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A joint Econometric Analysis of Seat Belt Use and Crash-Related Injury Severity Naveen Eluru


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** The numbers in the cell represent column percentages (the sum of the figures in each column is 100%)


TABLE 3 Estimates of the Seat Belt use Component of Joint Model


Variables

Coefficient

t-stats

Constant

3.351

12.77

Driver Characteristics







Male

-0.574

-6.17

Age Variables (age < 25 years is base)







25-29 years

0.327

2.25

30-64 years

0.222

2.56

65-74 years

1.226

2.92

Under the influence of alcohol

-2.255

-12.88

Vehicle Characteristics (pick-up is base)







Sedan

0.331

3.45

SUV

1.155

6.58

Minivan

0.606

3.24

Environmental Factors







9am-7pm

0.601

5.96



TABLE 4 Injury Severity Component of Joint Model


Variables

Coefficient

t-stats

Driver Characteristics







Male

-0.454

-7.59

Age Variables (age < 25 years is base)







25-74 years

0.207

2.81

> 74 years

0.371

2.46

Male Age < 25 years

-0.173

-1.63

Under the influence of alcohol

0.465

2.48

Vehicle Characteristics







Sedan

0.288

4.98

Sedan x snow / fog

0.714

3.17

Sedan x struck by a non-sedan

0.131

1.62

Roadway Design Attributes







Medium-to-high speed limit (26-64mph)

0.906

9.28

High speed limit (≥64 mph)

0.358

1.11

Standard Deviation

1.554

2.94

Environmental Factors







6am – 7pm

-0.308

-4.09

Lighting Conditions







Dusk

-0.237

-1.44

Dark

-0.398

-2.74

Standard Deviation

1.500

5.53

Adverse Weather Conditions







Rain

-0.144

-2.00

Snow and/or fog

-0.659

-3.80

Crash Characteristics







Driver ejected out of the vehicle

3.468

7.04

Vehicle rolled over

1.855

10.05

Crash with a Stationary Object (base is crash with another vehicle)







Large object

1.509

11.34

Small object

1.201

8.76

Manner of Collision in Two Vehicle Crashes (base is rear-end collision)







Head on

1.397

8.71

Angle

0.151

1.56

Standard Deviation

1.066

5.41

Swipe collision when vehicles are traveling in opposite directions

-0.666

-1.96

Swipe collision when vehicles are traveling in same direction

-1.302

-9.31

Vehicle Role in Two Vehicle Crashes (base is driver strikes other vehicle)







Driver struck by a vehicle

0.446

6.88

Driver involved in strike and struck

0.323

1.60

Seat belt

-0.752

-1.88

Standard deviation of common error component between seat belt use and injury severity propensities

0.926

3.10

Threshold Parameters







Threshold 1

2.366

3.89

Threshold 2

3.730

5.47

Threshold 3

5.218

6.99

Threshold 4

8.151

9.41

Log-likelihood at convergence

-10551.9


TABLE 5 Elasticity Effects for the Fatal Injury Category


Variables

IBO

IRBO

CRBO

Driver Characteristics










Male

-36.55

-36.23

-39.33

Age Variables










25-74 years

13.13

14.03

15.05

>74 years

26.57

27.39

31.17

Under the influence of Alcohol

18.55

19.67

38.86

Vehicle Characteristics










Sedan

19.83

20.47

23.27

Non-sedan (other vehicle type)

0.95

1.11

1.36

Roadway Design Attributes










Medium-to-high speed limit (26-64mph)

49.52

49.29

53.73

High speed limit (≥64 mph)

74.50

21.93

29.78

Environmental Factors










6am-7pm

-19.75

-19.60

-23.40

Lighting Conditions










Dusk

-16.15

-14.94

-16.22

Dark

-1.43

-25.98

-27.76

Adverse Weather Conditions










Rain

-8.76

-9.11

-10.29

Snow and/or fog

-11.38

-12.17

-13.38

Crash Attributes










Driver ejected out of the vehicle

808.90

871.37

1054.25

Vehicle rolled over

186.00

189.02

226.74

Crash with a Stationary Object (base is crash with another vehicle)










Large object

120.29

119.62

147.09

Small object

107.71

101.98

127.19

Manner of Collision in Two Vehicle Crashes

(base is rear-end collision)












Head on

133.97

132.49

167.92

Angle

29.63

6.31

11.41

Swipe collision when vehicles are traveling in opposite directions

-40.12

-37.55

-39.57

Swipe collision when vehicle are traveling in same direction

-62.75

-60.50

-63.95

Vehicle Role in Two Vehicle Crashes

(base is driver strikes other vehicle)












Driver struck by a vehicle

32.05

33.13

37.20

Driver involved in strike and struck

15.00

25.94

27.28

Seat belt use

-129.45

-132.06

-64.50



1 While the ordered-response models have been used only within the past 7-8 years in the safety analysis literature, they have a long history of use in other transportation contexts; see Kitamura and Bunch (1990), Bhat (1991), and Bhat and Koppelman (1993). The reader will also note that the ordered-response model is perhaps more suited than the multinomial logit model for injury severity because of the correlation between adjacent injury severity levels. However, a limitation of the ordered-response structure is that it imposes a certain kind of monotonic effect of exogenous variables on injury severity levels (see Bhat and Pulugurta, 1998 for a detailed exposition of the relationship between ordered and unordered response models). Ideally, one would consider an ordered generalized extreme value model for injury severity that combines the flexibility offered by the unordered-response structure with the proximate covariance characteristic due to the ordinality in the injury severity levels. The authors are currently undertaking a research study to compare such an OGEV structure with an ordered-response structure.

2 The seat belt use rate of 93.2% in the GES sample is on the high side relative to national seat belt use rates, perhaps due to potential misreporting/misrecording of seat belt use. As indicated by Schiff and Cummings (2004), police officers often classify unbelted survivors as belted when they were actually not. Given that there s a much higher proportion of survivors from crashes, the Schiff and Cummins study implies that seat belt use percentage will be much higher than it should be, as is the case in the current sample. Thus, the estimated effectiveness of seat belt use in reducing injury severity should be viewed with caution in the current study. However, this issue should not detract from the analysis in the paper of how much the seat belt effectiveness may be attributed to the “true” value of restraint systems and how much may be due to the spurious effect of seat belt non-users intrinsically being more risky drivers who get themselves into more severe accidents.

3 The GES data included information on drug use and airbag use. However, a large fraction of records had missing information on these variables, as well as their imputed counterparts. So we excluded these driver behavior variables from consideration. However, data was available for almost all records for an imputed version of driver alcohol use.

4 Time of day is represented in the following five categories: early morning (12am-6am), AM peak (6am-9am), midday (9am-3pm), PM peak (3pm-7pm), and evening (7pm-12pm).

5 We examined differential effects of teenagers (≤ 19 years of age) and adults between the ages of 20 and 24 years. However, we did not find statistically different propensities to wear seat belts between these two age groups, and so combined these two age groups into a single “age < 25 years” category.

6 As for the case of seat belt use, we examined differential injury severity effects for teenagers (≤ 19 years of age) and adults between the ages of 20 and 24 years. However, due to the lack of statistically different injury severity propensities between the two age groups, they were combined into a single “age < 25 years” category.


7 The injury severity component of the CRBO model is normalized with respect to a smaller overall scale relative to the injury severity component of the IRBO model (due to the additional presence of the term in the CRBO model). This smaller scaling should, in general, lead to larger coefficients in the CRBO model.

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