A simultaneous equations model of crash frequency by severity level for freeway sections

Xin Ye, Ram Pendyala, Venky Shankar, Karthik C. Konduri

Research output: Contribution to journalArticlepeer-review

63 Scopus citations


This paper presents a simultaneous equations model of crash frequencies by severity level for freeway sections using five-year crash severity frequency data for 275 multilane freeway segments in the State of Washington. Crash severity is a subject of much interest in the context of freeway safety due to higher speeds of travel on freeways and the desire of transportation professionals to implement measures that could potentially reduce crash severity on such facilities. This paper applies a joint Poisson regression model with multivariate normal heterogeneities using the method of Maximum Simulated Likelihood Estimation (MSLE). MSLE serves as a computationally viable alternative to the Bayesian approach that has been adopted in the literature for estimating multivariate simultaneous equations models of crash frequencies. The empirical results presented in this paper suggest the presence of statistically significant error correlations across crash frequencies by severity level. The significant error correlations point to the presence of common unobserved factors related to driver behavior and roadway, traffic and environmental characteristics that influence crash frequencies of different severity levels. It is found that the joint Poisson regression model can improve the efficiency of most model coefficient estimators by reducing their standard deviations. In addition, the empirical results show that observed factors generally do not have the same impact on crash frequencies at different levels of severity.

Original languageEnglish (US)
Pages (from-to)140-149
Number of pages10
JournalAccident Analysis and Prevention
StatePublished - 2013


  • Crash frequency
  • Crash severity
  • Freeway safety Maximum simulated likelihood estimation
  • Multivariate
  • Poisson regression model
  • Simultaneous equations model

ASJC Scopus subject areas

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


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