Analysis of Crash Data Using Quantile Regression for Counts

Abstract

Statistical models that describe the relationship between crash frequency and its influencing factors have been widely studied for the last three decades. Most of the existing methodologies use these models with count data and their variants to study the mean effects of covariates on crash frequency. This study seeks to explore the use of quantile regression for counts as a methodological alternative in analyzing crash frequency. Compared with existing models, the proposed model provides a fuller and more robust analysis of crash data for at least two reasons. First, crash data usually follow typical count distributions with a large proportion of zeros, and the remaining values highly skew toward the right. This nature of crash data makes quantile regression appealing because it can provide more comprehensive information about the effects of covariates on crash frequency rather than just the mean because quantile regression allows various quantiles of a population to be estimated. Second, as a semiparametric technique, quantile regression for counts allows researchers to relax restrictions in the form of the distribution function of the response variable, resulting in more robust estimation. In addition, two prediction methods are proposed to take advantage of such analysis results to yield better point prediction. To illustrate the application of quantile regression, crash data for interstate highways in urban areas in Washington State in 2002 were extracted from the Highway Safety Information System (HSIS) and analyzed with the proposed model. The analysis results and prediction performance were then compared with those from the negative binomial regression model. The numerical case study shows that although the significance and signs of the effects derived from both models are consistent, the proposed quantile regression model reveals more detailed information on the marginal effects of covariates change across the conditional distribution of the response variable and provides more robust and accurate predictions on crash counts.