A Copula-Based Approach for Accommodating the Underreporting Effect in Wildlife‒Vehicle Crash Analysis
Abstract
:1. Introduction
2. Data Description
3. Methodology
3.1. The Wildlife‒Vehicle Collision Model
3.2. The Underreporting Outcome Model
3.3. Linking the Wildlife‒Vehicle Collision Model and the Underreporting Outcome Model
4. Modeling Results
4.1. Variables Affecting the Number of Reported Wildlife‒Vehicle Collisions and the Underreporting Outcome
4.2. Comparison of the Hotspot Identification Results Using the Gaussian Copula-Based EB Method and NB-Based EB Method
Measure I
Measure II
Measure III
5. Discussion and Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Variables | Minimum | Maximum | Mean | S.D. a |
---|---|---|---|---|
Number of reported wildlife‒vehicle collisions per road segment | 0 | 22 | 0.24 | 0.81 |
Number of carcasses per road segment | 0 | 95 | 0.94 | 3.88 |
Underreporting indicator (Underreporting: 1; otherwise: 0) | Underreporting: 16%; otherwise: 84% | |||
Annual average daily traffic (AADT) over year 2002 to 2006 | 0.31 | 148.8 | 13.85 | 19.76 |
Restrictive access control (yes: 1; no: 0) b | yes: 24%; otherwise: 76% | |||
Posted speed limit (mph) | 20 | 70 | 52.76 | 10.79 |
Truck percentage (%) | 0 | 52.28 | 14.05 | 8.29 |
Median width (feet) | 0 | 60 | 7.9 | 15.62 |
Total number of lanes for both directions | 1 | 9 | 2.79 | 1.24 |
Roadway length (mile) | 0.01 | 6.99 | 0.22 | 0.4 |
Terrain type (rolling: 1; otherwise: 0) | rolling: 72%; otherwise: 28% | |||
Terrain type (mountainous: 1; otherwise: 0) | mountainous: 9.6%; otherwise: 90.4% | |||
Lane width (feet) | 10 | 20 | 12.5 | 1.88 |
Left shoulder width (feet) | 0 | 18 | 2.44 | 2.04 |
Right shoulder width (feet) | 0 | 20 | 4.03 | 3.52 |
Rural or Urban (urban: 0; rural: 1) | urban: 75.8%; rural: 24.2% | |||
White-tailed deer habitat (yes: 1; no: 0) | yes: 31%; no: 69% | |||
Mule deer habitat (yes: 1; no: 0) | yes: 51%; no: 49% | |||
Elk habitat (yes: 1; no: 0) | yes: 31%; no: 69% |
Name | Copula a | Parameter Range of | Parameter Range of Kendall’s tau |
---|---|---|---|
Gaussian | b | , is independence | , |
Farlie-Gumbel-Morgenstern | , is independence | , | |
Ali-Mikhail-Haq | , is independence | , | |
Clayton | , is independence | , | |
Frank | , is independence | c, | |
Gumbel | , is independence | , | |
Joe | , is independence | d, |
Gaussian Copula Model | Independent Copula Model | |
---|---|---|
Underreporting indicator variable | Estimate (Std. Error) | Estimate (Std. Error) |
Intercept | −4.103 (0.355) | −4.221 (0.355) |
Average daily traffic | −1.181 × 10−5 (4.77 × 10−6) | -* |
Restrictive access control | −0.780 (0.160) | −0.874 (0.157) |
Posted speed limit | 0.034 (0.006) | 0.039 (0.006) |
Total number of lanes for both directions | −0.159 (0.063) | −0.249 (0.052) |
Segment length | 1.187 (0.091) | 1.229 (0.085) |
Terrain type: rolling | 0.588 (0.115) | 0.575 (0.115) |
Terrain type: mountainous | 0.304 (0.156) | 0.315 (0.157) |
Left shoulder width | 0.085 (0.012) | 0.080 (0.012) |
White-tailed deer habitat | 1.274 (0.082) | 1.250 (0.082) |
Elk habitat | 0.491 (0.078) | 0.503 (0.078) |
Mule deer habitat | −0.288 (0.084) | −0.274 (0.083) |
Number of reported wildlife‒vehicle collisions variable | Estimate (Std. Error) | Estimate (Std. Error) |
Intercept | −6.240 (0.811) | −8.718 (0.596) |
Ln (Average daily traffic) | 0.497 (0.057) | 0.690 (0.052) |
Restrictive access control | −1.050 (0.141) | −0.958 (0.127) |
Posted speed limit | 0.059 (0.007) | 0.028 (0.006) |
Truck percentage | −0.036 (0.005) | −0.036 (0.005) |
Total number of lanes for both directions | −0.252 (0.048) | −0.177 (0.043) |
Terrain type: rolling | −0.244 (0.094) | −0.213 (0.084) |
Terrain type: mountainous | −0.742 (0.154) | −0.680 (0.140) |
Lane width | −0.132 (0.045) | -* |
Left shoulder width | 0.057 (0.011) | 0.057 (0.010) |
White-tailed deer habitat | 0.583 (0.075) | 0.523 (0.067) |
Elk habitat | 0.654 (0.075) | 0.705 (0.066) |
Measures | Threshold Values | ||
---|---|---|---|
Method I | c = 0.01 | c = 0.05 | c = 0.10 |
Copula model | 1031 | 2842 | 4056 |
NB model | 921 | 2624 | 3822 |
Method II | c = 0.01 | c = 0.05 | c = 0.10 |
Copula model | 13 | 86 | 213 |
NB model | 12 | 75 | 189 |
Method III | c = 0.01 | c = 0.05 | c = 0.10 |
Copula model | 8337 | 90,657 | 236,760 |
NB model | 11,490 | 114,093 | 294,874 |
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Zou, Y.; Zhong, X.; Tang, J.; Ye, X.; Wu, L.; Ijaz, M.; Wang, Y. A Copula-Based Approach for Accommodating the Underreporting Effect in Wildlife‒Vehicle Crash Analysis. Sustainability 2019, 11, 418. https://doi.org/10.3390/su11020418
Zou Y, Zhong X, Tang J, Ye X, Wu L, Ijaz M, Wang Y. A Copula-Based Approach for Accommodating the Underreporting Effect in Wildlife‒Vehicle Crash Analysis. Sustainability. 2019; 11(2):418. https://doi.org/10.3390/su11020418
Chicago/Turabian StyleZou, Yajie, Xinzhi Zhong, Jinjun Tang, Xin Ye, Lingtao Wu, Muhammad Ijaz, and Yinhai Wang. 2019. "A Copula-Based Approach for Accommodating the Underreporting Effect in Wildlife‒Vehicle Crash Analysis" Sustainability 11, no. 2: 418. https://doi.org/10.3390/su11020418