highway accident severities and the mixed logit model: an exploratory analysis john milton, venky...
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Highway accident severities and the mixed
logit model: An exploratory analysis
John Milton, Venky Shankar, Fred Mannering
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.
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.
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.
Past methodological approaches
Logistic regression and bivariate models.
Ordered probability models.
Multinomial and nested logit models.
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.
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).
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.
Define:
where Sin is a severity function determining the
injury-severity category i proportion on roadway segment n;
Xin is a vector of explanatory variables (weather, geometric, pavement, roadside and traffic variables);
βi is a vector of estimable parameters; and
εin is error term.
in i in inS X
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 .
i in
n
i InI
EXPP i
EXP
X
X
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 .
i inin
i InI
EXP XP f | d
EXP X
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.
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).
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.
Descriptive statisticsVariable Mean Std. Dev. Minimum Maximum
Average daily traffic 37,354 3,696 3,347 172,557
Average annual precipitation in inches 29.90 21.84 4.56 131.76
Average annual snowfall in inches 15.12 42.6 0 652
Percentage of trucks 14.16 6.68 3.20 32.00
Number of interchanges per mile 0.85 0.83 0 4
Speed limit in miles per hour 59.67 5.50 20.00 65
Friction number of pavement surface 46.82 5.63 20.00 61.5
Number of horizontal curves per mile 1.44 0.95 0 5
Number of changes in vertical profile per mile
1.88 1.69 0 20
Average daily truck traffic 4,165 3070 549 14,032
Estimation results: Variable
Value
Standard Error
t-statistic
Property damage only
Constant (Standard error of parameter distribution)
-0.6847 (1.7184)
0.2822 (0.8152)
-2.43 (2.11)
Average daily traffic per lane in thousands (Standard error of parameter distribution)
0.0792 (0.7143)
0.0365 (0.2438)
2.17 (2.93)
Average annual snowfall in inches (Standard error of parameter distribution)
0.0116 (0.0475)
0.0051 (0.0220)
2.29 (2.16)
Possible injury
Constant (Standard error of distribution)
-0.6205 (0.4338)
0.1995 (0.5507)
-3.11 (0.79)
Percentage of trucks (Standard error of parameter distribution)
-0.1617 (0.1350)
0.0506 (0.0453)
-3.20 (2.99)
Injury
Average daily truck traffic in thousands (Standard error of parameter distribution)
-0. 4669 (0. 6771)
0.1085 (0.1932)
-4.30 (3.51)
Number of horizontal curves per mile (Fixed parameter)
-0.3274 0.0761 -4.30
Number of changes in vertical profile per mile (Fixed parameter)
-0.0947 0.0257 -3.69
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.
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.
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.
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.
Findings: Number of horizontal curves
Defined for Injury
Fixed Parameter; mean = -0.3274
Drivers compensating by driving more cautiously?
Findings: Number of changes in vertical profile
Defined for Injury
Fixed Parameter; mean = -0.0947
Drivers compensating by driving more cautiously?
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.