# Investigating Highway–Rail Grade Crossing Inventory Data Quality’s Role in Crash Model Estimation and Crash Prediction

^{*}

## Abstract

**:**

## Featured Application

**In this study, the impact of errors and missing information in the inventory data of highway–rail grade crossings (HRGCs) on the crash frequency prediction models currently used in the US is investigated. Transportation authorities and safety regulators can apply the insights gained from this research to enhance the accuracy of crash frequency prediction models for HRGCs. By utilizing more accurate and complete inventory data, these models provide more reliable crash frequency predictions, enabling better resource allocation and more targeted safety interventions.**

## Abstract

## 1. Introduction

## 2. Literature Review

## 3. Data

## 4. Methodology

- (i)
- H
_{0}= There is no difference in the expected crashes estimated by utilizing FRA and field-validated data (α = 5%).

- (ii)
- H
_{0}= There is no difference in the estimated parameters’ coefficients of new crash frequency prediction models from the two datasets (FRA Vs field-validated) (α = 5%).

## 5. Results and Discussion

#### Comparative Analysis of Estimated Models

- The coefficients for Natural log-transformed Maximum Timetable Speed (IMAXTSPD) and Natural log-transformed Average Annual Daily Traffic (IAADT) exhibited positive signs in both models. However, the expected magnitude differed in both models, where the base model gave a higher coefficient expected magnitude for IAADT compared to the comparison model. Moreover, for IMAXTSPD, the comparison model gave a higher coefficient expected magnitude. The average marginal effect estimates presented in Table 8 show that a unit change in IAADT increases predicted crashes by 0.02681 in the base model and 0.02546 in the comparison model.
- The coefficients for warning-device-type flashing lights (WDTLIT) were negative for both models (i.e., compared to passive devices, warning flashing lights reduce predicted crashes). However, the coefficient expected magnitudes and average marginal effects (Table 8) of WDTLITs differ in both models, where the base model estimated a higher negative value compared to the comparison model.
- The coefficients of Ln-transformed total daily trains (ITDTRAINS) in the zero-inflated part in both the base and comparison models were negative, indicating that the probability of excess zeros decreases with the number of trains, as expected. However, the coefficient expected magnitudes of ITDTRAINS differed in both models.
- All the coefficients retained in both models indicated strong statistical significance. However, as shown in Table 9, the results of hypothesis tests revealed that the regression coefficients were not statistically significantly different when utilizing the two inventory datasets.

## 6. Conclusions

- Erroneous and missing data in the unaltered FRA HRGCs inventory database led to statistically different crash predictions (expected crashes) compared to corrected and complete (field-validated) HRGCs inventory data. These predictions also affected the crash hazard ranking of crossings based on the two datasets.
- Estimated crash prediction model parameters and their corresponding marginal values appeared to differ when comparing models based on the unaltered FRA HRGCs inventory database and the corrected and complete (field-validated) HRGCs inventory data. However, from a statistical standpoint, they did not exhibit significant differences. Nevertheless, the Zero-inflated Negative Binomial (ZINB) crash prediction model, utilizing the accurate inventory dataset, demonstrated superior performance according to fitness criteria such as the Akaike information criterion (AIC) and BIC (Bayesian information criterion).

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Research framework for crash prediction analysis [2].

**Figure 2.**FRA HRGCs data filtration process of a sample county (Cass) [2].

**Figure 3.**Validation checks for HRGCs inventory data collection [2].

**Figure 4.**Data correction example, crossing 064112B [19].

**Figure 5.**Data correction example, crossing 072946C [2].

**Figure 6.**Data correction example, crossing 064130Y [2].

**Figure 7.**Comparison of expected crashes: FRA vs. field-validated data [2].

**Figure 8.**Predicted crashes of base model for IMAXTSPD and WDTLITs [2].

**Figure 9.**Predicted crashes of comparison model for IMAXTSPD and WDTLITs [2].

**Table 1.**Salient features of relevant HRGCs crash frequency modeling studies [2].

Year | Authors | No of Observations | Data Type | Location | Context | Method Used | Types of Explanatory Variables |
---|---|---|---|---|---|---|---|

