Determination of Optimal Spatial Sample Sizes for Fitting Negative Binomial-Based Crash Prediction Models with Consideration of Statistical Modeling Assumptions

Round 1

Reviewer 1 Report

The structure of the paper is fine, the topic is up-to-date. I like the paper as a whole, although I have minor issues to clear:

- Could you please define the benefit of the results or with other words: could you please describe why the method and these result are usefull

- You defined 20 and 60 miles radius, is not too big? A radius with 20 miles (ca. 30 km) could have independent places, is it not necessarry to have the same road characteristics, micro weather situation, traffic quality and quantity. Could you please explain more detailed why this mathematicaly correct result also from the side of the transportation correct?

Author Response

Responses to Comments – Reviewer 1
Manuscript Number: Sustainability-2589564

General Overview of Revisions:

We would like to express our sincere appreciation for the valuable feedback provided by the reviewer. In this section, we outline the changes made in response to each reviewer's specific comments. In accordance with the instructions provided in the decision letter, we have revised the manuscript, and all the modified sections are highlighted in yellow for easy identification. To summarize these efforts, the following key revisions have been implemented:

(a) The "Conclusions and Future Work" section has been updated to provide a clearer understanding of the practical contributions of the proposed diagnostic test.

(b) In response to the reviewer's feedback, we have provided more detailed descriptions of the proposed radii values.

In the subsequent pages, we provide a comprehensive account of how each of the reviewer's comments has been addressed and incorporated into the revised manuscript.

 

 

 

 

 

Comments Made by Reviewer 1:

The structure of the paper is fine, the topic is up-to-date. I like the paper as a whole, although I have minor issues to clear:

 

- Could you please define the benefit of the results or with other words: could you please describe why the method and these result are usefull

 

- You defined 20 and 60 miles radius, is not too big? A radius with 20 miles (ca. 30 km) could have independent places, is it not necessarry to have the same road characteristics, micro weather situation, traffic quality and quantity. Could you please explain more detailed why this mathematicaly correct result also from the side of the transportation correct?

 

 

Responses from Authors:

We appreciate the time and effort invested by the reviewer for providing detailed comments that would help us in improving the overall quality of our paper.

The structure of the paper is fine, the topic is up-to-date. I like the paper as a whole, although I have minor issues to clear.

We thank the reviewer for his/her positive assessment of our overall approach.

1. Could you please define the benefit of the results or with other words: could you please describe why the method and these result are usefull.

We appreciate the reviewer's request for a clearer definition of the benefits of our proposed method and the significance of our results. In response, we would like to emphasize the following key points:

Improved Road Safety Assessment: The primary benefit of our method is that it enables transportation authorities to conduct more accurate and reliable road safety assessments. By identifying and addressing violations of statistical assumptions in Safety Performance Functions (SPFs), our diagnostic test ensures that the modeling process aligns with the underlying statistical properties of the data. This alignment leads to more precise predictions of crash rates, which is essential for proactive road safety management.

Targeted Resource Allocation: Our method guides practitioners in determining the appropriate spatial sample size for SPF modeling. This information is invaluable for transportation agencies in optimizing resource allocation for safety improvement projects. For instance, when predicting severe injury crashes, our method recommends a larger spatial region, which can help agencies focus their efforts on high-risk areas more effectively.

Context-Based Analysis: Our research has practical implications for road safety practitioners. It allows for a stratified analysis based on context classification systems, such as those implemented by the Florida Department of Transportation (FDOT). This context-based analysis considers the unique characteristics of different roadway segments, improving the precision of safety assessments within specific contexts.

Integration with Machine Learning: We propose that our method can be integrated with machine learning-based validation methods. This integration can enhance the accuracy and consistency of predictive tools for network screening. It opens the door to advanced data-driven approaches for road safety management.

In light of the reviewer's comments, we have revised the " Conclusions and Future Work" section in order to clarify the practical contribution of our proposed method.

“Thus, the suggested diagnostic test can conduct a segmented analysis using the context classification system implemented by the FDOT, which categorizes various types of roadway network facilities. Furthermore, the proposed method for determining an appropriate sample size has the potential to be integrated into machine learning-based validation techniques, thereby enhancing the accuracy and consistency of predictive tools for network screening [36]. In summary, the benefits of our method include more accurate road safety assessments, improved resource allocation, context-aware analysis, and the potential for advanced integration with machine learning techniques. These advantages contribute to the overall goal of reducing traffic accidents and enhancing road safety, which is of paramount importance for transportation authorities and society at large.”

2. You defined 20 and 60 miles radius, is not too big? A radius with 20 miles (ca. 30 km) could have independent places, is it not necessarry to have the same road characteristics, micro weather situation, traffic quality and quantity. Could you please explain more detailed why this mathematicaly correct result also from the side of the transportation correct?

We appreciate the reviewer's concern regarding the choice of a 20-mile and 60-mile radius for our diagnostic test and its practical implications in the context of transportation. We understand the need to ensure that our mathematical findings align with real-world transportation considerations. The choice of a 20-mile and 60-mile radius for our diagnostic test has been informed by comprehensive analysis and extensive experimentation with various radius values. Our aim was to identify radii that strike a balance between statistical assumptions and practical relevance. Specifically, we assessed the linearity in model parameters and overdispersion assumptions across a wide range of radius values, as summarized in Equation (9) to Equation (11) and depicted in FIGURE 4. These analyses demonstrated that the 20-mile radius provides the most favorable tradeoff between nonlinearity and overdispersion for all crash data (refer to FIGURE 4-a). It's worth noting that the summary metrics, defined as averages of model results from all segments within the study area, support the use of a 20-mile radius as an effective subregion size for analyzing roadway segments throughout District 4. However, for segments with characteristics highlighted in purple in FIGURE 3-c, a zero-inflated Negative Binomial regression is recommended. In the case of severe injury crashes (KABC), as shown in FIGURE 4-b, summary metrics continue to improve with increasing subregion radius but plateau around a 60-mile radius. Therefore, for modeling KABC crashes, a region with a radius of at least 60 miles is recommended to align with the assumptions of the SPF model. Our method offers flexibility, and these recommended radii provide practical solutions to meet statistical assumptions while accommodating the inherent variability in transportation networks. While a comprehensive explanation can be found in the "Methodology" section, we have included the following paragraph in the "Conclusions and Future Work" section to clarify the mathematical soundness and transportation relevance of these radius values, addressing the concerns raised by the reviewer.

