# Influential Factors Associated with Consecutive Crash Severity: A Two-Level Logistic Modeling Approach

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Data

^{6}units as the numbers were usually very large. Given the location of each crash, the speed limit and number of lanes of the road segment was also collected. If a crash occurred in a tunnel or on a bridge, the information was also recorded by the variable “location”, as the special driving environments may affect the transmission of the hazards produced by the primary crashes.

#### 2.2. Binary Logistic Regression

#### 2.3. Random-Effects Logistic Model

#### 2.4. Random-Parameters Logistic Model

#### 2.5. Two-Level Logistic Model

#### 2.6. Elasticity Analysis

#### 2.7. Model Comparison

## 3. Results

## 4. Discussion

#### 4.1. Crash-Related Factors and Interactions

#### 4.2. Environmental Factors

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Variable Name | Category/Explanation | Mean/Percentage | Standard Deviation |
---|---|---|---|

Dependent Variable | |||

Crash severity | Severe | 33.1% | |

Non-severe | 66.9% | ||

Independent Variables | |||

Environmental factors: | |||

Speed limit | km/h | 116.1 | 11.7 |

Number of lanes | 2.1 | 0.3 | |

Traffic volume | 10^{6} | 2.2 | 0.8 |

Weekend | Yes | 30.5% | |

No ^{†} | 69.5% | ||

Weather | Rainy | 38.7% | |

Cloudy | 52.1% | ||

Sunny ^{†} | 9.2% | ||

Location | Tunnel | 21.4% | |

Bridge | 2.4% | ||

Others ^{†} | 76.2% | ||

Crash attributes: | |||

Secondary CC | Yes | 61.2% | |

No ^{†} | 38.8% | ||

Truck involvement | Truck involved | 19.0% | |

No truck involved ^{†} | 81.0% | ||

Trailer truck involvement | Yes | 4.3% | |

No ^{†} | 95.7% | ||

Bus involvement | Yes | 2.1% | |

No ^{†} | 97.9% | ||

Crash type | Rear-end | 62.0% | |

Rollover | 6.4% | ||

Side-swipe | 2.7% | ||

Hitting objects ^{†} | 28.9% | ||

Number of vehicles involved | Single-vehicle | 42.2% | |

Double-vehicle | 34.0% | ||

Multi-vehicle ^{†} | 23.8% | ||

Attributes of the primary crash in the CC series: | |||

Crash type of the primary crash | Rear-end | 59.6% | |

Rollover | 6.4% | ||

Side-swipe | 0.6% | ||

Hitting objects ^{†} | 33.4% | ||

Number of vehicles involved in the primary crash | Single-vehicle | 52.4% | |

Double-vehicle | 30.2% | ||

Multi-vehicle ^{†} | 17.4% | ||

Truck involvement in the primary crash | Yes | 20.9% | |

No ^{†} | 79.1% | ||

Trailer truck involvement in the primary crash | Yes | 6.1% | |

No ^{†} | 95.9% | ||

Bus involvement in the primary crash | Yes | 2.4% | |

No ^{†} | 97.6% |

^{†}Reference group.

Basic binary Logistic Model | RE Logistic Model | RP Logistic Model | Two-Level Logistic Model | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Variables | Mean | SD | p-Value | Mean | SD | p-Value | Mean | SD | p-Value | Mean | SD | p-Value |

Intercept | –4.41 | 2.99 | 0.139 | –4.42 | 2.99 | 0.139 | –4.01 | 4.37 | 0.359 | –2.69 | 3.46 | 0.437 |

Environmental Factors | ||||||||||||

Speed limit | 0.40 ** | 0.01 | 0.007 | 0.40 ** | 0.01 | 0.007 | 0.06 ** | 0.02 | 0.016 | 0.04 ** | 0.02 | 0.035 |

Number of lanes | −2.91 ** | 1.04 | 0.005 | −2.91 ** | 1.04 | 0.005 | −4.90 ** | 1.99 | 0.014 | −4.29 ** | 1.29 | 0.008 |

Traffic volume | 0.72 ** | 0.20 | <0.001 | 0.72 ** | 0.20 | <0.001 | 1.14 ** | 0.35 | 0.001 | 1.41 ** | 0.40 | 0.004 |

Rainy | 3.24 ** | 1.13 | 0.004 | 3.24 ** | 1.13 | 0.004 | 4.22 ** | 1.35 | 0.002 | 2.84 ** | 1.26 | 0.024 |

