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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

7. Conclusions

We present the final models of this study in the form of equations and make a few remarks about their significance. Appendix 2 gives the equations in metric form.

The final models proposed in this study are the following:

I. Segments of two-lane rural roads (Table 27)

Extended Negative Binomial Model with K = .306

NOTE: Each set of weights WH{i}, WV{j}, and WG{k} separately must sum to 1. To ensure this, usually it is necessary to insert one artificial horizontal curve with DEG = 0, one artificial crest with V = 0, and one artificial straightaway with GR = 0, each one having whatever weight is needed to make the sum equal 1.

II. Three-legged intersections of two-lane rural roads, stop-controlled on the minor road (Table 35)

III. Four-legged intersections of two-lane rural roads, stop-controlled on the minor road (Table 35)


These models yield the Accident Reduction Factors shown in Table 49 below. Recall that the Accident Reduction Factor is the percentage decrease in mean predicted accident count when a variable is increased by one unit, all other variables being held fixed. A negative value signifies that accidents increase by that percentage when the variable is increased by one unit.

Table 49. Accident Reduction Factors for the Final Models


Segment Model (Table 27)

3-Legged Intersection

Model (Table 35)

4-Legged Intersection

Model (Table 35)



































































The Accident Reduction Factors for DD and ND are roughly comparable. Since DD = ND times 5280 divided by 500, the coefficient 0.0084 of DD in the segment model (Table 27) translates into a coefficient 0.0887 of ND and an Accident Reduction Factor of -9.3% for an intersection model, as compared with -13.1% in the actual four-legged intersection model (Tables 35 and 49).

The ultimate use of models such as these is to aid the highway designer to improve highway safety and to determine what design measures will do this most effectively. The coefficients proposed for each of the models - in Tables 27 and 35 and in the equations above - are directly translatable into predicted accident counts and Accident Reduction Factors. Even if the models considered here were taken to be definitive, each coefficient has an estimated standard deviation or standard error (shown in Tables 27 through 35), and there is no reason to believe that the estimated coefficients are known to much greater accuracy than one standard deviation. For a normal random variable about 68% of measured values lie within one standard deviation of the mean. In addition there are numerous uncertainties that cannot be quantified in the highway variables. Variables such as ADT are crude averages over time, and some variables are incorrect for unknown causes (new construction without plans to confirm the change, data entry errors in one of the multiple data bases from which the data are obtained, inaccuracies in location of accidents, mileposts, alignments, etc.).

One informal way to estimate the error in a coefficient is to examine alternative models and note how coefficients vary from model to model. As well as referring to the literature for models obtained by other investigators, one may compare the different models in this study in Tables 21 through 37. Although there is some stability in coefficients as one passes from Poisson to negative binomial to extended negative binomial, there is less as one passes from one State to another, or from all accidents to injury accidents.

Of great importance for the practical utility of models such as the ones presented here is the issue of how to adapt them to different States and regions and/or different time epochs. In general what is needed is a multiplier that can be applied to a standard model to adjust it to a different State or region (for example, New England versus the Great Plains) and/or a different era (1999 versus 2001-2005), to circumstances in which drivers, vehicles, law enforcement, and demographics may differ from those under which the standard model was developed. Engineering judgment together with historical data from different States and eras can be used to develop multipliers. Alternatively, a small recent sample of accidents in a region can be compared with predictions from the standard model and an adjustment factor derived from the sample. Yet another approach is the Empirical Bayesian one: combine past data on a particular segment or intersection with a standard model of negative binomial type as discussed in Hauer et al. (1988).

Although the segment model developed here summarizes data from two reasonably diverse States (and two epochs), the intersection models are based on Minnesota alone. In Table 42 they have only partial success when applied to Washington State. Moreover, the design variables (e.g., Roadside Hazard Rating, number of driveways, channelization, and intersection angle) behave in unexpected ways as one moves from three-legged intersections to four-legged ones. These peculiarities, as well as the relatively high accident rates at intersections, suggest that intersection studies should continue as a highway safety research priority.


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