“The selection of 20-mile and 60-mile radii for our diagnostic test is rooted in rigorous mathematical analysis based on crash data and statistical modeling. These radii are chosen to ensure the fulfillment of statistical assumptions, particularly in negative binomial regression, despite the inherent variability within transportation networks. Transportation systems naturally exhibit variations in road attributes, weather conditions, and traffic, even within relatively small areas. Our approach acknowledges these real-world complexities and guides practitioners in assessing SPF conformity with statistical assumptions while allowing flexibility for adjustments to suit specific conditions and goals. This method strikes a balance between statistical rigor and practical applicability, offering valuable insights for road safety assessments within the dynamic context of transportation systems.”

Author Response File: Author Response.pdf

Reviewer 2 Report

The research aimed at enhancing road safety by identifying risky locations and implementing appropriate safety measures. It focuses on the Highway Safety Manual (HSM) as a resource for creating predictive models (Safety Performance Functions or SPFs) for crash incidents. These models use Negative Binomial distribution-based regression. Unmet statistical assumptions can lead to incorrect conclusions and are particularly problematic when incorporating context classifications introduced by the Florida Department of Transportation (FDOT) into HSM SPFs. The manuscript is well established. However, here are some remarks for improvement.

 

1.       Could you elaborate on why this specific regression method is chosen?

2.       The literature review lacks from recent studies (2021, 2022, and 2023). Here are some suggestions to include:

https://doi.org/10.1016/j.treng.2023.100181

https://doi.org/10.3390/su13126945

https://doi.org/10.1016/j.ssci.2022.105722

3.       Could you explain why Florida roads were chosen for this case study (Specifically; district 4)?

4.       A 60-mile radius is suggested for severe injury crashes. Could you explain the rationale behind this specific radius?

5.       Elaborate more on the generalizability of the proposed methodology beyond the context of the Florida. How might other transportation authorities or regions benefit from the findings of this study?

6.       Please do not cite any references in the conclusions

 

 

Author Response

Responses to Comments – Reviewer 2
Manuscript Number: Sustainability-2589564

General Overview of Revisions:

We appreciate the constructive feedback provided by the reviewer. In response to the reviewer's comments and in accordance with the instructions from the decision letter, we have made several revisions to the manuscript. These revisions have been highlighted in yellow for clarity. Specifically, we have:

(a) Provided further elaboration on the focused study area to enhance the reader's understanding,

(b) Included additional explanations regarding the selection of the 60-mile buffer radius, addressing the rationale behind this choice,

(c) Expanded upon the generalizability of our proposed methodology, demonstrating how it can be applied beyond the Florida context, in line with the reviewer's inquiry,

(d) Included more references to reinforce the literature review and highlight gaps.

The following pages provide a detailed account of how each of these changes was implemented in response to the reviewer's comments.

 

 

 

 

 

 

Comments Made by Reviewer 2:

The research aimed at enhancing road safety by identifying risky locations and implementing appropriate safety measures. It focuses on the Highway Safety Manual (HSM) as a resource for creating predictive models (Safety Performance Functions or SPFs) for crash incidents. These models use Negative Binomial distribution-based regression. Unmet statistical assumptions can lead to incorrect conclusions and are particularly problematic when incorporating context classifications introduced by the Florida Department of Transportation (FDOT) into HSM SPFs. The manuscript is well established. However, here are some remarks for improvement.

 

1. Could you elaborate on why this specific regression method is chosen?
2. The literature review lacks from recent studies (2021, 2022, and 2023). Here are some suggestions to include:

https://doi.org/10.1016/j.treng.2023.100181

https://doi.org/10.3390/su13126945

https://doi.org/10.1016/j.ssci.2022.105722

3. Could you explain why Florida roads were chosen for this case study (Specifically; district 4)?
4. A 60-mile radius is suggested for severe injury crashes. Could you explain the rationale behind this specific radius?
5. Elaborate more on the generalizability of the proposed methodology beyond the context of the Florida. How might other transportation authorities or regions benefit from the findings of this study?
6. Please do not cite any references in the conclusions

 

 

Responses from Authors:

We would like to express our gratitude to the reviewer for dedicating their time and effort to offer comprehensive comments that will contribute to enhancing the overall quality of our paper.

The research aimed at enhancing road safety by identifying risky locations and implementing appropriate safety measures. It focuses on the Highway Safety Manual (HSM) as a resource for creating predictive models (Safety Performance Functions or SPFs) for crash incidents. These models use Negative Binomial distribution-based regression. Unmet statistical assumptions can lead to incorrect conclusions and are particularly problematic when incorporating context classifications introduced by the Florida Department of Transportation (FDOT) into HSM SPFs. The manuscript is well established. However, here are some remarks for improvement.

We thank the reviewer for his/her positive assessment of our overall approach and characterization of our contributions.

1. Could you elaborate on why this specific regression method is chosen?

We appreciate the reviewer's interest in understanding why we chose the specific regression method for our study. Negative binomial regression is well-suited for modeling count data, which is the nature of crash data. In road safety analysis, the goal is to predict the number of crashes, which is inherently a count variable. Moreover, negative binomial regression is a robust method for modeling count data, allowing for overdispersion, which often occurs in crash data due to variations in crash frequencies. Negative binomial regression accounts for the specific statistical characteristics of count data, including overdispersion and excess zeros. These features are essential for accurate modeling of crash frequencies, as they address the inherent variability and structural properties of crash data. However, it's important to clarify that the choice of the negative binomial regression model was not made by us but is inherent to the methodology recommended by the Highway Safety Manual (HSM) for modeling crash frequencies. In this paper, our primary objective is not to select a regression model but rather to provide guidance on determining the optimal spatial sample size for the existing models, including those prescribed by the HSM. The HSM, a vital resource for transportation professionals, relies on Negative Binomial distribution-based regression models, including Safety Performance Functions (SPFs), for predicting crash frequencies. These models are widely accepted and utilized in road safety analysis due to their suitability for count data, flexibility in handling various predictor variables, and ability to address the inherent characteristics of crash data, such as overdispersion and excess zeros. Our research aims to enhance the practical application of these existing models by identifying the optimal spatial sample size. Therefore, the specific regression method, including the choice of negative binomial regression, is not within the scope of our study but is instead an established component of the HSM methodology. Our contribution lies in refining the spatial considerations to improve the accuracy of road safety assessments while adhering to the existing modeling framework recommended by the HSM. While a comprehensive explanation is available in the "Methodology" section, we have appended the following paragraph to the conclusion of the "Introduction" section to succinctly outline the primary research objective and to respond to the concerns raised by the reviewer.

“It is noteworthy to emphasize that the adoption of the negative binomial regression model was not a matter of our discretion but an inherent aspect of the methodology endorsed by the Highway Safety Manual (HSM) for the modeling of crash frequencies. In this paper, our principal objective does not pertain to the selection of a regression model; instead, it centers on offering guidance for the determination of the optimal spatial sample size for preexisting models, including those prescribed by the HSM.”

