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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-RD-98-133
Date: October 1998

Accident Models for Two-Lane Rural Roads: Segment and Intersections

2. Literature Review

Intersection Models

The methodology and statistical techniques used in a series of three reports (Lau and May, 1989; Lau and May, 1988; Naclerio et al., 1989) on signalized and unsignalized intersections are of interest to intersection modelers. Accident prediction models were developed to identify locations where accident experience was more frequent or more severe than normal, and to evaluate the safety consequences of alternative improvements. Factors and highway characteristics reported in the California data base were included in the model: accident data, traffic volumes, intersection features, and control types. However, variables such as degree of horizontal curvature and rate of vertical curvature, believed to be important, were not included. Unlike other partial studies, these models encompass all types of intersections, and the methodology addresses the successive stages of planning, design, and site improvement.

Three types of accident severity were modeled separately: fatal, injury, and property damage only. Collision types such as angle, rear-end, etc., that may further explain the cause of accidents were missing from the model. A nonparametric statistical modeling technique known as the Classification Regression Tree (CART) was used to group intersections by significance of prediction. The response variable was number of accidents per year, with traffic volume used only as an explanatory variable. The CART technique has particular applicability to categorical and discontinuous variables. However, the classification obtained was not sufficiently detailed to reveal the effect of individual highway factors. For injury accidents, nine groups of signalized intersections were identified, and eight groups were identified for property damage only accidents. The model for fatal accidents was not reliable, with a correlation coefficient of only 0.009. As a starting point for the analysis of relationships, intersections are categorized by highway functional classification into groups that are assumed to perform differently. The potential for application to optimization, i.e., to help the designer choose highway characteristics that will minimize the expected number of accidents, was noted but no application was made. Another caveat of this methodology is implied in its tendency to produce a grouping not much different from the existing conventional State grouping.

Hauer et al. (1988) developed accident prediction models for signalized intersections by maneuver patterns (15 defined conflict patterns) before the occurrence of accidents. Each pattern involved at most two conflicting flows. A typical model form is as follows:


  • E(m) = expected number of accidents for maneuver pattern m
  • F1 = traffic flow of turning movement 1
  • b1 = power of F1
  • F2 = traffic flow of turning movement 2
  • b2 = power of F2.

Equations were derived for each of the 15 pre-accident patterns to compute the expected number of accidents. These equations can also be used to estimate the kinds of accident caused by traffic flow patterns. Their design consequences are limited because they are based exclusively on traffic flow variables, and these are uncontrollable. Unlike traffic flow patterns, physical elements such as channelization and alignment are manageable safety improvements. On the other hand, the models are negative binomial in form. This form, as the authors indicate, has the attractive feature that it can be modified by empirical Bayesian techniques to incorporate actual experience at an individual intersection.

Garber and Srinivasan (1991) used traffic flow (left-turn volumes) movements as explanatory variables for predicting accidents during peak-hours and otherwise. Besides safety evaluations, these models are favorable for improvements such as installing left turn lanes and adding protected phasing. Despite high R2 values, the simple linear regression models used in this study are inadequate for discrete events such as accidents that have a very low mean and are not normally distributed. Moreover, these models predict accidents for elderly drivers, a small segment of the driver population.


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