Cloudy | 2.74 ** | 1.11 | 0.014 | 2.74 ** | 1.11 | 0.014 | 2.96 ** | 1.27 | 0.020 | 2.42 ** | 1.20 | 0.044 |

Tunnel | 1.97 ** | 0.66 | 0.003 | 1.97 ** | 0.66 | 0.003 | 2.25 ** | 0.94 | 0.016 | 2.47 ** | 0.63 | <0.001 |

Bridge | 2.62 ** | 1.10 | 0.017 | 2.62 ** | 1.10 | 0.017 | 3.72 ** | 1.58 | 0.018 | |||

Crash attributes | ||||||||||||

Truck involvement | 0.67 * | 0.38 | 0.075 | 0.67 * | 0.38 | 0.075 | 0.83 * | 0.48 | 0.085 | |||

Trailer truck involvement | 1.99 ** | 0.73 | 0.006 | 1.99 ** | 0.73 | 0.006 | 3.06 ** | 1.14 | 0.007 | |||

Interactions | ||||||||||||

Single-vehicle primary crash × secondary CC | −0.11 | 0.34 | 0.748 | −0.11 | 0.34 | 0.748 | −0.61 | 0.50 | 0.222 | 0.09 | 0.55 | 0.875 |

Two-vehicle primary crash × secondary CC | −1.33 ** | 0.52 | 0.010 | −1.33 ** | 0.52 | 0.010 | −2.15 ** | 0.81 | 0.008 | −1.80 ** | 0.87 | 0.012 |

Weekend × secondary CC | −1.01 ** | 0.43 | 0.017 | −1.01 ** | 0.43 | 0.017 | −1.45 ** | 0.64 | 0.023 | |||

Tunnel × secondary CC | 1.31 * | 0.71 | 0.064 | 1.31 * | 0.71 | 0.064 | 2.48 * | 1.15 | 0.031 | |||

Truck involvement × secondary CC | 2.80 ** | 0.87 | 0.001 | |||||||||

Random Effects (SD) | ||||||||||||

Cloudy | 2.75 ** | 1.06 | 0.009 | |||||||||

Double-vehicle primary crash × secondary CC | 0.002 | 1.22 | 0.989 | |||||||||

Truck involvement × secondary CC | 4.24 × 10^{−5} | 0.89 | 0.999 | |||||||||

${\sigma}_{v}$ (random intercept) | 0.23 | 1.13 | 0.984 | 1.00 ** | 0.50 | 0.045 | ||||||

$\rho $ | 0.13 | ―― | ―― |

Model | Log-Likelihood at Convergence | McFadden Pseudo R^{2} | AIC |
---|---|---|---|

Basic logistic model | −162.70 | ―― | 353.4 |

RE logistic model | −162.70 | 0.372 | 355.4 |

RP logistic model | −159.88 | 0.383 | 349.8 |

Two-level logistic model | −149.68 | 0.423 | 325.4 |

Variables | Mean | SD | p-Value |
---|---|---|---|

Intercept | –1.21 ** | 0.02 | <0.001 |

Speed limit | 2.60 ** | 0.07 | <0.001 |

Number of lanes | −5.11 ** | 0.17 | <0.001 |

Traffic volume | 1.64 ** | 0.06 | <0.001 |

Rainy | 52.5 ** | 4.00 | <0.001 |

Cloudy | 66.6 ** | 4.12 | <0.001 |

Tunnel | 19.4 ** | 2.28 | <0.001 |

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## Share and Cite

**MDPI and ACS Style**

Meng, F.; Xu, P.; Song, C.; Gao, K.; Zhou, Z.; Yang, L. Influential Factors Associated with Consecutive Crash Severity: A Two-Level Logistic Modeling Approach. *Int. J. Environ. Res. Public Health* **2020**, *17*, 5623.
https://doi.org/10.3390/ijerph17155623

**AMA Style**

Meng F, Xu P, Song C, Gao K, Zhou Z, Yang L. Influential Factors Associated with Consecutive Crash Severity: A Two-Level Logistic Modeling Approach. *International Journal of Environmental Research and Public Health*. 2020; 17(15):5623.
https://doi.org/10.3390/ijerph17155623

**Chicago/Turabian Style**

Meng, Fanyu, Pengpeng Xu, Cancan Song, Kun Gao, Zichu Zhou, and Lili Yang. 2020. "Influential Factors Associated with Consecutive Crash Severity: A Two-Level Logistic Modeling Approach" *International Journal of Environmental Research and Public Health* 17, no. 15: 5623.
https://doi.org/10.3390/ijerph17155623