2. The literature review lacks from recent studies (2021, 2022, and 2023). Here are some suggestions to include:

https://doi.org/10.1016/j.treng.2023.100181

https://doi.org/10.3390/su13126945

https://doi.org/10.1016/j.ssci.2022.105722

We appreciate the reviewer's valuable suggestion to include recent studies from 2021, 2022, and 2023 in our literature review. We have incorporated the suggested papers into our review to ensure the inclusion of the latest research findings and developments in the field. Your input is highly appreciated, and we believe that the addition of these recent studies will enhance the comprehensiveness of our literature review. Thank you for your thoughtful guidance. The following paragraphs have been incorporated into the "Introduction" and "Literature Review" sections to address the reviewer's concerns.

“Previous studies have delved deeply into the examination of how environmental factors influence the frequency of traffic crashes within specific geographical areas. These investigations have aimed to uncover the intricate relationships between various environmental elements, such as road design, weather conditions, land use patterns, pavement condition, and geographic features, and their collective impact on road safety (Jaber et al., 2021; Sedigh Bavar et al., 2023).”

“Although numerous studies extensively explore the effectiveness of various spatial models like Geographically Weighted Poisson Regression, Bayesian Conditional Autoregressive models (CAR), and various iterations of Extreme Gradient Boosting (XGBoost), this study has a distinct focus (Ziakopoulos et al., 2022). The current study intends to introduce statistical diagnostic tests for the detection of model violations and put forward an innovative methodology for determining the optimal spatial regions for the Empirical Bayes adjustment used in HSM-SPFs.”

Added References

Jaber, A., Juhász, J., Csonka, B., 2021. An Analysis of Factors Affecting the Severity of Cycling Crashes Using Binary Regression Model. Sustainability 13, 6945. https://doi.org/10.3390/su13126945

Sedigh Bavar, M., Naderan, A., Saffarzadeh, M., 2023. Evaluating the spatial effects of environmental influencing factors on the frequency of urban crashes using the spatial Bayes method based on Euclidean distance and contiguity. Transp. Eng. 12, 100181. https://doi.org/10.1016/j.treng.2023.100181

Ziakopoulos, A., Vlahogianni, E., Antoniou, C., Yannis, G., 2022. Spatial predictions of harsh driving events using statistical and machine learning methods. Saf. Sci. 150, 105722. https://doi.org/10.1016/j.ssci.2022.105722

 

3. Could you explain why Florida roads were chosen for this case study (Specifically; district 4)?

We appreciate the reviewer's inquiry regarding our selection of Florida roads, specifically District 4, as the focus of our case study. This decision was influenced by several significant factors. Firstly, our study is part of a project sponsored by the Florida Department of Transportation (FDOT), which facilitated access to the essential data and resources required for our research. Additionally, our primary aim was to investigate established statistical diagnostic tests to identify model violations within the context of Safety Performance Functions (SPFs). Collaborating with FDOT allowed us to access relevant data and collaborate with experts in the field, ensuring the study's rigor and relevance. Furthermore, our research aimed to propose a novel approach to determine optimal spatial regions for Empirical Bayes adjustment, aligning HSM-SPFs with regression assumptions. District 4 provided an ideal testing ground for this purpose due to its substantial dataset, comprising 1,067 roadway segments, which ensured statistical robustness and diverse crash types. Moreover, District 4 exhibited the necessary spatial variation, including different context classes, essential for a comprehensive analysis of model violations and the development of suitable spatial regions for adjustment. In summary, our choice of District 4 in Florida was driven by its sponsorship by FDOT, the need to investigate model violations, and the district's suitability for our research objectives, allowing us to conduct a robust and informative case study contributing to the advancement of road safety assessments. In response to the reviewer's concern, we have incorporated the following paragraph into the "Study Area and Data Sources" section.

“The selection of District 4 in Florida was predicated on several key factors, including its sponsorship by FDOT, the imperative to scrutinize model violations, and the alignment of the district's data and spatial variability with the objectives of our research. This choice has afforded us the opportunity to conduct a rigorous and enlightening case study that holds significant implications for the progression of road safety assessments. It is note-worthy that the proposed diagnostic test possesses the adaptability to be extended to other states and study regions with the incorporation of essential localized customizations.”

4. A 60-mile radius is suggested for severe injury crashes. Could you explain the rationale behind this specific radius?

Thank you for providing us with the opportunity to clarify. we are happy to explain the rationale behind our choice of a 60-mile radius for severe injury crashes in our study. The selection of a 60-mile radius was based on a comprehensive analysis of statistical performance measures and the specific characteristics of the data. In our research, we sought to determine the optimal spatial sample size for modeling severe injury crashes (KABC) while ensuring that statistical assumptions are met. As we extended the analysis to various radius values, ranging from 20 to 80 miles, we observed that summary metrics continued to improve with increasing subregion radius but eventually plateaued around the 60-mile radius. This plateauing effect signifies that, beyond a 60-mile radius, the improvement in statistical model performance becomes marginal. Thus, the 60-mile radius represents a point of diminishing returns in terms of model accuracy while considering practical feasibility. By choosing this radius, we strike a balance between achieving statistical validity, capturing sufficient data, and recognizing the spatial limitations of road safety assessments. Moreover, severe injury crashes tend to be less frequent and more challenging to predict accurately compared to other crash types. Therefore, the 60-mile radius was selected to ensure that the sample size is adequate for modeling these rarer events, improving the reliability of our predictions. In summary, the choice of a 60-mile radius for severe injury crashes is rooted in a careful analysis of statistical performance and practical considerations. This radius provides an optimal balance between achieving statistical rigor and accommodating the inherent variability in transportation networks, ultimately contributing to the accuracy of our road safety assessments. Despite providing a thorough rationale for the selected radii values in the "Results and Discussions" section, we have included the following paragraph in the "Conclusions and Future Work" section to provide a concise summary of the explanation.

“The selection of 20-mile and 60-mile radii for our diagnostic test is rooted in rigorous mathematical analysis based on crash data and statistical modeling. These radii are chosen to ensure the fulfillment of statistical assumptions, particularly in negative binomial regression, despite the inherent variability within transportation networks. Transportation systems naturally exhibit variations in road attributes, weather conditions, and traffic, even within relatively small areas. Our approach acknowledges these real-world complexities and guides practitioners in assessing SPF conformity with statistical assumptions while allowing flexibility for adjustments to suit specific conditions and goals. This method strikes a balance between statistical rigor and practical applicability, offering valuable insights for road safety assessments within the dynamic context of transportation systems.”

