# Analysis of the Effects of Highway Geometric Design Features on the Frequency of Truck-Involved Rear-End Crashes Using the Random Effect Zero-Inflated Negative Binomial Regression Model

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## Abstract

**:**

## 1. Introduction

#### 1.1. Research Background

#### 1.2. Research Gaps and Objectives

## 2. Highway Geometric Design Features on the Frequency of Truck-Involved Crashes

## 3. Methods Section

#### 3.1. Data Collection

#### 3.2. Model Development

_{i}, can be computed using the following expression:

_{i}occurring on road segment i and ${\lambda}_{i}$ is the Poisson parameter; POI was obtained for each road segment. $E\left[{y}_{i}\right]$ is the expected number of TIRCs that occur on each road, where $E\left[{y}_{i}\right]$ is the predicted number of events that occur due to an explanatory variable, for example, traffic surface, curve, or straight line, etc. The relationship between the explanatory variable and the Poisson parameter is in the form of a logarithmic model,

## 4. Results

#### 4.1. Model Statistics

^{2}value stands notably high at 0.04010. However, the predicted dispersion ratio was 4.676, indicating the importance of having a p-value < 0.000. As a result, it became crucial to develop the Negative Binomial Regression Model (NBR), and the mean zero probability forecast was 0.910. Many road segments exhibited zero crashes, necessitating the development of a zero-inflated Negative Binomial Regression (ZINB) Model. To determine the most suitable model, the Akaike Information Criterion (AIC) was considered, which revealed that the AIC of NBR (12,946.76) was higher than that of ZINB (12,416.14). This suggests that the model with zero state separation is more appropriate. Additionally, the dispersion ratio serves as an indicator of the suitability of the negative binomial model. Discrepancies between the Department of Highways Branch (DOHB)-controlled areas were acknowledged, and a spatial correlation analysis indicated an intra-area variance of 0.396 (39.6%) [46]. Consequently, it was deemed appropriate to incorporate the random effect into the ZINB model, leading to the development of the Spatial Zero-Inflated Negative Binomial Regression (SZINB). The AIC value for SZINB was calculated to be 12,198.59, which is lower than that of ZINB, suggesting that SZINB is more suitable. Thus, parameter interpretations should be derived from the SZINB model based on the research by Raihan, et al. [23], considering its superior suitability compared to ZINB.

#### 4.2. Correlations and Parameter Estimations

## 5. Discussion

## 6. Conclusions and Implementations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Control areas of Department of Highways Office (DOH) and (

**b**) Truck-Involved Rear-end Crash Points. The colors within the diagram denote the geographical jurisdictions of the Department of Highway offices. To illustrate, the symbol ‘DOH1’ signifies Department of Highway Offices Number 1, encompassing their operational purview over four provinces situated in the northern region of the country, namely Mae Hong Son, Chiang Mai, Lamphun, and Lampang.

**Figure 2.**Correlation between explanatory variables in truck-involved rear-end crashes (TIRC). The depiction of the factors is in reference to Table 2.

Collision Type/Crash Severity | Fatal Crash | Severe Crash | Minor Injury Crash | PDO | Total | ||||
---|---|---|---|---|---|---|---|---|---|

Pedestrian collision | 70 | 14.55% | 33 | 6.86% | 104 | 21.62% | 274 | 56.96% | 481 |

Rear-end collision | 930 | 24.36% | 517 | 13.54% | 1139 | 29.84% | 1231 | 32.25% | 3817 |

Sideswipe collision | 272 | 19.93% | 125 | 9.16% | 412 | 30.18% | 556 | 40.73% | 1365 |

Single collision | 308 | 4.59% | 309 | 4.60% | 1697 | 25.26% | 4403 | 65.55% | 6717 |

Head on collision | 236 | 46.83% | 91 | 18.06% | 118 | 23.41% | 59 | 11.71% | 504 |

