AbstractPrevious studies used to estimate count-data models for the investigation of crash factors. In this study, an alternative method based on Tobit regression by simply viewing crash rates as a continuous variable was explored. Three years of data collected from four freeways in China were used to estimate the models. A correlated random parameters Tobit with heterogeneity in means (CRPTHM) model was proposed and thoroughly compared with traditional fixed parameters Tobit (FPT), random parameters Tobit (RPT), and correlated random parameters Tobit (CRPT) models. Results show that the CRPTHM model outperformed its three model counterparts by further grasping the correlation of unobserved heterogeneity. In addition, many crash factors were uncovered, including many appealing and important factors that have seldom been investigated for Chinese freeways previously (e.g., the safety effects of pavement conditions). More importantly, additional insights into the interactive safety effects of crash factors, such as the combined effects of interchange area and traffic volume, were inferred based on the CRPTHM model. In short, this study demonstrates the CRPTHM model to be an effective method to investigate road safety, especially when unobserved heterogeneity exists. Additionally, findings from the current study are believed to provide more knowledge of crash occurrence and be beneficial for the development of effective safety countermeasures.