rates.

Numerous studies have previously used a variety of count-data models to investigate factors that affect the number of crashes over a certain period of time on roadway segments. Unlike past studies which deal with crash frequency, this study views the crash rates directly as a continuous variable left-censored at zero and explores the application of an alternate approach based on tobit regression. To thoroughly investigate the factors affecting freeway crash rates and the potentially temporal instability in the effects of crash factors involving traffic volume, freeway geometries and pavement conditions, a classic uncorrelated random parameters tobit (URPT) model and a correlated random parameters tobit (CRPT) model were estimated, along with a conventional fixed parameters tobit (FPT) model. The analysis revealed a large number of safety factors, including several appealing and interesting factors rarely studied in the past, such as the safety effects of climbing lanes and distance along composite descending grade. The results also showed that the CRPT model was not only able to reflect the heterogeneous effects of various factors, but also able to estimate the underlying interactions among unobserved characteristics, and therefore provide better statistical fit and offer more insights into factors contributing to freeway crashes than its model counterparts. Additionally, the results showed significant temporal instability in CRPT models across the studied time periods indicating that crash factors (including unobserved characteristics and the underlying interactions among them) and their effects on crash rates varied over time, and more attentions should be paid when interpreting crash data-analysis findings and making safety policies. The modeling technique in this study demonstrates the potential of CRPT model as an effective approach to gain new insights into safety factors, particularly when the heterogeneous effects of factors on safety are interactive. Additionally, findings from this study are also expected to assist in developing more effective countermeasures by better understanding the safety effects of factors associated with freeway design characteristics and pavement conditions.