# Investigating Rural Single-Vehicle Crash Severity by Vehicle Types Using Full Bayesian Spatial Random Parameters Logit Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Covariates Analysis of Rural Single-Vehicle Crashes

#### 2.1.1. Driver Characteristics

#### 2.1.2. Crash-Specific Characteristics

#### 2.1.3. Environmental Characteristics

#### 2.1.4. Temporal Characteristics

#### 2.2. Statistical Techniques for Crash Severity

#### 2.2.1. Unobserved Heterogeneity in Crash Analysis

#### 2.2.2. Spatial Correlation in Crash Analysis

#### 2.3. The Current Research

## 3. Data

## 4. Methodology

#### 4.1. Model Specifications

#### 4.1.1. Multinomial Logit Model

#### 4.1.2. Random Parameters Logit Model

#### 4.1.3. Random Intercept Logit Model

#### 4.1.4. Spatial Random Parameters Logit Model

#### 4.2. Model Transferability

#### 4.3. Model Diagnosis

_{1}, CA

_{2,}and CA

_{3}, respectively.

#### 4.4. Average Marginal Effect

## 5. Modeling Results and Discussion

#### 5.1. Full Bayesian Estimation

#### 5.2. Model Comparison

_{1}, CA

_{2}, CA

_{3}, and CA

_{whole}in the SRP-logit model were 79.1%, 27.6%, 15.2%, and 75.8%, respectively, and in the RP-logit model were 73.6%, 20.8%, 8.9%, and 66.3%, respectively. It can be easily found that the prediction accuracy of the SRP-logit model outperforms that of the RP-logit model.

#### 5.3. Discussion

#### 5.4. Model Transferability

#### 5.5. Recommendations

## 6. Conclusions

## 7. Limitations of This Study

- (1)
- Although many potential risk factors are considered in this research, some real-time factors that may also have effects on the severity of rural SV crashes are unavailable in police collision reports, such as real-time traffic volume and vehicle speed. It is expected that the fitting performance of the SRP-logit model can be improved if these variables are accommodated. Transportation facilities are not perfect in rural areas of China, which leads to a lack of traffic data; hence, some data collection equipment should be set up in specific rural locations for further research.
- (2)
- The insignificant variables were removed from the final model, which may introduce omitted variable bias. We will consider optimizing the statistical modeling framework to propose more reasonable judgments.
- (3)
- The research results showed that the transferability of the crash severity model between different vehicle types is unsatisfactory. This may be due to substantial differences between different motor vehicle types. In the future, more advanced methods need to be explored to improve model transferability. Further, due to the differences in cultural backgrounds and driving habits among different countries, the applicability of statistical methods proposed in this research needs to be explored.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Variables | Categories | Count(Ratio/%) | |||
---|---|---|---|---|---|

Passenger Car | Motorcycle | Pickup | Truck | ||

Number | 11,419 | 9703 | 2913 | 5489 | |

Driver gender | Male | 9858 (86.3) | 8995 (92.7) | 2734 (93.8) | 5478 (99.7) |

Female * | 1561 (13.7) | 708 (7.2) | 179 (6.1) | 11 (0.2) | |

Driver age | <30 | 3515 (30.8) | 2204 (22.7) | 783 (26.9) | 687 (12.5) |

30–60 * | 6214 (54.4) | 4064 (41.8) | 1722 (59.1) | 4219 (76.8) | |

>60 | 1690 (14.8) | 3435 (35.4) | 408 (14.0) | 583 (10.6) | |

Drunk driving | Yes | 1718 (15.0) | 2512 (25.8) | 264 (9.1) | 33 (0.6) |

No * | 9701 (85.0) | 7191 (74.2) | 2649 (90.9) | 5456 (99.4) | |

Weather | Non-clear | 1575 (13.7) | 1219 (12.5) | 445 (15.3) | 866 (15.7) |

Clear * | 9844 (86.2) | 8484 (87.4) | 2468 (84.7) | 4623 (84.2) | |

Road surface | Non-dry | 1293 (11.3) | 984 (10.1) | 315 (10.8) | 632 (11.5) |

Dry * | 10,126 (88.7) | 8719 (89.9) | 2598 (89.2) | 4857 (88.5) | |

Crash type | Non-fixed object * | 8984 (78.6) | 7766 (80.0) | 2252 (77.3) | 4058 (73.9) |

