# Accident Frequency Prediction Model for Flat Rural Roads in Serbia

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Models in Accident Frequency Analysis

#### 1.2. Factors Affecting the Accident Frequency

#### 1.3. Aims of the Research

## 2. Materials and Methods

#### 2.1. Data

- Accident data, collected and maintained by the Ministry of Internal Affairs of the Republic of Serbia.
- Traffic data, collected and maintained by the Public Enterprise “Roads of Serbia”.
- Roadway geometrics, cross-sectional elements, and traffic signalization data; collected and maintained by the Public Enterprise “Roads of Serbia”.

#### 2.2. Statistical Models

^{th}explanatory variable, ${x}_{itj}$ is the value of the j

^{th}explanatory variable for road segment i in year t.

## 3. Results

^{2}had the lowest value in the zero-inflated models, i.e., ZIP (0.255) and ZINB (0.277) models, which increased to 0.336 and 0.338 in the Poisson and NB models, respectively. The highest value of McFadden ρ

^{2}had a RENB model (0.348), which indicated the best fit of the model with the actual data. The Vuong test showed that the data set (with the Poisson and NB models) was superior to the ZIP and ZINB model, with the values of the tests being V = 1.71 and V = 1.60, respectively. To compare the competition models based on information criteria, the same set of independent variables had to be applied to all models. The lowest value of the information criteria had the RENB model, i.e., AIC (594.50) and BIC (629.44); then, the NB (AIC = 604.78; BIC = 635.54) and the Poisson model (AIC = 607.61; BIC = 636.20). The highest value of AIC and BIC had zero-inflated models. Based on the above tests, it has been determined that the RENB model has the best performance and the best goodness-of-fit statistics.

^{2}by only 1%.

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Comparison between the five competing models regarding the observed and predicted accident frequencies.

Variables | Description | Min | Max | Mean | Std. Dev |
---|---|---|---|---|---|

Dependent variable | |||||

RTA | Number of traffic accidents | 0 | 20 | 2.16 | 3.00 |

Independent variables | |||||

L | Segment length (km) | 0.23 | 13.31 | 3.38 | 3.11 |

AADT | Annual average daily traffic (veh/day) | 760 | 15195 | 3785.72 | 2391.52 |

SPEEDLIMIT | Posted speed limit (km/h) | 40 | 80 | 74.07 | 10.94 |

NRCURVE | Number of horizontal curves | 0 | 7 | 1.64 | 2.04 |

DAR | Access road density (no. roads/km) | 0 | 42.52 | 7.46 | 8.11 |

IRI | International roughness index | 0 | 4.53 | 2.47 | 1.07 |

Year 2015 | Year of occurrence indicator (1—if 2015, 0—otherwise) | ||||

Year 2016 | Year of occurrence indicator (1—if 2016, 0—otherwise) | ||||

Year 2017 | Year of occurrence indicator (1—if 2017, 0—otherwise) |

Variables | Poisson (S.E) | NB (S.E) | RENB (S.E) | ZIP (S.E.) ^{2} | ZINB (S.E.) ^{2} |
---|---|---|---|---|---|

Intercept | −3.0234 (0.7328) ^{1} | −2.8188 (0.7770) ^{1} | −0.7516 (0.5065) ^{1} | 4.7542 (4.9658) | 8.3044 (4.6790) |

L | 0.0877 (0.0221) ^{1} | 0.1014 (0.0268) ^{1} | 0.1151 (0.0348) ^{1} | −1.4961 (1.4624) | −2.3008 (1.7572) |

AADT | 0.0001 (0.00002) ^{1} | 0.0001 (0.00003) ^{1} | 0.0001(0.00003) ^{1} | −0.00002 (0.0002) | 0.00003 (0.0001) |

SPEEDLIMIT | 0.0236 (0.0089) ^{1} | 0.0216 (0.0095) ^{1} | 0.0231 (0.0119) | −0.0693 (0.0616) | −0.1138 (0.0652) |

NRCURVE | 0.1332 (0.0300) ^{1} | 0.1171 (0.0358) ^{1} | 0.1039 (0.0465) ^{1} | 0.5901 (0.7187) | 0.2767 (0.9915) |

DAR | 0.0336 (0.0060) ^{1} | 0.0319 (0.0070) ^{1} | 0.0315 (0.0090) ^{1} | 0.0304 (0.0727) | 0.0751 (0.0751) |

IRI | 0.1589 (0.0613) ^{1} | 0.1502 (0.0671) ^{1} | 0.1339 (0.0822) | −0.1986 (0.5081) | −0.5073 (0.4828) |

Year2015 | 0.0927 (0.1295) | 0.0997 (0.1545) | 0.0811 (0.1402) | 0.2768 (1.1022) | 0.0939 (1.2694) |

Year2016 | 0.2126 (0.1253) | 0.1797 (0.1510) | 0.2175 (0.1345) | 0.1720 (1.1126) | −0.2815 (1.2653) |

Dispersion parameter | 0.122 ^{1} | 0.060 | |||

a | 61.16802 | ||||

b | 9.02539 | ||||

Summary statistics | |||||

McFadden ρ² | 0.336 | 0.338 | 0.348 | 0.255 | 0.277 |

MAD | 0.22 | 0.20 | 0.16 | 3.87 | 3.97 |

MSPE | 8.34 | 7.23 | 4.41 | 2657.42 | 2793.77 |

Vuong test | 1.71 | 1.60 | - | 1.71 | 1.60 |

AIC | 607.61 | 604.78 | 594.50 | 609.48 | 608.69 |

BIC | 636.20 | 635.54 | 629.44 | 666.65 | 660.04 |

No of observations | 177 | 177 | 177 | 177 | 177 |

No of parameters | 8 | 8 | 8 | 8 | 8 |

^{1}means significant at a 0.05 significance level,

^{2}inflated part.

Independent Variable | Mean | Coefficient | Elasticity Coefficient |
---|---|---|---|

L | 3.384 | 0.0927 | 0.15 |

AADT | 3785.72 | 0.0001 | 0.18 |

NRCURVE | 1.644 | 0.1278 | 0.06 |

DAR | 7.462 | 0.0336 | 0.10 |

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**MDPI and ACS Style**

Mićić, S.; Vujadinović, R.; Amidžić, G.; Damjanović, M.; Matović, B.
Accident Frequency Prediction Model for Flat Rural Roads in Serbia. *Sustainability* **2022**, *14*, 7704.
https://doi.org/10.3390/su14137704

**AMA Style**

Mićić S, Vujadinović R, Amidžić G, Damjanović M, Matović B.
Accident Frequency Prediction Model for Flat Rural Roads in Serbia. *Sustainability*. 2022; 14(13):7704.
https://doi.org/10.3390/su14137704

**Chicago/Turabian Style**

Mićić, Spasoje, Radoje Vujadinović, Goran Amidžić, Milanko Damjanović, and Boško Matović.
2022. "Accident Frequency Prediction Model for Flat Rural Roads in Serbia" *Sustainability* 14, no. 13: 7704.
https://doi.org/10.3390/su14137704