2003 | Saccomanno et al. [15] | 10,456 HRGCs crashes | Canadian Public HRGCs data | Canada | Collision prediction models for highway–rail grade crossings in Canada | Negative Binomial Regression | Female highway users, higher train speeds, very old drivers, open areas, concrete road surface types, and railroad equipment striking highway users before crash. |

2006 | Oh et al. [7] | Crash data of 162 HRGCs | 1998–2002 Korean National Railroad (KNR) accident database | South Korea | Accident prediction model for railway–highway interfaces | Poisson Model, Gamma model, and Zero-inflated Poisson Model | Traffic volume, average daily train volumes, the proximity of crossings to commercial areas, time duration between the activation of warning signals and gates, and the distance of the train detector from crossings. |

2006 | Nam and Lee [17] | 100 highway–rail grade crossings crash data | Korean National Railroad accident database | South Korea | Accident frequency model using zero probability process | Zero-inflated Models | Roadway characteristics, guardrails, number of tracks, control device indicator, warning time. |

2010 | Yan at al. [4] | 6244 train–vehicle crashes | 27 years of FRA HRGCs database (1980–2006) | United States | Using hierarchical tree-based model to predict train–vehicle crashes at passive HRGCs | Hierarchical Tree-Based Regression Model | Crossbucks only, and crossbucks combined with stop signs, and Stop sign treatment. |

2016 | Lu and Tolliver [11] | 344 HRGCs crash data from 1996 to 2014 in North Dakota | FRA HRGC incident and inventory data | North Dakota, United States | Accident prediction model for public highway–rail grade crossings | Conway–Maxwell–Poisson Model, Bernoulli model, Hurdle Poisson Model | Warning devices, highway pavement condition, appearance of pavement markings, appearance of interconnection/pre-emption, smallest crossing angle, appearance of pullout lane, functional classifications of highway, train traffic density, highway user types, weather conditions, track conditions, highway traffic density, maximum train speed, and location. |

2019 | Khan et al. [16] | Crash Data from 2000 to 2016 in North Dakota Involving HRGCs | North Dakota DOT crash data | United States | Developing a Highway Rail Grade Crossing Accident Probability Prediction Model: A North Dakota Case Study | Binary Logit Regression Model | AADT, exposure, crossing angle, gates, and pavement markings. |

2019 | Zheng et al. [13] | Past 19 years 354 crashes on 5713 HRGCs | FRA HRGCs incident and inventory data | North Dakota, United States | Predicting Highway–Rail Grade Crossing Collision Risk by Neural Network Systems | Neural Network (NN) Model | AADT, presence of flashing lights, highway stop signs, and presence of crossbuck signs. |

2020 | Lu et al. [6] | Past 19 years crashes on 5713 HRGCs | FRA HRGC incident and inventory data | North Dakota, United States | A Gradient Boosting Crash Prediction Approach for Highway–Rail Grade Crossing Crash Analysis | Gradient Boosting (GB) Model | Traffic exposure factors such as, highway traffic volume, railway traffic volume, and train travel speed. |

2020 | Keramati et al. [18] | 3310 HRGCs, with 475 crash records | FRA HRGCs incident and inventory data | North Dakota, United States | A Simultaneous Safety Analysis of Crash Frequency and Severity for Highway–Rail Grade Crossings: The Competing Risks Method | Competing Risks Method | Crash information, type of train service, train detection, availability of commercial power, and distance to nearby roadway intersection. |

2020 | Brod et al. [3] | Crash and Inventory data of 9870 HRGCs | FRA HRGC incident/accident and inventory data | United States | New Model for Highway–Rail Grade Crossing Accident Prediction and Severity | Zero-inflated Negative Binomial Model and Ordered Logit Model | Exposure, average annual daily traffic, maximum timetable train speed, total trains, surface-type, warning flashing lights, and gates. |

**Table 2.**Field validation summary of corrections and added missing values (N = 560) [2].

County | Number of Corrected Values | Number of Missing Values Added | HRGCs Visited | Abandoned/Non-Existent HRGCs (Excluding Private Crossings) | Percent Corrected and Added Missing Values |
---|---|---|---|---|---|