Fixed object | 838 (7.3) | 1087 (11.2) | 188 (6.4) | 937 (17.0) | |

Collision with pedestrian | 1492 (13.0) | 766 (7.8) | 434 (14.8) | 445 (8.1) | |

Others | 105 (0.9) | 84 (0.8) | 39 (1.3) | 49 (0.8) | |

Week | Monday–Tuesday | 3314 (29.0) | 2780 (28.7) | 844 (29.0) | 1525 (27.8) |

Wednesday * | 1591 (13.9) | 1419 (14.6) | 419 (14.3) | 767 (13.9) | |

Thursday–Friday | 3330 (29.2) | 2810 (29.0) | 841 (28.9) | 1653 (30.1) | |

Weekend | 3184 (27.9) | 2694 (27.7) | 809 (27.8) | 1544 (28.2) | |

Month | Early in month | 3788 (33.1) | 3145 (32.4) | 933 (32.0) | 1783 (32.4) |

Middle in month * | 3730 (32.7) | 3249 (33.5) | 965 (33.2) | 1809 (33.0) | |

Late in month | 3901 (34.2) | 3309 (34.1) | 1015 (34.8) | 1897 (34.6) | |

Season | Spring * | 2872 (25.2) | 2632 (27.1) | 762 (26.1) | 1532 (27.9) |

Summer | 2805 (24.6) | 2539 (26.1) | 676 (23.2) | 1415 (25.7) | |

Fall | 3094 (27.0) | 2614 (26.9) | 782 (26.8) | 1573 (28.6) | |

Winter | 2648 (23.1) | 1918 (19.8) | 693 (23.8) | 969 (17.7) | |

Light | Daylight * | 7314 (64.0) | 6011 (61.9) | 1966 (67.5) | 2946 (53.6) |

Dark (with street lighting) | 2485 (21.7) | 1661 (17.1) | 465 (15.9) | 798 (14.5) | |

Dark (without street lighting) | 1620 (14.2) | 2031 (20.9) | 482 (16.5) | 1745 (31.7) | |

Crash time | Day * | 6561 (57.5) | 5345 (55.1) | 1780 (61.1) | 2550 (46.5) |

Night | 4858 (42.5) | 4358 (44.9) | 1133 (38.9) | 2939 (53.5) | |

Traffic | Controlled | 7603 (66.5) | 6376 (65.7) | 1874 (64.3) | 3668 (66.8) |

control | Uncontrolled * | 3816 (33.4) | 3327 (34.2) | 1039 (35.6) | 1821 (33.1) |

Models | Types | Characteristics |
---|---|---|

MN-logit model | Fixed effects model | Cannot capture unobserved heterogeneity and spatial correlation. |

RP-logit model | Random effects model | Captures unobserved heterogeneity by allowing parameters of risk factors to vary randomly and cannot capture spatial correlation. |

RI-logit model | Captures unobserved heterogeneity by only allowing the intercept to vary randomly and cannot capture spatial correlation. | |

SRP-logit model | Captures unobserved heterogeneity by allowing parameters of risk factors to vary randomly and captures spatial correlation by structured spatial error term. |

Index | MN-Logit Model | RP-Logit Model | RI-Logit Model | SRP-Logit Model | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

PA | MO | PI | TR | PA | MO | PI | TR | PA | MO | PI | TR | PA | MO | PI | TR | |

$\overline{D}$ | 8797 | 8599 | 2104 | 4176 | 8712 | 8496 | 2037 | 4112 | 8756 | 8553 | 2068 | 4158 | 8683 | 8479 | 2014 | 4067 |

pD | 62 | 58 | 51 | 54 | 115 | 119 | 91 | 93 | 83 | 78 | 69 | 73 | 138 | 131 | 112 | 117 |

