Maximum likelihood method of estimating the conflict-crash relationship

• Published in: Accident analysis and prevention 2023-01, Vol.179, p.106875-106875, Article 106875
• Main Author: Tarko, Andrew P.
• Format: Article
• Language: English
• Subjects: Conflict-crash relationship; ML estimation; Traffic conflicts
• ISSN: 0001-4575; 1879-2057
• DOI: 10.1016/j.aap.2022.106875

•ML estimator of probability of crash given traffic conflict proposed. Proposed ML estimation requires assumption of Lomax scale parameter.•ML and OLS estimates are compared and found comparable. The estimation error caused by incorrect scale parameters is limited.•Estimation of both Lomax parameters is discussed.•Reparameterization of Lomax distribution proposed based on published work. The fundamental matters of how traffic conflicts are connected to crashes and how to estimate this connection with traffic conflict data is an active subject of research and refinements. There are still open questions about traffic events that can be analytically extrapolated to related crashes, and how to efficiently estimate the probability of crash associated with such events to enable conversion of observed events to the corresponding expected number of crashes. There are two important uses of a working estimation method: (1) rapid assessment of safety at specific roads locations and evaluation of countermeasures by safety engineers, (2) modeling of safety effects by analysts based on relatively short observations at multiple locations or at limited number of locations but during extended periods. This paper focuses on the application of traffic conflicts by safety engineers where the method practicality is important. The paper first recalls the OLS method of estimating the shape parameter of the underlying Lomax distribution proposed in (Tarko, 2018). Then, the ML method is introduced and the Lomax-based crash estimates obtained with the two methods are compared. Both the methods assume the scale parameter to estimate the shape parameter. The effect of assuming the scale parameter on estimates of the expected number of crashes is evaluated. To bring the scale parameter’s effect into a meaningful perspective, it is compared to two other effects: (1) type of driver, and (2) limited number of observations. Finally, re-parametrized Lomax distribution is pointed out as a potential way to address the difficulties with estimating the two distribution parameters simultaneously. The summary of the results closes the paper.