5. Elaborate more on the generalizability of the proposed methodology beyond the context of the Florida. How might other transportation authorities or regions benefit from the findings of this study?

we appreciate the reviewer's inquiry about the generalizability of our proposed methodology beyond the specific context of Florida and how other transportation authorities or regions might benefit from our study. While our case study was conducted in the context of Florida, the methodology and findings of our research have broader implications and can be applied to various transportation authorities and regions. Here are several points to elaborate on the generalizability of our methodology:

Methodological Transferability: The core methodology we have developed, which involves assessing the conformity of Safety Performance Functions (SPFs) with statistical assumptions and determining optimal spatial sample sizes, can be applied to any region or transportation network that utilizes SPFs for road safety assessments. SPFs are a fundamental tool in road safety analysis, and our approach offers a systematic way to enhance their accuracy. According to the HSM recommendations, SPFs can be employed for other regions by incorporating localized Crash Frequencies (CFs) and Crash Modification Factors (CMFs) to account for variations from the base conditions.

Data Adaptability: Our methodology is adaptable to different datasets and crash data characteristics. While our case study used Florida-specific data, transportation authorities in other regions can employ our approach with their own data, provided they have access to crash records and relevant roadway information.

Contextual Considerations: The concept of assessing spatial variations in crash data and aligning sample sizes with specific road characteristics and contexts is applicable universally. Transportation authorities in diverse regions can benefit from tailoring their road safety assessments to local conditions and characteristics, much like we have done for different context classes in Florida.

Improved Resource Allocation: The ability to determine optimal spatial sample sizes enables transportation authorities to allocate resources more effectively. By identifying high-risk areas accurately, regions can prioritize safety improvement projects and interventions where they are needed the most, thereby enhancing road safety outcomes.

In addition to the provided explanations, we have included the following paragraph in the "Conclusions and Future Work" section to elucidate the broader applicability and generalizability of the proposed methodology:

“It is noteworthy that although our case study was conducted in Florida, the methodology we have devised and the principles we have established possess transferability and can be effectively employed by transportation authorities and regions outside of Florida. Through the adoption of our approach, authorities have the potential to enhance the precision of their road safety assessments, optimize resource allocation, and ultimately make strides in reducing traffic accidents and elevating road safety conditions within their specific ju-risdictions.”

6. Please do not cite any references in the conclusions.

Thank you for the feedback. We have relocated the references and their associated sections to the "Results and Discussions" section as requested. This adjustment ensures that the conclusions remain focused solely on summarizing the key findings and implications of our study, without citing any references. We appreciate your guidance, and this change aligns with your suggestion.

Author Response File: Author Response.pdf

Reviewer 3 Report

This research focused investigates established statistical diagnostic tests to identify model violations and proposes a novel approach to determine optimal spatial regions for Empirical Bayes adjustment. The reviewer believes that the current version of the manuscript is not yet ready for publication; the authors are encouraged to consider the following comments and suggestion and revise the manuscript accordingly.

1. The authors should consider improve the Introduction section. The authors should move some contents of the Introduction section to the literature review b section. The introduction section should focus on introducing the research objectives and research questions, while the Background section should focus on literature review of related work and discussing why a review paper is important on this subject. The authors should also review more related literature. For example, the authors mentioned that the road network geometries and as the reviewer knows, most of the time the data are not available or not accurate. The authors should review and cite the paper of Drivable Space Extraction from Airborne LiDAR and Aerial Photos and discuss how to improve their research based on extracted roadway geometry data.

2. The authors should review the equations to make sure all symbols have been appropriately denoted. In addition, a document should be provided to further explain the equations. Additionally, the authors should provide more information about the software or codebase that were used to achieve the proposed image processing algorithms.

3. The authors need to provide detailed information about the parameters and their values. How were the values being collected?

4. Most of the figures need to be revised to make them more legible. It is very blurry and hard to read. If at all possible, vector images should be used.

N/A

Author Response

Responses to Comments – Reviewer 3
Manuscript Number: Sustainability-2589564

General Overview of Revisions:

We sincerely appreciate the constructive feedback provided by the reviewers. The following outlines the modifications made in response to the specific points raised by the reviewers. In accordance with the guidelines stipulated in the decision letter, we have diligently revised the current version of the manuscript, denoting all revisions with yellow highlights. Summarizing these efforts, the following revisions have been implemented in the paper:

(a) The "Introduction" section has undergone revision, and certain portions have been relocated to the "Literature Review" section, addressing the reviewer's suggestions,

(b) We have incorporated additional references to fortify the literature review and underscore existing gaps,

(c) High-resolution figures have been included to enhance their clarity and legibility,

(d) The manuscript has been meticulously reviewed to ensure the inclusion of necessary definitions for notations.

In the subsequent pages, we provide an in-depth account of how each of the reviewer's comments has been addressed and integrated into the revised manuscript.

 

 

 

 

 

 

Comments Made by Reviewer 3:

This research focused investigates established statistical diagnostic tests to identify model violations and proposes a novel approach to determine optimal spatial regions for Empirical Bayes adjustment. The reviewer believes that the current version of the manuscript is not yet ready for publication; the authors are encouraged to consider the following comments and suggestion and revise the manuscript accordingly.

1. The authors should consider improve the Introduction section. The authors should move some contents of the Introduction section to the literature review b section. The introduction section should focus on introducing the research objectives and research questions, while the Background section should focus on literature review of related work and discussing why a review paper is important on this subject. The authors should also review more related literature. For example, the authors mentioned that the road network geometries and as the reviewer knows, most of the time the data are not available or not accurate. The authors should review and cite the paper of Drivable Space Extraction from Airborne LiDAR and Aerial Photos and discuss how to improve their research based on extracted roadway geometry data.
2. The authors should review the equations to make sure all symbols have been appropriately denoted. In addition, a document should be provided to further explain the equations. Additionally, the authors should provide more information about the software or codebase that were used to achieve the proposed image processing algorithms.
3. The authors need to provide detailed information about the parameters and their values. How were the values being collected?
4. Most of the figures need to be revised to make them more legible. It is very blurry and hard to read. If at all possible, vector images should be used.

 

 

Responses from Authors:

We express our gratitude for the reviewer's dedicated time and effort in providing detailed comments, which will significantly contribute to enhancing the overall quality of our paper.

This research focused investigates established statistical diagnostic tests to identify model violations and proposes a novel approach to determine optimal spatial regions for Empirical Bayes adjustment. The reviewer believes that the current version of the manuscript is not yet ready for publication; the authors are encouraged to consider the following comments and suggestion and revise the manuscript accordingly.

We extend our appreciation to the reviewer for their positive evaluation of our overall approach and acknowledgment of our contributions. We have diligently addressed all comments to enhance the manuscript's quality.