Cass | 307 | 83 | 56 | 0 | 7.1 |

Douglas | 286 | 108 | 67 | 4 | 5.9 |

Gage | 115 | 347 | 41 | 0 | 11.3 |

Jefferson | 174 | 25 | 45 | 0 | 4.3 |

Lancaster | 376 | 657 | 112 | 0 | 9.2 |

Otoe | 285 | 46 | 77 | 2 | 4.2 |

Saline | 119 | 37 | 61 | 0 | 4.1 |

Sarpy | 144 | 59 | 25 | 0 | 8.1 |

Saunders | 435 | 370 | 76 | 0 | 10.6 |

Total | 2241 | 1732 | 560 | 6 | 7.4 |

**Table 3.**Candidate variables for inclusion in base and comparison crash prediction models [2].

Variables | Variable Coding |
---|---|

Discrete Variables | |

Warning flashing lights | 1 if there are flashing lights at crossing, 0 otherwise |

Gates | 1 if there are gates at crossing, 0 otherwise |

Rural/urban classification | 1 if crossing is in urban area, 0 if crossing is in rural area |

Pavement markings | 1 if there are pavement markings near crossing, 0 otherwise |

Crossing surface type | Timber = 1, Asphalt = 2, Asphalt and Timber or Concrete or Rubber = 3, Concrete and Rubber = 4, other = 5 |

Crossing illuminated | 1 if crossing is illuminated, 0 otherwise |

Crossing angle | 1 = 0–29°, 2 = 30–59°, 3 = 60–90° |

Continuous Variables | |

Number of bells | Count |

Number of crossbucks | Count |

Number of total tracks | Count |

Ln AADT | Natural Log-transformed count |

Ln Total daily trains | Natural Log-transformed count |

Ln Maximum timetable speed | Natural Log-transformed count |

Number of traffic lanes | Count |

**Table 4.**Statistical testing of normality and disparities in expected crashes [2].

Tests Performed | ||
---|---|---|

Shapiro–Wilk Normality Test | ||

Variable | W | p-value |

Original FRA data crash predictions | 0.87519 | 2.2 × 10^{−16} |

Field-validated data crash predictions | 0.84692 | 2.2 × 10^{−16} |

Wilcoxon Rank Sum Test for Differences in Expected Crashes | ||

Original FRA Vs FV data crash predictions | 122,640 | 3.622 × 10^{−10} |

Alternative hypothesis | True location shift is not equal to 0 |

**Table 5.**Comparison of hazard ranking based on crash predictions: FRA vs. field-validated data [2].

Crossing ID | 2020 AP Ranking Using Original FRA Inventory Data | Crossing ID | 2020 AP Ranking Using Field-Validated Inventory Data |
---|---|---|---|

074952M | 1 | 064128X | 1 |

074945C | 2 | 064129E | 2 |

064128X | 3 | 074929T | 3 |

064129E | 4 | 073326S | 4 |

074929T | 5 | 074938S | 5 |

073326S | 6 | 073456N | 6 |

816859H | 7 | 816859H | 7 |

073456N | 8 | 073342B | 8 |

074938S | 9 | 073345W | 9 |

073342B | 10 | 073455G | 10 |

**Table 6.**Estimated base ZINB model utilizing original FRA inventory data [2].

Variable (Code Name) | Estimate | Std. Error | Z-Value | p-Value | ||
---|---|---|---|---|---|---|

Constant (_cons) | −8.7615 | 2.5845 | −3.39 | 0.000 | ||

Ln-transformed AADT (IAADT) | 0.47160 | 0.1674 | 2.81 | 0.004 | ||

Warning flashing lights (WDTLITs) | −2.1517 | 0.6984 | −3.08 | 0.002 | ||

Ln-transformed max train speed (IMAXTSPD) | 1.40840 | 0.5615 | 2.508 | 0.012 | ||

Log (theta) | 10.0436 | 107.89 | 0.093 | 0.925 | ||

ZINB regression zero-inflation coefficients (binomial with logit link) | ||||||

Constant (_cons) | 2.2206 | 1.0151 | 2.188 | 0.028 | ||

Ln-transformed total daily trains (ITDTRAINS) | −0.9539 | 0.3596 | −2.652 | 0.007 | ||