DIC | 8859 | 8657 | 2155 | 4230 | 8827 | 8615 | 2128 | 4205 | 8839 | 8631 | 2137 | 4217 | 8821 | 8610 | 2126 | 4184 |

CA_{1}/% | 79.5 | 22.0 | 68.1 | 75.2 | 82.5 | 30.2 | 73.6 | 79.1 | 81.2 | 29.4 | 69.5 | 74.1 | 84.6 | 36.4 | 79.1 | 81.3 |

CA_{2}/% | 28.1 | 64.9 | 17.4 | 29.1 | 26.3 | 73.0 | 20.8 | 30.1 | 27.3 | 62.0 | 15.4 | 32.9 | 32.2 | 80.5 | 27.6 | 30.7 |

CA_{3}/% | 6.4 | 28.1 | 9.2 | 11.6 | 10.4 | 33.9 | 8.9 | 18.7 | 9.5 | 29.1 | 10.7 | 16.5 | 16.0 | 38.2 | 15.2 | 22.6 |

CA_{whole}/% | 72.6 | 47.9 | 61.5 | 68.3 | 75.2 | 55.7 | 66.3 | 72.1 | 74.1 | 48.5 | 62.3 | 68.2 | 79.1 | 62.1 | 75.8 | 74.5 |

Variables | MN-Logit Model | RI-Logit Model | ||||||
---|---|---|---|---|---|---|---|---|

PA | MO | PI | TR | PA | MO | PI | TR | |

Male | 0.320 ** | –0.150 *** | 0.160 ** | – | 0.311 ** | –0.139 *** | 0.142 * | – |

No-–clear | −0.435 * | 0.305 ** | −0.284 * | −0.250 ** | −0.442 * | 0.317 ** | −0.253 * | −0.241 * |

Controlled | 0.174 * | – | – | – | 0.177 * | – | – | – |

Age > 60 | 0.334 ** | 0.376 *** | 0.488 ** | – | 0.342 ** | 0.351 *** | 0.504 ** | – |

Drunk driving | 0.345 *** | 0.161 *** | 1.349 ** | – | 0.339 *** | 0.159 *** | 1.296 *** | – |

Weekend | – | 0.087 * | 0.154 * | 0.710 * | 0.235 ** | 0.101 * | 0.147 * | 0.716 * |

Early in month | – | – | 0.161 * | −0.172 ** | – | – | 0.157* | −0.178 ** |

Late in month | – | – | – | 0.157 * | – | – | – | 0.161 * |

Fall | – | −0.071 * | – | −0.246 * | – | −0.083 * | – | −0.239 * |

Winter | 0.376 * | 0.144 * | 0.198 * | – | 0.395 * | 0.160 ** | 0.202 * | – |

Dark (with street lighting) | – | 0.327 ** | – | – | – | 0.355 * | – | – |

Dark (without street lighting) | 0.831 * | 0.349 * | 0.708 * | 0.718 ** | 0.836 * | 0.352 ** | 0.764 * | 0.737 * |

Collision with fixed object | 1.231 ** | 1.105 *** | 1.315 * | 0.498 * | 1.248 ** | 1.124 *** | 1.307 ** | 0.510 * |

Collision with pedestrian | −2.126 ** | −2.401 * | −1.125 * | −1.105 ** | −2.092 ** | −2.437 * | −1.164 * | −1.094 *** |

Intercept | −2.441 ** | 0.698 * | −2.273 * | −1.386 *** | −2.608 ** | 0.762 ** | −2.494 * | −1.327 *** |

s.d. intercept | – | – | – | – | 0.632 | 0.455 | 0.318 | 0.269 |

Variables | RP-Logit Model | SRP-Logit Model | ||||||
---|---|---|---|---|---|---|---|---|