1. The authors should consider improve the Introduction section. The authors should move some contents of the Introduction section to the literature review b section. The introduction section should focus on introducing the research objectives and research questions, while the Background section should focus on literature review of related work and discussing why a review paper is important on this subject. The authors should also review more related literature. For example, the authors mentioned that the road network geometries and as the reviewer knows, most of the time the data are not available or not accurate. The authors should review and cite the paper of Drivable Space Extraction from Airborne LiDAR and Aerial Photos and discuss how to improve their research based on extracted roadway geometry data.

We appreciate the reviewer's valuable feedback regarding the structure and content of the Introduction and Background sections. In response to the suggestions provided, we have made several revisions to improve the organization of these sections. Firstly, we have restructured the Introduction section to align it more closely with the recommended approach. The revised Introduction now primarily focuses on introducing the research objectives and research questions, providing a clear and concise overview of the study's purpose and goals. To enhance the Background section, we have moved relevant content from the Introduction section to the Literature Review section, as per the reviewer's recommendation. This adjustment allows the Background section to provide a more comprehensive review of related work and to emphasize the significance of our research within the broader context of existing literature. Furthermore, in response to the reviewer's suggestion, we have expanded our literature review by incorporating additional related literature. Specifically, we have included a discussion of the paper on "Drivable Space Extraction from Airborne LiDAR and Aerial Photos," illustrating how it is relevant to our research in improving roadway geometry data. This addition enriches the literature review by offering a broader perspective on the challenges and opportunities in this field. In light of the reviewer's comments, we have added the following paragraphs to the " Literature Review " section.

“Although numerous studies extensively explore the effectiveness of various spatial models like Geographically Weighted Poisson Regression, Bayesian Conditional Autoregressive models (CAR), and various iterations of Extreme Gradient Boosting (XGBoost), this study has a distinct focus (Ziakopoulos et al., 2022). Furthermore, the adoption of innovative data collection techniques, such as Airborne LiDAR (Dow et al., 2022) and Aerial Photography Look-Up System (APLUS) (Karaer et al., 2023), facilitated the acquisition of high-spatial-resolution aerial imagery. This imagery, in turn, enabled the extraction of detailed information regarding drivable spaces and roadway geometry within intricate terrains. However, it is essential to note that the existing HSM-SPFs models warrant further investigation for potential statistical violations that may not necessarily align with the requisite assumptions. Hence, the current study intends to introduce statistical diagnostic tests for the detection of model violations and put forward an innovative methodology for determining the optimal spatial regions for the Empirical Bayes adjustment used in HSM-SPFs.”

Added References

Dow, R., Zhang, S., Bogus, S.M., Han, F., 2022. Drivable Space Extraction from Airborne LiDAR and Aerial Photos, in: Construction Research Congress 2022. American Society of Civil Engineers, Reston, VA, pp. 154–163. https://doi.org/10.1061/9780784483961.017

Karaer, A., Kaczmarek, W., Mank, E., Ghorbanzadeh, M., Koloushani, M., Dulebenets, M.A., Moses, R., Sando, T., Ozguven, E.E., 2023. Traffic Data on-the-Fly: Developing a Statewide Crosswalk Inventory Using Artificial Intelligence and Aerial Images (AI2) for Pedestrian Safety Policy Improvements in Florida. Data Sci. Transp. 5, 7. https://doi.org/10.1007/s42421-023-00070-1

Ziakopoulos, A., Vlahogianni, E., Antoniou, C., Yannis, G., 2022. Spatial predictions of harsh driving events using statistical and machine learning methods. Saf. Sci. 150, 105722. https://doi.org/10.1016/j.ssci.2022.105722

 

2. The authors should review the equations to make sure all symbols have been appropriately denoted. In addition, a document should be provided to further explain the equations. Additionally, the authors should provide more information about the software or codebase that were used to achieve the proposed image processing algorithms.

We appreciate the reviewer's diligence in reviewing the equations and their symbols in the manuscript. Upon thorough examination, we have confirmed that all notations have been appropriately denoted and are consistent throughout the paper. Regarding the request for additional documents to explain the equations, we acknowledge the suggestion; however, we believe that providing further documentation may not be necessary in this context. Many of the equations we utilized are well-established and widely recognized, particularly those employed within the Highway Safety Manual (HSM) framework. Furthermore, we have taken care to explain any custom-developed equations clearly within the text to ensure reader comprehension. Lastly, we appreciate the clarification regarding the use of image processing software. This paper does not involve image processing but rather focuses on statistical analysis and diagnostic tests. As such, we used R-Studio as the primary tool for developing the diagnostic test and conducting statistical analyses, which is a standard practice in statistical research. We are grateful for the reviewer's attention to detail and their valuable feedback. If there are any specific equations or aspects that require further clarification, we are more than willing to provide additional explanations or context to ensure the reader's understanding.

3. The authors need to provide detailed information about the parameters and their values. How were the values being collected?

Thank you for your comment and for highlighting the information provided in the "Study Area and Data Sources" section. We have carefully considered your concern about the need for detailed information on parameters and their values. As you correctly pointed out, our paper provides comprehensive information about the data sources, including the databases used, data collection methods, and the values obtained from these sources. Additionally, we have cited and referenced the Highway Safety Manual (HSM) for SPF coefficients (See Table 2), making it clear that these values are derived from authoritative sources. Upon reviewing your comment and our manuscript, we confirm that all relevant parameters and their values have been elaborated upon in the paper. Moreover, multivehicle non-driveway crashes from years 2015, 2016, 2017 and 2018 are obtained from crash reports maintained by the Florida Department of Highway Safety and Motor Vehicles (FLHSMV). The crash data consists of individual points distributed across the road network, with each point denoting a vehicle crash and geospatially linked to the GIS shapefile through longitude and latitude coordinates. Table 1 summarizes the crash data categorized with respect to their associated KABCO scale that occurred in Florida District 4 during the study period. Furthermore, Figure 1 illustrates how the aforemen-tioned crashes are distributed throughout the study area. We appreciate your attention to detail, and we believe that the information presented in the "Study Area and Data Sources" section adequately addresses your concern by providing a clear description of the data and its sources, thereby ensuring transparency in our research methodology. If you have any further questions or require additional information on specific parameters, please do not hesitate to let us know, and we will gladly provide further clarification as needed.

4. Most of the figures need to be revised to make them more legible. It is very blurry and hard to read. If at all possible, vector images should be used.

We appreciate the reviewer's feedback regarding the legibility of the figures in our manuscript. We understand the importance of clear and legible visuals to enhance the reader's understanding of our research. For the final submission of our manuscript, we have taken steps to address this concern. High-resolution figures have been provided to ensure that the images are sharp, clear, and easy to read. These high-resolution figures are designed to improve the overall visual quality of our paper and enhance the clarity of the content. Additionally, we would like to inform the reviewer that the revised version of the manuscript is in Word format and includes the original version of the figures with the best resolutions. This ensures that readers have access to the highest-quality images, allowing for a more thorough and comprehensible review of our work. We would like to assure the reviewer that we are committed to delivering a high-quality manuscript with clear and legible figures for the benefit of our readers. We appreciate the reviewer's attention to detail and value their feedback in helping us enhance the overall presentation of our research.