Pearson Residuals | ||||||

Min | 1Q | Median | 3Q | Max | ||

−0.72413 | −0.21093 | −0.11057 | −0.05989 | 26.92213 | ||

Summary Statistics | ||||||

Number of observations = 555 | ||||||

Theta = 23,008.3433 | ||||||

Number of iterations = 85 | ||||||

Log-likelihood = −97.36 | ||||||

Degrees of freedom = 7 | ||||||

Inflation model = logit | ||||||

AIC = 210.0122 | ||||||

BIC = 240.2197 |

**Table 7.**Estimated ZINB comparison model utilizing field-validated inventory data [2].

Variable (Code Name) | Estimate | Std. Error | Z-Value | p-Value | ||
---|---|---|---|---|---|---|

Constant (_cons) | −8.9899 | 2.5874 | −3.47 | 0.000 | ||

Ln-transformed AADT (IAADT) | 0.4422 | 0.1648 | 2.68 | 0.007 | ||

Warning flashing lights (WDTLITs) | −2.0443 | 0.6982 | −2.92 | 0.003 | ||

Ln-transformed max train speed (IMAXTSPD) | 1.5135 | 0.5667 | 2.67 | 0.007 | ||

Log (theta) | 10.4522 | 129.44 | 0.81 | 0.936 | ||

ZINB regression zero-inflation coefficients (binomial with logit link) | ||||||

Constant (_cons) | 2.1266 | 1.0165 | 2.092 | 0.036 | ||

Ln-transformed total daily trains (ITDTRAINS) | −0.8793 | 0.3484 | −2.524 | 0.011 | ||

Pearson Residuals | ||||||

Min | 1Q | Median | 3Q | Max | ||

−0.55149 | −0.22451 | −0.11469 | −0.05974 | 26.7747 | ||

Summary Statistics | ||||||

Number of observations = 555 | ||||||

Theta = 34,620.8247 | ||||||

Number of iterations = 84 | ||||||

Log-likelihood = −98.01 | ||||||

Degrees of freedom = 7 | ||||||

Inflation model = logit | ||||||

AIC = 208.7160 | ||||||

BIC = 239.0117 |

**Table 8.**Average marginal effects for base and comparison models [2].

Model Type | Variable | Effect | Std. Error | Z-Value | p-Value |
---|---|---|---|---|---|

Base model (based on original FRA inventory data) | IAADT | 0.02681 | 0.01099 | 2.440 | 0.0146774 |

WDTLITs | −0.12232 | 0.04714 | −2.595 | 0.0094708 | |

IMAXTSPD | 0.08008 | 0.03567 | 2.245 | 0.0247619 | |

ITDTRAINS | 0.02431 | 0.01124 | 2.391 | 0.0166414 | |

Comparison model (based on field-validated inventory data) | IAADT | 0.02546 | 0.01082 | 2.353 | 0.018636 |

WDTLITs | −0.11768 | 0.04713 | −2.497 | 0.012539 | |

IMAXTSPD | 0.08714 | 0.03704 | 2.352 | 0.018663 | |

ITDTRAINS | 0.02383 | 0.01124 | 2.2912 | 0.021725 |

**Table 9.**Comparison of coefficients of the base and comparison ZINB models [2].

Comparing Regression Coefficients of the Base and Comparison ZINB Models H0: There is no Statistically Significant Difference between Coefficients of the Two Models | ||
---|---|---|

Compared Parameters | Z statistic | p Values |

IAADT | 0.00802 | 0.9935 |

WDTLITs | −0.10875 | 0.9134 |

IMAXTSPD | 0.13174 | 0.8951 |

ITDTRAINS | −0.14899 | 0.8815 |

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## Share and Cite

**MDPI and ACS Style**

Farooq, M.U.; Khattak, A.J.
Investigating Highway–Rail Grade Crossing Inventory Data Quality’s Role in Crash Model Estimation and Crash Prediction. *Appl. Sci.* **2023**, *13*, 11537.
https://doi.org/10.3390/app132011537

**AMA Style**

Farooq MU, Khattak AJ.
Investigating Highway–Rail Grade Crossing Inventory Data Quality’s Role in Crash Model Estimation and Crash Prediction. *Applied Sciences*. 2023; 13(20):11537.
https://doi.org/10.3390/app132011537

**Chicago/Turabian Style**

Farooq, Muhammad Umer, and Aemal J. Khattak.
2023. "Investigating Highway–Rail Grade Crossing Inventory Data Quality’s Role in Crash Model Estimation and Crash Prediction" *Applied Sciences* 13, no. 20: 11537.
https://doi.org/10.3390/app132011537