Safety impacts of signal-warning flashers and speed control at high-speed signalized intersections

Hierarchical Bayesian random intercept model-based cross-level interaction decomposition for truck driver injury severity investigations

“…Random parameters models are a group of models that simulate individual unobserved heterogeneity by assuming a distribution for parameters of interest to allow them vary across observations or (group of observations) and/or determine observation groups, and include popular models such as random parameter logit (mixed logit) model (Anastasopoulos and Mannering, 2011;Gkritza and Mannering, 2008;Gan, 2015, 2013;Kim et al, 2010Kim et al, , 2008Malyshkina and Mannering, 2010;Milton et al, 2008;Moore et al, 2011;Pai et al, 2009;Shaheed et al, 2013;Wu et al, 2014), random parameter probit model (Christoforou et al, 2010;Russo et al, 2014;Tay, 2015), random parameter negative binomial models (Chen and Tarko, 2014;Dong et al, 2014;Flask et al, 2014;Venkataraman et al, 2014Venkataraman et al, , 2013Wu et al, 2013), random parameter Tobit model (Anastasopoulos et al, 2012a,b;Yu et al, 2015) and Markov switching models Xiong et al, 2014). Milton et al (2008) were the first to apply random parameter model in traffic crash analysis, and verified its effectiveness in traffic crash data modeling.…”

Effects of extraordinary snowfall on traffic safety

“…To capture heterogeneity in observations, we chose a randomparameter model where we permitted regression parameters to vary across observations (Lord and Mannering, 2010;Wu et al, 2013). To consider heterogeneity in the jth regression parameter b j , we write this parameter as b i,j = b j + ' i,j for observation i, where b j is the same for each observation and ' i is a randomly distributed term that can take a variety of distributions such as normal and lognormal distributions.…”

“…Following this, we set l i jw i ¼ expðb  x i Þ in the NB models, where w i is a vector if multiple random parameters are considered in the model. In the literature (Lord and Mannering 2010;Wu et al, 2013), l i jw i is formulated as expðb  x i þ e i Þ for a random-parameter NB model. The two formulations are the same with our formulation separating the error term from l. The log-likelihood function for the random-parameters NB models can be written as…”

“…Because maximum likelihood estimation of the random-parameter models is computationally cumbersome due to the integration over the distribution of the random parameters, simulation-based maximum likelihood methods are usually used. In our analysis, we used Halton draws since it provides an efficient distribution of draws for numerical integration (Wu et al, 2013).…”

Exploring Driver Injury Severity at Intersection: An Ordered Probit Analysis

“…Over the years, a mountain of studies has been conducted to analyze the crash frequency at intersections [4][5][6]. However, only a few studies have focused on the crash injury severity.…”