Author Response File: Author Response.pdf

Reviewer 4 Report

Predictive crash models are helpful for local and state transportation officials to determine and assess the potential safety of roadways and the effectiveness of the corresponding countermeasures. The topic is useful and valuable in traffic safety analysis and prevention. The paper is well-written and organized. Some issues are suggested to be considered.

(1) It is suggested to highlight this paper's novelty and contribution that is clearly distinct from previous studies.

(2) The paper uses the negative binomial distribution to fit the crash prediction model. It is suggested to compare with other mathematical models to showcase the advantage of the Negative Binomial in fitting the crash prediction model.

 

(3) The proposed method and model are based on the crash data collected from FDOT District 4 during years 2015-2018. It will be interesting to demonstrate the performance of the model in other regions.

Author Response

Responses to Comments – Reviewer 4
Manuscript Number: Sustainability-2589564

General Overview of Revisions:

We are grateful for the constructive feedback offered by the reviewer. In response to the reviewer's input and in compliance with the instructions from the decision letter, we have made several revisions to the manuscript, which have been highlighted in yellow for clarity. Specifically, we have:

(a) Enhanced our explanations to underscore the novelty and significant contribution of the paper,

(b) Clarified the "Introduction" section to provide a concise and clear exposition of the research's primary objective,

(c) Elaborated on the applicability of our proposed methodology, demonstrating its relevance beyond the context of Florida, as per the reviewer's query.

The subsequent pages provide a comprehensive account of how we have implemented each of these changes in response to the reviewer's valuable comments.

Comments Made by Reviewer 4:

Predictive crash models are helpful for local and state transportation officials to determine and assess the potential safety of roadways and the effectiveness of the corresponding countermeasures. The topic is useful and valuable in traffic safety analysis and prevention. The paper is well-written and organized. Some issues are suggested to be considered.

 

(1) It is suggested to highlight this paper's novelty and contribution that is clearly distinct from previous studies.

(2) The paper uses the negative binomial distribution to fit the crash prediction model. It is suggested to compare with other mathematical models to showcase the advantage of the Negative Binomial in fitting the crash prediction model.

(3) The proposed method and model are based on the crash data collected from FDOT District 4 during years 2015-2018. It will be interesting to demonstrate the performance of the model in other regions.

 

 

Responses from Authors:

We extend our gratitude to the reviewer for their dedicated time and effort in offering detailed comments that will assist us in enhancing the overall quality of our paper.

Predictive crash models are helpful for local and state transportation officials to determine and assess the potential safety of roadways and the effectiveness of the corresponding countermeasures. The topic is useful and valuable in traffic safety analysis and prevention. The paper is well-written and organized. Some issues are suggested to be considered.

We thank the reviewer for his/her positive assessment of our overall approach and characterization of our contributions.

1. It is suggested to highlight this paper's novelty and contribution that is clearly distinct from previous studies.

Thank you for bringing these points to our attention. In the recent revision of the manuscript, we have taken the reviewer's suggestion into consideration. Specifically, we have refined the "Introduction" section to emphasize the unique contribution of our research. Additionally, we have revised the "Conclusions and Future Work" section to provide a concise summary of our research's distinctive contribution, setting it apart from previous studies in the field. These revisions serve to underscore the novelty and value of our work compared to existing research.

2. The paper uses the negative binomial distribution to fit the crash prediction model. It is suggested to compare with other mathematical models to showcase the advantage of the Negative Binomial in fitting the crash prediction model.

We appreciate the reviewer's suggestion to compare the negative binomial distribution with other mathematical models for crash prediction. We understand the importance of evaluating different modeling approaches to showcase the advantages of the chosen method. However, we would like to provide some context and clarification regarding our research focus. Negative binomial regression is well-suited for modeling count data, which is the nature of crash data. In road safety analysis, our primary goal is to predict the number of crashes, which inherently falls under the category of count variables. Furthermore, negative binomial regression is a robust method specifically designed for modeling count data, and it offers several advantages for crash prediction. One of the key reasons for selecting negative binomial regression is its ability to handle overdispersion, which is common in crash data due to variations in crash frequencies. Overdispersion arises from the inherent variability in crash data, and negative binomial regression accounts for this characteristic. It also addresses the issue of excess zeros, which can occur when certain segments or areas experience no crashes during a specific time frame. It is important to note that the choice of the negative binomial regression model was not made by us but is inherent to the methodology recommended by the Highway Safety Manual (HSM) for modeling crash frequencies.

The HSM is a widely accepted and respected resource for transportation professionals, and it relies on Negative Binomial distribution-based regression models, including Safety Performance Functions (SPFs), for predicting crash frequencies. These models are specifically designed to handle the count nature of crash data, making them appropriate choices for road safety analysis. In our research, our primary objective is not to select or compare different regression models. Instead, we aim to provide guidance on determining the optimal spatial sample size for the existing models, including those prescribed by the HSM. Our contribution lies in refining the spatial considerations to improve the accuracy of road safety assessments while adhering to the established modeling framework recommended by the HSM. In summary, while we appreciate the suggestion to compare various regression models, our research's core focus is on developing a diagnostic test to determine the optimal spatial sample size for existing HSM-SPFs while considering statistical modeling assumptions. Our goal is to enhance the accuracy of crash prediction results within the existing modeling framework. Therefore, the specific choice of negative binomial regression aligns with the HSM's methodology and the nature of crash data, which is central to our research objectives. While a comprehensive explanation is available in the "Methodology" section, we have appended the following paragraph to the conclusion of the "Introduction" section to succinctly outline the primary research objective and to respond to the concerns raised by the reviewer.

“It is noteworthy to emphasize that the adoption of the negative binomial regression model was not a matter of our discretion but an inherent aspect of the methodology endorsed by the Highway Safety Manual (HSM) for the modeling of crash frequencies. In this paper, our principal objective does not pertain to the selection of a regression model; instead, it centers on offering guidance for the determination of the optimal spatial sample size for preexisting models, including those prescribed by the HSM.”

3. The proposed method and model are based on the crash data collected from FDOT District 4 during years 2015-2018. It will be interesting to demonstrate the performance of the model in other regions.

We appreciate the reviewer's interest in the performance of our proposed method and model in regions beyond Florida District 4. We understand the importance of demonstrating the generalizability of our approach and its applicability to other regions. We would like to provide clarification and context regarding our choice of Florida District 4 and the potential for the proposed method to be applied more broadly.

