Crash Frequency Modeling using Negative Binomial Models: An Application of Generalized Estimating Equation to Longitudinal Data

Abstract

The prediction of crash frequency models can be improved when several years of crash data are utilized, instead of three to five years of data most commonly used in research. Crash data, however, generates multiple observations over the years that can be correlated. This temporal correlation affects the estimated coefficients and their variances in commonly used crash frequency models (such as negative binomial (NB), Poisson models, and their generalized forms). Despite the obvious temporal correlation of crashes, research analyses of such correlation have been limited and the consequences of this omission are not completely known. The objective of this study is to explore the effects of temporal correlation in crash frequency models at the highway segment level. In this paper, a negative binomial model has been developed using a generalized estimating equation (GEE) procedure that incorporates the temporal correlations amongst yearly crash counts. The longitudinal model employs an autoregressive correlation structure to compare to the more traditional NB model, which uses a Maximum Likelihood Estimation (MLE) method that cannot accommodate temporal correlations. The GEE model with temporal correlation was found to be superior compared to the MLE model, as it does not underestimate the variance in the coefficient estimates, and it provides more accurate and less biased estimates. Furthermore, an autoregressive correlation structure was found to be an appropriate structure for longitudinal type of data used in this study. Ten years (2002-2011) of Missouri Interstate highway crash data have been utilized in this paper. The crash data comprises of traffic characteristics and geometric properties of highway segments. © 2014 Elsevier Ltd.

Department(s)

Mathematics and Statistics

Second Department

Civil, Architectural and Environmental Engineering

Keywords and Phrases

Autocorrelation; Autoregressive; Crash frequency model; Generalized estimation equation; Longitudinal analysis; Temporal correlation

International Standard Serial Number (ISSN)

2213-6657

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Elsevier, All rights reserved.

Publication Date

01 Jan 2014

Link to Full Text

Share

 
COinS