A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods

Abstract

The following paper is a pre-print and the final publication can be found in Accident Analysis and Prevention, 40 (3):964-975, 2008. Presented at the 86 th Annual Meeting of the Transportation Research Board, January 2007 ABSTRACT Numerous efforts have been devoted to investigating crash occurrence as related to roadway design features, environmental and traffic conditions. However, most of the research has relied on univariate count models; that is, traffic crash counts at different levels of severity are estimated separately, which may neglect shared information in unobserved error terms, reduce efficiency in parameter estimates, and lead to potential biases in sample databases. This paper offers a multivariate Poisson-lognormal (MVPLN) specification that simultaneously models injuries by severity. The MVPLN specification allows for a more general correlation structure as well as overdispersion. This approach addresses some questions that are difficult to answer by estimating them separately. With recent advancements in crash modeling and Bayesian statistics, the parameter estimation is done within the Bayesian paradigm, using a Gibbs Sampler and the Metropolis-Hastings (M-H) algorithms for crashes on Washington State rural two-lane highways.The estimation results from the MVPLN approach did show statistically significant correlations between crash counts at different levels of injury severity. The non-zero diagonal elements suggested overdispersion in crash counts at all levels of severity. The results lend themselves to several recommendations for highway safety treatments and design policies. For example, wide lanes and shoulders are key for reducing crash frequencies, as are longer vertical curves. KEY WORDS INTRODUCTIONRoadway safety is a major concern for the general public and public agencies. Roadway crashes claim many lives and cause substantial economic losses each year. In the U.S. traffic crashes bring about more loss of human life (as measured in human-years) than almost any other causefalling behind only cancer and heart disease (NHTSA, 2005). The situation is of particular interest on rural two-lane roadways, which experience significantly higher fatality rates than urban roads. The annual cost of traffic crashes is estimated to be $231 billion, or $820 per capita in 2000(Blincoe et al., 2000. These costs do not include the cost of delays imposed on other travelers, which also are significant, particularly when crashes occur on busy roadways. Schrank and Lomax (2002) estimate that over half of all traffic delays are due to non-recurring events, such as crashes, costing on the order of $1,000 per peak-period driver per year, particularly in urban areas. Thus, while vehicle and roadway design are improving, and growing congestion may be reducing impact speeds, crashes are becoming more critical in many ways, particularly in societies that continue to motorize. Given the importance of roadways safety, there has been considerable crash prediction research (see, e.g., Hauer, 1986Hauer, , 1997Hauer,...

Injury severity analysis: comparison of multilevel logistic regression models and effects of collision data aggregation

“…Different approaches can be used for collision severity analysis: (a) incorporating severity into the collision frequency models by modeling collisions classified by severity types [31][32][33][34]; and (b) modeling the conditional probability of each severity level for a given collision [14,15,17,35,36]. In this research, we adopted the second approach for three reasons: (i) different factors could have different effects on collision occurrence and severity (e.g., seat belt use has nothing to do with collision occurrence, but is an important factor in severity analysis); (ii) data that could be used for joint models are limited in nature because most of the data are collected after the collision has happened [12]; and, (iii) consequence outcomes and injury data are at the individual, vehicle, or accident level.…”

Predicting accident frequency at their severity levels and its application in site ranking using a two-stage mixed multivariate model

“…Several multivariate models have been employed such as multivariate spatial models (Song, 2004;Song et al, 2006), multivariate Poisson (MVP) models (Ma and Kockelman, 2006), and multivariate Poisson-lognormal (MVPLN) models (Park and Lord, 2007;Ma et al, 2008;Aguero-Valverde and Jovanis, 2009;El-Basyouny and Sayed, 2009). Compared to the univariate modelling approach, the multivariate models (i.e.…”

“…MVP or MVPLN) are argued to be superior since multivariate models can take account of correlation between different types of accidents, or in other words to "borrow strength" from similar sources (Song et al, 2006). However, as pointed out by Ma et al (2008), the superiority of the multivariate models compared to univariate models is not "theoretical" but rather "empirical". By comparing several Poisson based models using both the multivariate and univariate approach, Lan and Persaud (2010) found that univariate models fit the data better and outperform the multivariate models, and thus univariate models were recommended.…”

Mathematical modeling of a vehicle crash test based on elasto-plastic unloading scenarios of spring-mass models

“…It is of key importance to relate crash occurrence with roadway design features too. In [19], a multivariate Poisson-lognormal specification is presented, that simultaneously models crash counts by injury severity. The results of such approach are useful for recommendations for highway safety treatments and design policies.…”