The selection of Florida District 4 as the study area for our research was influenced by several significant factors. Firstly, our study is part of a project sponsored by the Florida Department of Transportation (FDOT), which provided us with access to the essential data and resources required for our research. This collaboration with FDOT was instrumental in ensuring the study's rigor and relevance, as it allowed us to work with experts in the field and access relevant data sources. Additionally, our primary aim was to investigate established statistical diagnostic tests to identify model violations within the context of Safety Performance Functions (SPFs). District 4's substantial dataset, comprising 1,067 roadway segments, ensured statistical robustness and encompassed diverse crash types. This diversity was essential for a comprehensive analysis of model violations and the development of suitable spatial regions for Empirical Bayes adjustment, which aligns HSM-SPFs with regression assumptions. Furthermore, District 4 exhibited the necessary spatial variation, including different context classes, which was essential for our research objectives. It provided an ideal testing ground for our novel approach to determine optimal spatial regions for adjustment.

However, it's crucial to highlight that the core methodology we have developed, which involves assessing the conformity of SPFs with statistical assumptions and determining optimal spatial sample sizes, can be applied to any region or transportation network that utilizes SPFs for road safety assessments. SPFs are a fundamental tool in road safety analysis, and our approach offers a systematic way to enhance their accuracy. For regions outside of Florida District 4, the methodology can be adapted by incorporating localized Crash Frequencies (CFs) and Crash Modification Factors (CMFs) to account for variations from the base conditions, as recommended by the Highway Safety Manual (HSM). Therefore, while our case study focused on District 4, the principles and techniques we have developed are generalizable and can be applied to improve road safety assessments in other regions as well.

In summary, our choice of District 4 in Florida was driven by its sponsorship by FDOT, the need to investigate model violations, and the district's suitability for our research objectives. However, the core methodology we have developed can be extended and applied to enhance road safety assessments in a broader context. We appreciate the reviewer's interest in the generalizability of our approach and its potential impact on road safety assessments in other regions.

In addition to the provided explanations, we have included the following paragraph in the "Conclusions and Future Work" section to elucidate the broader applicability and generalizability of the proposed methodology:

“It is noteworthy that although our case study was conducted in Florida, the methodology we have devised and the principles we have established possess transferability and can be effectively employed by transportation authorities and regions outside of Florida. Through the adoption of our approach, authorities have the potential to enhance the precision of their road safety assessments, optimize resource allocation, and ultimately make strides in reducing traffic accidents and elevating road safety conditions within their specific jurisdictions.”

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

 

The authors have responded satisfactorily to my inquiries. In my opinion, the paper has improved over the original version.

One remark: Please add the doi instead of the url in the references.

Author Response

Thank you for your feedback and for acknowledging the improvements in our manuscript. We have taken your suggestion into account and have revised the bibliography list to include DOIs instead of URLs for the references.

Here is the revised reference list:

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[2]         A. Jaber, J. Juhász, and B. Csonka, “An Analysis of Factors Affecting the Severity of Cycling Crashes Using Binary Regression Model,” Sustainability, vol. 13, no. 12, p. 6945, Jun. 2021, doi: 10.3390/su13126945.

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[4]         AASHTO, Highway Safety Manual. Washington, 2010.

[5]         M. A. Abdel-Aty, C. Lee, J. Park, J.-H. Wang, M. Abuzwidah, and S. Al-Arifi, “Validation and application of highway safety manual (part D) in Florida,” 2014. [Online]. Available: https://rosap.ntl.bts.gov/view/dot/27272

[6]         P. Alluri, D. Saha, K. Liu, and A. Gan, “Improved processes for meeting the data requirements for implementing the Highway Safety Manual (HSM) and Safety Analyst in Florida,” 2014. [Online]. Available: https://rosap.ntl.bts.gov/view/dot/27226

[7]         R. Srinivasan and D. Carter, Development of Safety Performance Functions for North Carolina. 2011. [Online]. Available: http://www.ncdot.org/doh/preconstruct/tpb/research/download/2010-09finalreport.pdf%5Cnhttps://trid.trb.org/view/1127558%5Cnhttps://connect.ncdot.gov/projects/planning/RNAProjDocs/2010-09FinalReport.pdf

[8]         J.-H. Wang, M. Abdel-Aty, and J. Lee, “Examination of the Transferability of Safety Performance Functions for Developing Crash Modification Factors: Using the Empirical Bayes Method,” Transp. Res. Rec. J. Transp. Res. Board, vol. 2583, no. 1, pp. 73–80, Jan. 2016, doi: 10.3141/2583-10.

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[10]       Q. Dong, X. Jiang, B. Huang, and S. H. Richards, “Analyzing Influence Factors of Transverse Cracking on LTPP Resurfaced Asphalt Pavements through NB and ZINB Models,” J. Transp. Eng., vol. 139, no. 9, pp. 889–895, Sep. 2013, doi: 10.1061/(ASCE)TE.1943-5436.0000568.

[11]       A. Ziakopoulos, E. Vlahogianni, C. Antoniou, and G. Yannis, “Spatial predictions of harsh driving events using statistical and machine learning methods,” Saf. Sci., vol. 150, p. 105722, Jun. 2022, doi: 10.1016/j.ssci.2022.105722.

[12]       R. Dow, S. Zhang, S. M. Bogus, and F. Han, “Drivable Space Extraction from Airborne LiDAR and Aerial Photos,” in Construction Research Congress 2022, Reston, VA: American Society of Civil Engineers, Mar. 2022, pp. 154–163. doi: 10.1061/9780784483961.017.

[13]       A. Karaer et al., “Traffic Data on-the-Fly: Developing a Statewide Crosswalk Inventory Using Artificial Intelligence and Aerial Images (AI2) for Pedestrian Safety Policy Improvements in Florida,” Data Sci. Transp., vol. 5, no. 2, p. 7, Aug. 2023, doi: 10.1007/s42421-023-00070-1.

[14]       J. Lu, K. Haleem, P. Alluri, A. Gan, and K. Liu, “Developing local safety performance functions versus calculating calibration factors for SafetyAnalyst applications: A Florida case study,” Saf. Sci., vol. 65, pp. 93–105, Jun. 2014, doi: 10.1016/j.ssci.2014.01.004.

[15]       C. Sun, H. Brown, P. Edara, B. Claros, and K. Nam, “Calibration of the Highway Safety Manual for Missouri,” 2013.

