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Federal Highway Administration Research and Technology
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Publication Number: FHWA-RD-98-133
Date: October 1998
Accident Models for Two-Lane Rural Roads: Segment and Intersections
Estimating the number of accidents that may result for a given highway design is a matter of great interest to the highway engineering community. Numerous studies have been performed in this area (see McGee et al. and references cited therein) with the aim of determining the effects of different design elements and their relative importance. Since safety is a primary consideration in highway design, the safety consequences of highway design features have been and will remain a matter of continuing interest.
The present study was undertaken in connection with the development of the Interactive Highway Safety Design Model (IHSDM). The IHSDM is envisioned as a set of tools to assist the highway designer. In particular it is expected to include an Accident Analysis Module that will relate accidents to highway variables along segments and at intersections. Rural roadways tend to have high accident rates, and adequate models for these roadways are especially desirable. This study focuses on segments of rural two-lane roads and on three- and four-legged intersections on such roads, stop-controlled on the minor leg or legs.
The study makes use of Highway Safety Information System (HSIS) data for two States, Minnesota and Washington. Accident data (including both severity and type), traffic data, lane and shoulder width data, and some alignment data are available in HSIS files. Data were also obtained from photologs and, in the case of Minnesota, construction plans. These data include horizontal and vertical alignments, channelization, driveways, and Roadside Hazard Rating. The latter is a measure of sideslope and clear zone proposed by Zegeer et al. (1987).
The analysis and modeling on the data sets have been performed with SAS software. SAS includes a variety of procedures for summarizing univariate and multivariate statistics and for modeling the relationship between a variable such as number of accidents and covariates such as traffic volumes and highway design variables.
Accident models are typically of Poisson and generalized linear form. The number of accidents in in a given space-time region is regarded as a random variable that takes values 0, 1, 2, ... with probabilities obeying the Poisson distribution. A characteristic feature of this distribution is that the variance, or mean squared deviation of this variable, is equal to its mean. The mean number of accidents is assumed to be an exponential applied to a suitable linear combination of highway variables. Thus the model falls under the heading of a generalized linear model. The exponential function guarantees that the mean is positive.
More recently negative binomial models, a variant of the Poisson, have been used in accident modeling. Such models generalize the Poisson form by permitting the variance to be overdispersed, equal to the mean plus a quadratic term in the mean whose coefficient is called the overdispersion parameter. When this parameter is zero, a Poisson model results. When it is larger than zero, it represents variation above and beyond that due to the highway variables present in the model. Such variation is due to accident-related factors pertaining to drivers, vehicles, and location not encompassed by the highway variables. The LIMDEP software package, or SAS-based programs, can be used to develop negative binomial models.
In addition, Shaw-Pin Miaou has developed an "extended" negative binomial model that permits variables with multiple values along a roadway to be treated in disaggregate form, value by value, rather than in aggregate form, by averages over the whole roadway. Highway segments are not truly homogeneous even if shoulder widths, lane widths, speed limits, and the like stay constant along them. Other variables, such as horizontal and vertical alignments, are subject to variation within the typical segment. The extended negative binomial model aims to capture the effect of such inhomogeneities.
In the following chapters the literature is reviewed; the data collection methodology is described in detail; the data analysis is presented; accident models of Poisson, negative binomial, and extended negative binomial type are exhibited; and validation and additional analyses are performed. The modeling chapter includes logistic modeling of accident severities on the Minnesota data. The last chapter presents the final models (obtained earlier in Tables 27 and 35) in the form of equations and exhibits associated Accident Reduction Factors. Two appendices offer additional information about the Minnesota population and the final model equations in metric form, respectively.
Some of the results in this report are to be found in the article by Vogt and Bared (1998).