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 S in is a severity function determining the injury- severity category i proportion on roadway segment n ; X in is a vector of explanatory variables (weather, geometric, pavement, roadside and traffic variables); β i is a vector of estimable parameters; and ε in is error term.

10. If ε in’s are assumed to be generalized extreme value distributed, where P n (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 φ referring 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.