[16]       Y. Kweon and I. Lim, “Development of Safety Performance Functions for Multilane Highway and Freeway Segments Maintained by the Virginia Department of Transportation,” 2014. [Online]. Available: http://www.virginiadot.org/vtrc/main/online_reports/pdf/14-r14.pdf%0AYOUNG-JUN

[17]       E. T. Donnell, V. V Gayah, and L. Li, “Regionalized Safety Performance Functions,” Final Rep. Pennsylvania Dep. Transp. FHWA-PA-2016-001-PSU WO 17, 2016, [Online]. Available: https://rosap.ntl.bts.gov/view/dot/39904

[18]       A. Khattak, N. Ahmad, A. Mohammadnazar, I. MahdiNia, B. Wali, and R. Arvin, “Highway Safety Manual Safety Performance Functions & Roadway Calibration Factors: Roadway Segments Phase 2, Part,” 2020.

[19]       H. Al-Deek, A. Sandt, G. Gamaleldin, J. McCombs, and P. Blue, “A Roadway Context Classification Approach for Developing Safety Performance Functions and Determining Traffic Operational Effects for Florida Intersections,” 2020.

[20]       A. E. Kitali, T. Sando, A. Castro, D. Kobelo, and J. Mwakalonge, “Using Crash Modification Factors to Appraise the Safety Effects of Pedestrian Countdown Signals for Drivers,” J. Transp. Eng. Part A Syst., vol. 144, no. 5, May 2018, doi: 10.1061/JTEPBS.0000130.

[21]       B. Brimley, M. Saito, and G. Schultz, “Calibration of highway safety manual safety performance function: Development of New Models for Rural Two-Lane Two-Way Highways,” Transportation Research Record, no. 2279. pp. 82–89, 2012. doi: 10.3141/2279-10.

[22]       F. Gross, B. Persaud, and C. Lyon, “A Guide to Developing Quality Crash Modification Factors,” 2010. [Online]. Available: http://www.cmfclearinghouse.org/collateral/cmf_guide.pdf

[23]       J. Young and P. Y. Park, “Benefits of small municipalities using jurisdiction-specific safety performance functions rather than the Highway Safety Manual’s calibrated or uncalibrated safety performance functions,” Can. J. Civ. Eng., vol. 40, no. 6, pp. 517–527, Jun. 2013, doi: 10.1139/cjce-2012-0501.

[24]       M. B. Ulak, E. E. Ozguven, H. H. Karabag, M. Ghorbanzadeh, R. Moses, and M. Dulebenets, “Development of Safety Performance Functions for Restricted Crossing U-Turn Intersections,” J. Transp. Eng. Part A Syst., vol. 146, no. 6, 2020, doi: 10.1061/JTEPBS.0000346.

[25]       R. Srinivasan, M. Colety, G. Bahar, B. Crowther, and M. Farmen, “Estimation of Calibration Functions for Predicting Crashes on Rural Two-Lane Roads in Arizona,” Transp. Res. Rec. J. Transp. Res. Board, vol. 2583, no. 1, pp. 17–24, Jan. 2016, doi: 10.3141/2583-03.

[26]       A. Farid, M. Abdel-Aty, and J. Lee, “A new approach for calibrating safety performance functions,” Accid. Anal. Prev., vol. 119, no. July, pp. 188–194, 2018, doi: 10.1016/j.aap.2018.07.023.

[27]       R. Srinivasan and K. Bauer, “Safety Performance Function Development Guide: Developing JurisdictionSpecific SPFs,” 2013.

[28]       E. Hauer, “Overdispersion in modelling accidents on road sections and in Empirical Bayes estimation,” Accid. Anal. Prev., vol. 33, no. 6, pp. 799–808, Nov. 2001, doi: 10.1016/S0001-4575(00)00094-4.

[29]       E. Hauer, D. W. Harwood, F. M. Council, and M. S. Griffith, “Estimating Safety by the Empirical Bayes Method: A Tutorial,” Transp. Res. Rec. J. Transp. Res. Board, vol. 1784, no. 1, pp. 126–131, Jan. 2002, doi: 10.3141/1784-16.

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[31]       A. Farid, M. Abdel-Aty, J. Lee, N. Eluru, and J. H. Wang, “Exploring the transferability of safety performance functions,” Accid. Anal. Prev., vol. 94, pp. 143–152, 2016, doi: 10.1016/j.aap.2016.04.031.

[32]       B. Persaud, B. Lan, C. Lyon, and R. Bhim, “Comparison of empirical Bayes and full Bayes approaches for before–after road safety evaluations,” Accid. Anal. Prev., vol. 42, no. 1, pp. 38–43, Jan. 2010, doi: 10.1016/j.aap.2009.06.028.

[33]       S. Das, I. Tsapakis, and A. Khodadadi, “Safety performance functions for low-volume rural minor collector two-lane roadways,” IATSS Res., vol. 45, no. 3, pp. 347–356, Oct. 2021, doi: 10.1016/j.iatssr.2021.02.004.

[34]       G. R. Wood, “Generalised linear accident models and goodness of fit testing,” Accid. Anal. Prev., vol. 34, no. 4, pp. 417–427, Jul. 2002, doi: 10.1016/S0001-4575(01)00037-9.

[35]       D. Lord, “Modeling motor vehicle crashes using Poisson-gamma models: Examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter,” Accid. Anal. Prev., vol. 38, no. 4, pp. 751–766, Jul. 2006, doi: 10.1016/j.aap.2006.02.001.

[36]       Florida Department of Transportation (FDOT), “Statewide Traffic Data Files.” [Online]. Available: https://www.fdot.gov/statistics/trafficdata/default.shtm

[37]       FDOT Safety Office, “FDOT Highway Safety Manual User Guide 2015.” [Online]. Available: https://www.fdot.gov/safety/safetyengineering/publications-and-manuals.shtm

[38]       J. J. Faraway, Extending the Linear Model with R. New York: Chapman and Hall/CRC, 2016. doi: 10.1201/9781315382722.

[39]       Florida Department of Transportation, “FDOT Context Classification Guide,” 2020. [Online]. Available: https://fdotwww.blob.core.windows.net/sitefinity/docs/default-source/roadway/completestreets/files/fdot-context-classification.pdf?sfvrsn=12be90da_2

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[41]       S. Tayebikhorami and E. Sacchi, “Validation of Machine Learning Algorithms as Predictive Tool in the Road Safety Management Process: Case of Network Screening,” J. Transp. Eng. Part A Syst., vol. 148, no. 9, Sep. 2022, doi: 10.1061/JTEPBS.0000719.

Reviewer 3 Report

The authors have addressed all my comments. 

N/A

Author Response

Thank you for reviewing our manuscript and confirming that all your comments have been addressed. Your feedback has been invaluable in enhancing the quality of our work.

Reviewer 4 Report

Thank you for the revision. The issues have been solved and it can be published as it is.

Author Response

We sincerely appreciate your positive feedback and your confirmation that the issues have been resolved satisfactorily. Your support and guidance have been invaluable in improving our manuscript.