Analysis of Severe Injury Accident Rates on Interstate Highways Using a Random Parameter Tobit Model

Minho Park,Dongmin Lee

doi:10.1155/2017/7273630

Abstract

In this study, a random parameter Tobit regression model approach was used to account for the distinct censoring problem and unobserved heterogeneity in accident data. We used accident rate data (continuous data) instead of accident frequency data (discrete count data) to address the zero cell problems from data where roadway segments do not have any recorded accidents over the observed time period. The unobserved heterogeneity problem is also considered by using random parameters, which are parameter estimates that vary across observations instead of fixed parameters, which are parameter estimates that are fixed/constant over observations. Nine years (1999–2007) of panel data related to severe injury accidents in Washington State, USA, were used to develop the random parameter Tobit model. The results showed that the Tobit regression model with random parameters is a better approach to explore factors influencing severe injury accident rates on roadway segments under consideration of unobserved heterogeneity problems.

Highlights

Over the last decade, numerous studies have been conducted to explore the factors that cause accidents on roadway segments; various statistical modeling techniques have been employed, especially count models
The Poisson regression model incorrectly estimates the likelihood of accident frequencies and, to overcome this overdispersion problem, a negative binomial model was suggested, which relaxes the constraint that the mean is equal to the variance
N is the number of observations, Yi is the dependent variable, β is a vector of estimable parameters, Xi is a vector of independent variables, and εi is a normally and independently distributed error term with zero mean and constant variance σ2

Summary

Introduction

Numerous studies have been conducted to explore the factors that cause accidents on roadway segments; various statistical modeling techniques have been employed, especially count models. Negative accident count values are predicted which should be greater than or equal to zero in reality [1]. To address these problems that the linear regression model had, previous investigators suggested a Poisson regression model wherein accident frequency is translated as a discrete random variable [2]. The Poisson regression model incorrectly estimates the likelihood of accident frequencies and, to overcome this overdispersion problem, a negative binomial model was suggested, which relaxes the constraint that the mean is equal to the variance. A variety of attempts to analyze accident frequencies were made, and these resulted in a reduction in accidents and improved accident prevention (random effects models [9, 10], zero-inflated count models [11,12,13], and random parameters count models [14,15,16,17,18])

Methods

Results

Conclusion