Highway accident severities and the mixed logit model: An exploratory analysis

1. Highway accident severities and the mixed logit model: An exploratory analysis John Milton, Venky Shankar, Fred Mannering

2. Background • State agencies generally look only at accident frequencies when programming safety highway improvement. • Example: Washington State uses negative binomial and zero-inflated models to forecast accident frequencies.

3. Problems with frequency-dominated approaches • Some do not consider severity which may be the critical element. • Some only simplistically consider severity leading to problematic assumptions. • Frequency-dominated approaches tend to overlly favor urban areas.

4. How to forecast injury severity? • Detailed severity models based on individual accidents. • Too complex for forecasting purposes (require information on age and gender of driver, type of car, restraint usage, alcohol consumption, etc.). • Separate frequency models for different severity types. • Ignores correlation among severity outcomes. • Can lead to very complex modeling structures.

5. Past methodological approaches • Logistic regression and bivariate models. • Ordered probability models. • Multinomial and nested logit models.

6. Proposed approach • Assume the frequency of accidents is known (well developed methods exist for determining these). • Divide highways into segments. • Develop a model to forecast the proportion of accidents by severity levels on highway segments.

7. Differences relative to existing approaches: • More aggregate – cannot include specific accident characteristics (driver characteristics, vehicle characteristics, restraint usage, alcohol consumption, etc.). • Has advantage of easy application (does not require forecasting of many accident-specific variables).

8. Methodological approach • Without detailed accident information, our approach potentially introduces a heterogeneity problem. • Heterogeneity could result in varying effects of X that could be captured with random parameters. • Mixed logit may be appropriate.

9. Define: where Sin is a severity function determining the injury-severity category i proportion on roadway segment n; Xinis a vector of explanatory variables (weather, geometric, pavement, roadside and traffic variables); βiis a vector of estimable parameters; and εin is error term.

10. If εin’s are assumed to be generalized extreme value distributed, where Pn(i) is the proportion of injury-severity category (from the set of all injury-severity categories I) on roadway segment n.

11. The mixed logit is: where f (β | φ) is the density function of β with φreferring to a vector of parameters of the density function (mean and variance). • With this, β can now account for segment-specific variations of the effect of X on injury-severity proportions, with the density function f (β | φ) used to determine β.

12. Mixed logit • Relaxes possible IIA problems with a more general error-term structure. • Can test a variety of distribution options for β . • Estimated with simulation based maximum likelihood.

13. Empirical setting • Seek to model the annual proportion of accidents by injury severity on roadway segments. • Injury-severities: property damage only; possible injury; injury. • Multilane divided highways in Washington State. • 274 roadway segments defined (average length 2.7 miles).

14. Empirical setting • Accident data from 1990-94 (22,568 accidents; 56% property damage only; 22% possible injury; 22% injury). • Accident data linked with weather, geometric, pavement, roadside and traffic data.

15. Descriptive statistics

16. Estimation results:

17. Findings: Average Daily Traffic • Defined for Property damage only • Parameter normally distributed; mean = 0.0792; s.d. = 0.7143 • For roadway segments, 45.6% less than zero, 54.4% greater than zero. • Possible differences in driver behavior across the state changes this effect.

18. Findings: Average Annual Snowfall • Defined for Property damage only • Parameter normally distributed; mean = 0.1390; s.d. = 0.5703 • For roadway segments, 37.9% less than zero, 62.1% greater than zero. • Most sections reduce severity but not all. Again, driver behavior differences.

19. Findings: Percentage of trucks • Defined for Possible Injury • Parameter normally distributed; mean = -0.1617; s.d. = 0.1350 • For roadway segments, 88.1% less than zero, 11.9% greater than zero. • For most sections increasing percentages push severities to high/low extremes.

20. Findings: Average daily number of trucks • Defined for Injury • Parameter normally distributed; mean = -0.4669; s.d. = 0.6771 • For roadway segments, 76% less than zero, 24% greater than zero. • For most sections increasing number of trucks reduces “injury” proportions.

21. Findings: Number of horizontal curves • Defined for Injury • Fixed Parameter; mean = -0.3274 • Drivers compensating by driving more cautiously?

22. Findings: Number of changes in vertical profile • Defined for Injury • Fixed Parameter; mean = -0.0947 • Drivers compensating by driving more cautiously?

23. Summary • Mixed logit has the potential to provide highway agencies with a new way of estimating injury severities. • Method needs to be applied to more diverse road classes, such as two-lane highways.