Highway-rail grade crossings accident prediction using Zero Inflated Negative Binomial and Empirical Bayes method

Jacob Mathew, Rahim F. Benekohal

Research output: Contribution to journalArticlepeer-review


Introduction: Recently the Federal Railroad Administration (FRA) released a new model for accident prediction at railroad grade crossings using a Zero Inflated Negative Binomial (ZINB) model with Empirical Bayes (EB) adjustments for accident history (2). This new model is adopted from the work that was conducted by the authors (3–6). The unique feature of the new FRA model is that it has a single equation for all three warning devices (crossbuck, flashing light, and gates) and uses the same variables regardless of the warning devices at the crossing. Since the New FRA model incorporates the warning device category as one of the variables in its model equation, the predicted accident frequency is higher when a crossing has crossbucks than flashing lights, and higher when it has flashing lights than gates. While this model is significantly better than the old USDOT model (7), its shortcoming is that the single equation does not accurately represent the field condition. Method: This paper presents the ZINEBS model (Zero Inflated Negative binomial with Empirical Bayes adjustment System). The ZINEBS model gives three different equations depending on the type of warning device used at the crossings (gates, flashing lights, and crossbucks). The three equations use variables, some of which are common across all warning devices, while other variables are specific to a warning device. The predicted values for the ZINEBS model show a closer agreement with the field data than the new FRA model. This observation was true for all three warning device types analyzed. Practical Applications: Based on the results of this study, the ZINEBS compliments the new FRA model and should be used when the single equation is not adequately representing the role of traffic control device types and relevant variables associated with that device type.

Original languageEnglish (US)
Pages (from-to)211-236
Number of pages26
JournalJournal of Safety Research
StatePublished - Dec 2021


  • Accident prediction
  • Empirical Bayes
  • Highway rail grade crossings
  • Zero-inflated negative binomial

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality


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