Predicting expressway crash frequency using a random effect negative binomial model: A case study in China

Zhuanglin Ma, Honglu Zhang, Steven I.Jy Chien, Jin Wang, Chunjiao Dong

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


To investigate the relationship between crash frequency and potential influence factors, the accident data for events occurring on a 50 km long expressway in China, including 567 crash records (2006–2008), were collected and analyzed. Both the fixed-length and the homogeneous longitudinal grade methods were applied to divide the study expressway section into segments. A negative binomial (NB) model and a random effect negative binomial (RENB) model were developed to predict crash frequency. The parameters of both models were determined using the maximum likelihood (ML) method, and the mixed stepwise procedure was applied to examine the significance of explanatory variables. Three explanatory variables, including longitudinal grade, road width, and ratio of longitudinal grade and curve radius (RGR), were found as significantly affecting crash frequency. The marginal effects of significant explanatory variables to the crash frequency were analyzed. The model performance was determined by the relative prediction error and the cumulative standardized residual. The results show that the RENB model outperforms the NB model. It was also found that the model performance with the fixed-length segment method is superior to that with the homogeneous longitudinal grade segment method.

Original languageEnglish (US)
Pages (from-to)214-222
Number of pages9
JournalAccident Analysis and Prevention
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • Public Health, Environmental and Occupational Health
  • Safety, Risk, Reliability and Quality
  • Law
  • Human Factors and Ergonomics


  • Crash frequency
  • Goodness-of-fit
  • Negative binomial model
  • Prediction
  • Random effects negative binomial model


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