Accident Frequency Prediction Model for Flat Rural Roads in Serbia
, Goran Amidžić 3, Milanko Damjanović 2 and Boško Matović 2,*
Round 1
Reviewer 1 Report
Please find the attached file.
Comments for author File: 
Comments.pdf
Author Response
Dear Reviewer,
We want to extend our appreciation for taking the time and effort necessary to provide such insightful guidance. We would like to thank you for your comments and suggestions.
The revision, based on the review team’s collective input, includes a number of positive changes. We have revised the manuscript according to your suggestions. The changes were highlighted in the revised manuscript.
We hope that these revisions improve the paper so that you now deem it worthy of publication in Sustainability.
The revised version contains the following changes and amendments:
REVIEWER 1:
In this study, different count models are used to find the significant explanatory variables, which linearly regress the count explained variable “number of accidents”. The topic of the stated study is very interesting and well written in scientific form. The manuscript is well presented, and the outcomes of this research are significant. Before the final acceptance, kindly consider the following points in the revised manuscript.
- Please avoid acronyms in the abstract such as IB, NB, RENB, ZIP and ZINB.
Response:
It was corrected.
- What is AADT and ADT?
Response:
The text has been revised to clarify this issue.
- In lines 182 and 184, correct „Roads of Serbia“ as “Roads of Serbia”. The same issue is to be also correct in lines 213 and 220.
Response:
It was corrected.
- The authors applied many count models, but they did not provide distribution fitting of the road accidents. I suggest seeing the second paragraph of section 5.2.1 [1] and presenting the results in Table as presented in Table 2 of studies [1-3].
Response:
Thank you for the comment. There are many ways to report a model estimation results. Our idea was to help reader to follow results easily. For example, Hou et al. (see https://doi.org/10.1016/j.aap.2018.07.010) reported model estimation results in Table 2 in a similar way. Therefore, we believe that reporting style which we presented in Table 2 should be adequate.
- It is suggested to highlight the importance of count models as some applications are briefly discussed in [4].
Response:
Thanks for the comments. We have made the changes as suggested by the Reviewer (see lines 100-106).
- Usually, accident data is over-dispersed. However, in some cases, it is underdisperse. So, there is no surety about which model to be used, either underdispersed or over-dispersed. In this scenario, Conway-Maxwell Poisson (COMPoisson) regression or zero-inflated COM-Poisson regression will be the best alternatives [5]. It is suggested to consider COM-Poisson regression or its zeroinflated version along with the considered models.
- Haq, W.; Raza, S.H.; Mahmood, T. The pandemic paradox: domestic violence and happiness of women. PeerJ 2020, 8, e10472.
- Jamal, A.; Mahmood, T.; Riaz, M.; Al-Ahmadi, H.M. GLM-based flexible monitoring methods: an application to real-time highway safety surveillance. Symmetry 2021, 13, 362.
Response:
Thank you for the exhaustive comment and recommendation. The Conway–Maxwell–Poisson (COM-Poisson) was used by researchers to analyze count data subjected to over- and under-dispersion. Several previous research have shown that COM-Poisson perform as well as negative binomial (NB) models in terms of GOF statistics and predictive performance (e.g., https://doi.org/10.3390/sym13020362; https://doi.org/10.1016/j.aap.2007.12.003). Given the fact the COM-Poisson distribution can also handle under-dispersed data, the COM-Poisson model might offer a better alternative over the Poisson and NB models for modeling road crashes. According to Reviewer’s suggestions we examined the COM-Poisson model using the COMPoissonReg package in R Statistics. The results of our research showed that the COM-Poisson models offer similar or poorer statistical performance compared to other five models. In addition, the present findings indicated a presence of over-dispersion in our data. Lord and Mannering argued that main advantage of the COM-Poisson model „is related to data characterized by under-dispersion. On the down side, this model can be negatively influenced by low sample-mean, small-sample bias and, to date, there have not been any multivariate applications of the approach (see https://doi.org/10.1016/j.tra.2010.02.001)“. In order to present a more more parsimonious framework to present results, we decided to exclude the COM-Poisson model from further analysis.There is no doubt that the COM-Poisson model might offer potential for modeling accident frequency, and an opportunity for further research in this area. The paragraph related to recommendations for future research was reformulated and the suggestion has been applied in the revised manuscript.
Author Response File: 
Author Response.docx
Reviewer 2 Report
The results of the research presented in the article allow for making decisions on investments and modernization of the road network. The developed model is a useful tool for road safety, especially on rural roads, as it is a new method of predicting the frequency of accidents that can help in making a decision when choosing a design variant. The results of the authors' research have shown that it is necessary to reduce the number of horizontal curves as much as possible. Moreover, it was found that a large number of access roads to the main road affects the frequency of accidents. In order to reduce the number of accidents, it is advisable to reduce the number of access roads.