PA | MO | PI | TR | PA | MO | PI | TR | |

Male | 0.317 ** | −0.144 *** | 0.157 * | – | 0.315 ** | −0.147 *** | 0.152 * | – |

s.d. male | 1.218 | 0.497 | 0.937 | – | 1.197 | 0.503 | 1.043 | – |

Non–clear | −0.447 * | 0.312 ** | −0.255* | −0.236 * | −0.439* | 0.342 *** | −0.261 * | −0.239 * |

s.d. non–clear | 0.134 | – | 0.107 | 0.513 | 0.140 | – | 0.210 | 0.522 |

Controlled | 0.181 * | – | – | – | – | – | – | – |

Age > 60 | 0.340 ** | 0.349 *** | 0.494 ** | – | 0.357 ** | 0.346 *** | 0.473 ** | – |

Drunk driving | 0.340 *** | 0.166 *** | 1.251 *** | – | 0.343 ** | 0.163 *** | 1.248 *** | – |

s.d. drunk driving | – | 1.552 | – | – | – | 1.408 | – | – |

Weekend | 0.237 ** | 0.105 * | 0.165 * | 0.712 * | 0.232 ** | 0.092 * | 0.151 * | 0.707 ** |

s.d. weekend | – | 0.371 | – | 1.030 | – | 0.401 | – | 1.206 |

Early in month | – | – | 0.167* | −0.169 ** | – | – | 0.165 * | −0.167 ** |

Late in month | – | – | – | 0.168 * | – | – | – | 0.165 * |

Fall | – | −0.066 * | – | −0.232 * | – | −0.057 * | – | −0.238 * |

Winter | 0.393 ** | 0.168 ** | 0.227 * | – | 0.358** | 0.157 ** | 0.219* | – |

Dark(with street lighting) | – | 0.324 * | – | – | – | – | – | – |

Dark(without street lighting) | 0.847 * | 0.341 ** | 0.693 * | 0.769 * | 0.845 * | 0.347 ** | 0.725 * | 0.771 * |

Collision with fixed object | 1.257 ** | 1.151 *** | 1.240 * | 0.509 * | 1.268 ** | 1.147 *** | 1.251 * | 0.512 * |

Collision with pedestrian | −2.125 ** | −2.409 * | −1.094 ** | −1.065 *** | −2.157 ** | −2.416 * | −1.119 ** | −1.061 *** |

Intercept | −2.637 ** | 0.519 * | −2.179 * | −1.270 *** | −2.590 *** | 0.507 * | −2.165 ** | −1.238 *** |

${\tau}_{s}^{1}$ | – | – | – | – | 0.712 | – | 0.723 | 0.595 |

${\tau}_{s}^{2}$ | – | – | – | – | 0.543 | 0.691 | – | 0.749 |

${\tau}_{s}^{3}$ | – | – | – | – | – | 0.850 | – | – |

Application Data | Established Model | |||
---|---|---|---|---|

Passenger Car | Motorcycle | Pickup | Truck | |

Passenger car | 1 | −1.260 | 0.329 | −0.895 |

Motorcycle | −0.378 | 1 | −0.437 | −1.139 |

Pickup | 0.417 | −0.917 | 1 | −0.743 |

Truck | −0.129 | −2.031 | −0.154 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Wei, F.; Cai, Z.; Wang, Z.; Guo, Y.; Li, X.; Wu, X.
Investigating Rural Single-Vehicle Crash Severity by Vehicle Types Using Full Bayesian Spatial Random Parameters Logit Model. *Appl. Sci.* **2021**, *11*, 7819.
https://doi.org/10.3390/app11177819

**AMA Style**

Wei F, Cai Z, Wang Z, Guo Y, Li X, Wu X.
Investigating Rural Single-Vehicle Crash Severity by Vehicle Types Using Full Bayesian Spatial Random Parameters Logit Model. *Applied Sciences*. 2021; 11(17):7819.
https://doi.org/10.3390/app11177819

**Chicago/Turabian Style**

Wei, Fulu, Zhenggan Cai, Zhenyu Wang, Yongqing Guo, Xin Li, and Xiaoyan Wu.
2021. "Investigating Rural Single-Vehicle Crash Severity by Vehicle Types Using Full Bayesian Spatial Random Parameters Logit Model" *Applied Sciences* 11, no. 17: 7819.
https://doi.org/10.3390/app11177819