Variable | Value | Description | Frequency | Percentage |
---|---|---|---|---|

Rear-end crash with truck involvement (mean, S.D.) | (0.291, 2.071) | |||

Length (mean, S.D.) | (3.082, 5.023) | |||

AADT (mean, S.D.) | (14,473.9, 24,292.1) | |||

Percent Truck (mean, S.D.) | (16.328, 11.771) | |||

Number of lanes per direction | 0 | 2 lanes road | 9707 | 57.32% |

1 | 4 lanes road | 5459 | 32.23% | |

2 | 6 lanes road | 1015 | 5.99% | |

3 | 6 lanes and more | 755 | 4.46% | |

Speed Limit | 0 | 80 Km/h and less | 2497 | 14.74% |

1 | 90 Km/h | 4794 | 28.31% | |

2 | >90 Km/h | 9645 | 56.95% | |

Pavement | 0 | Asphalt concrete | 15,258 | 90.09% |

1 | Concrete | 1678 | 9.91% | |

Lane width | 0 | ≤3 m | 1025 | 6.05% |

1 | 3.1–3.5 m | 15,638 | 92.34% | |

2 | >3.5 m | 273 | 1.61% | |

Footpath | 0 | No | 16,131 | 95.25% |

1 | Yes | 805 | 4.75% | |

Shoulder width | 0 | ≤1 m | 6364 | 37.58% |

1 | 1.1–2 m | 3533 | 20.86% | |

2 | 2.1–3 m | 6604 | 38.99% | |

3 | >3 m | 435 | 2.57% | |

Right-of-Way | 0 | ≤40 m | 11,131 | 65.72% |

1 | 40.1–60 m | 3412 | 20.15% | |

2 | 60.1–80 m | 1803 | 10.65% | |

3 | >80 m | 590 | 3.48% | |

Median | 0 | Yes | 5608 | 33.11% |

1 | No | 11,328 | 66.89% | |

Median width | 0 | No median | 11,328 | 66.89% |

1 | ≤2 m | 987 | 5.83% | |

2 | 2.1–4 m | 664 | 3.92% | |

3 | 4.1–6 m | 2438 | 14.40% | |

4 | >6 m | 1519 | 8.97% | |

Curve ^{a} | 0 | Straight | 16,728 | 98.77% |

1 | Curve (R > 100) | 208 | 1.23% | |

Slope ^{a} | 0 | Normal | 16,734 | 98.81% |

1 | Slope (>3% grade) | 202 | 1.19% | |

Median opening ^{a} | 0 | Non median opening | 16,757 | 98.94% |

1 | Median Opening with auxiliary lane | 179 | 1.06% |

^{a}counted only the road segment that had a crash at least 1 time.

Model Statistics | POI | NBR | ZINB | SZINB |
---|---|---|---|---|

Log−likelihood intercept-only model | −17,834.9 | −7348.39 | −7348.39 | −6984.54 |

Log−likelihood convergence model | −10,682.3 | −6448.38 | −6159.07 | −6049.3 |

McFadden ρ^{2} | 0.4010 | 0.1225 | 0.1618 | 0.1339 |

The Akaike Information Criterion (AIC) | 21,412.55 | 12,946.76 | 12,416.14 | 12,198.59 |

Mean zero probability | 0.910 | |||

Dispersion ratio | 4.676 *** | |||

Over-dispersion | 0.841 | |||

Spatial correlation | 0.396 |

Estimate | S.D. | t-Stat | p-Value | Sig. | CMF | |
---|---|---|---|---|---|---|

Random Effect (intercept) | 5.970 | 2.443 | 2.443 | 0.0201 | ** | |

Conditional model: | ||||||

(Intercept) | −1.363 | 0.313 | −4.361 | <0.000 | *** | |

2 lanes road | 0.114 | 0.132 | 0.865 | 0.387 | ||

4 lanes road | 0.240 | 0.183 | 1.313 | 0.189 | ||

6 lanes road | 0.465 | 0.178 | 2.611 | 0.009 | ** | 1.5914 |

90 Km/h | −0.074 | 0.214 | −0.345 | 0.730 | ||

>90 Km/h | 0.544 | 0.134 | 4.049 | <0.000 | *** | 1.7229 |

Concrete Pavement | −0.407 | 0.119 | −3.423 | 0.001 | ** | 0.6658 |

Lane width [3.1–3.5 m] | −0.219 | 0.271 | −0.808 | 0.419 | ||

Lane width [>3.5 m] | −0.578 | 0.385 | −1.499 | 0.134 | ||

Footpath | 0.364 | 0.164 | 2.226 | 0.026 | ** | 1.4393 |

Shoulder width [1.1–2 m] | 0.359 | 0.154 | 2.324 | 0.020 | ** | 1.4318 |

Shoulder width [2.1–3 m] | 0.485 | 0.152 | 3.180 | 0.001 | ** | 1.6240 |

Shoulder width [>3 m] | 0.134 | 0.234 | 0.574 | 0.566 | ||

Right-of-way [40.1–60 m] | 0.447 | 0.111 | 4.017 | <0.000 | *** | 1.5643 |

Right-of-way [60.1–80 m] | 0.334 | 0.133 | 2.518 | 0.012 | ** | 1.3967 |

Right-of-way [>80 m] | 0.480 | 0.207 | 2.319 | 0.020 | ** | 1.6158 |

Median width [≤2 m] | 0.119 | 1.509 | 0.079 | 0.937 | ||

Median width [2.1–4 m] | 0.278 | 1.507 | 0.185 | 0.853 | ||

Median width [4.1–6 m] | 0.412 | 1.490 | 0.276 | 0.782 | ||

Median width [>6 m] | 0.564 | 1.495 | 0.377 | 0.706 | ||

Curve | 1.617 | 0.120 | 13.502 | <0.000 | *** | 5.0369 |

Slope | 0.746 | 0.192 | 3.881 | <0.000 | *** | 2.1089 |

Median opening | 1.604 | 0.161 | 9.948 | <0.000 | *** | 4.9738 |

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## Share and Cite

**MDPI and ACS Style**

Champahom, T.; Se, C.; Jomnonkwao, S.; Kasemsri, R.; Ratanavaraha, V.
Analysis of the Effects of Highway Geometric Design Features on the Frequency of Truck-Involved Rear-End Crashes Using the Random Effect Zero-Inflated Negative Binomial Regression Model. *Safety* **2023**, *9*, 76.
https://doi.org/10.3390/safety9040076

**AMA Style**

Champahom T, Se C, Jomnonkwao S, Kasemsri R, Ratanavaraha V.
Analysis of the Effects of Highway Geometric Design Features on the Frequency of Truck-Involved Rear-End Crashes Using the Random Effect Zero-Inflated Negative Binomial Regression Model. *Safety*. 2023; 9(4):76.
https://doi.org/10.3390/safety9040076

**Chicago/Turabian Style**

Champahom, Thanapong, Chamroeun Se, Sajjakaj Jomnonkwao, Rattanaporn Kasemsri, and Vatanavongs Ratanavaraha.
2023. "Analysis of the Effects of Highway Geometric Design Features on the Frequency of Truck-Involved Rear-End Crashes Using the Random Effect Zero-Inflated Negative Binomial Regression Model" *Safety* 9, no. 4: 76.
https://doi.org/10.3390/safety9040076