The authors of the study chose horizontal roads without taking into account driving in mountainous terrain and residential infrastructure. They are to present this as the results of further research.
Author Response
Dear Reviewer,
We want to extend our appreciation for taking the time and effort necessary to provide such insightful guidance. We would like to thank you for your comments and suggestions.
The revision, based on the review team’s collective input, includes a number of positive changes. We have revised the manuscript according to your suggestions. The changes were highlighted in the revised manuscript.
We hope that these revisions improve the paper so that you now deem it worthy of publication in Sustainability.
The revised version contains the following changes and amendments:
REVIEWER 2:
Comments and Suggestions for Authors
The results of the research presented in the article allow for making decisions on investments and modernization of the road network. The developed model is a useful tool for road safety, especially on rural roads, as it is a new method of predicting the frequency of accidents that can help in making a decision when choosing a design variant. The results of the authors' research have shown that it is necessary to reduce the number of horizontal curves as much as possible. Moreover, it was found that a large number of access roads to the main road affects the frequency of accidents. In order to reduce the number of accidents, it is advisable to reduce the number of access roads.
The authors of the study chose horizontal roads without taking into account driving in mountainous terrain and residential infrastructure. They are to present this as the results of further research.
Response:
Thank you for your helpful suggestions. The „Discussion and conclusions” section was revised and the comments were adopted in our revision.
Reviewer 3 Report
This study aimed to examine the relationship between accident frequency and the factors influencing accident frequency on flat rural IB state roads in Serbia. Five different statistical models were used in the investigation: Poisson, negative binomial (NB), negative binomial model with random effects (RENB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) models. Goodness-of-fit measures indicated that RENB outperformed the other compared models, and it was selected as an accident prediction model for rural roads with flat surfaces. Four variables were found to have a significant impact on accident frequency, including annual average daily traffic, segment length, the number of horizontal curves, and access road density.
The topic of this paper is interesting, and I believe that further investigations into this matter may result in decisions about how to fix and invest in the highway system and how to build and fix new roads. However, I would recommend modifying the following points:
- Even though the authors used 63 references in their paper, only two references, 2019 & 2021, were from the last three years (2019 - 2022). The authors need to update their references with newly published sources.
- Have the authors tried to use the latest tools in their analysis and modeling, such as machine learning?
- Abbreviations must be explained when they first appear in the search, such as AADT in line 112. The authors need to review this issue for the entire manuscript.
Author Response
Dear Reviewer,
We want to extend our appreciation for taking the time and effort necessary to provide such insightful guidance. We would like to thank you for your comments and suggestions.
The revision, based on the review team’s collective input, includes a number of positive changes. We have revised the manuscript according to your suggestions. The changes were highlighted in the revised manuscript.
We hope that these revisions improve the paper so that you now deem it worthy of publication in Sustainability.
The revised version contains the following changes and amendments:
REVIEWER 3:
Comments and Suggestions for Authors
This study aimed to examine the relationship between accident frequency and the factors influencing accident frequency on flat rural IB state roads in Serbia. Five different statistical models were used in the investigation: Poisson, negative binomial (NB), negative binomial model with random effects (RENB), zero-inflated Poisson (ZIP), and zero-inflated negative binomial (ZINB) models. Goodness-of-fit measures indicated that RENB outperformed the other compared models, and it was selected as an accident prediction model for rural roads with flat surfaces. Four variables were found to have a significant impact on accident frequency, including annual average daily traffic, segment length, the number of horizontal curves, and access road density.
The topic of this paper is interesting, and I believe that further investigations into this matter may result in decisions about how to fix and invest in the highway system and how to build and fix new roads. However, I would recommend modifying the following points:
- Even though the authors used 63 references in their paper, only two references, 2019 & 2021, were from the last three years (2019 - 2022). The authors need to update their references with newly published sources.
Response:
The suggestion has been applied in the revised manuscript. We have updated references with newly published sources.
- Have the authors tried to use the latest tools in their analysis and modeling, such as machine learning?
Response:
Thank you for your helpful suggestion. In the present study, we didn’t consider the tools and applications using machine learning algorithms. However, we are aware of the usefulness of the machine learning approach in predicting traffic accidents. There is no doubt that the machine learning approach might offer potential for modeling accident frequency, and an opportunity for further research in this area. The paragraph related to recommendations for future research was reformulated and the suggestion has been applied in the revised manuscript.
- Abbreviations must be explained when they first appear in the search, such as AADT in line 112. The authors need to review this issue for the entire manuscript.
Response:
It was corrected.
Round 2
Reviewer 1 Report
I would like to congratulate the authors for their excellent work. They have made a very detailed revision and convinced me with good arguments. Therefore, I recommend this article for the possible publication.
Reviewer 3 Report
Accept in present form.
