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approach for analyzing low temporal (daily) and large spatial count data of fatal crashes over a ten-year period (March 2014 to March 2022) in Iran.", "language": "english", "position": {"atoms": [{"position_id": 576, "txt": " This study introduces the Negative Binomial Generalized Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (GSARIMAX) model as an innovative approach for analyzing low temporal (daily) and large spatial count data of fatal crashes over a ten-year period (March 2014 to March 2022) in Iran.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 23, "edu_l1_label": "IOS"}, {"txt": " Unlike traditional models that predominantly focus on aggregated monthly or high-resolution data, the proposed negative binomial GSARIMAX model leverages daily count data, accommodating over-dispersion inherent in crash counts and providing a more granular and accurate analysis across extensive spatial regions.", "language": "english", "position": {"atoms": [{"position_id": 577, "txt": " Unlike traditional models that predominantly focus on aggregated monthly or high-resolution data, the proposed negative binomial GSARIMAX model leverages daily count data, accommodating over-dispersion inherent in crash counts and providing a more granular and accurate analysis across extensive spatial regions.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 24, "edu_l1_label": "IOS"}, {"txt": " The model integrates significant exogenous variables, including traffic volume, maximum and minimum temperatures, wind speed, and wind direction, alongside harmonic seasonal components to capture both annual and semi-annual periodic fluctuations in crash occurrences.", "language": "english", "position": {"atoms": [{"position_id": 578, "txt": " The model integrates significant exogenous variables, including traffic volume, maximum and minimum temperatures, wind speed, and wind direction, alongside harmonic seasonal components to capture both annual and semi-annual periodic fluctuations in crash occurrences.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 25, "edu_l1_label": "IOS"}, {"txt": " Model performance was rigorously evaluated using Deviance Information Criterion (DIC) and Mean Absolute Relative Error (MARE) metrics, alongside out-of-sample predictive accuracy assessments.", "language": "english", "position": {"atoms": [{"position_id": 579, "txt": " Model performance was rigorously evaluated using Deviance Information Criterion (DIC) and Mean Absolute Relative Error (MARE) metrics, alongside out-of-sample predictive accuracy assessments.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 26, "edu_l1_label": "IOS"}, {"txt": " The negative binomial GSARIMAX (0,1,2)-SOH model demonstrated superior performance compared to the Gaussian GSARIMAX counterpart, evidenced by lower MARE and DIC values.", "language": "english", "position": {"atoms": [{"position_id": 580, "txt": " The negative binomial GSARIMAX (0,1,2)-SOH model demonstrated superior performance compared to the Gaussian GSARIMAX counterpart, evidenced by lower MARE and DIC values.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 27, "edu_l1_label": "IOS"}, {"txt": " Notably, traffic volume and maximum temperature emerged as significant predictors of fatal crashes, while seasonal harmonic terms further enhanced model accuracy by effectively capturing temporal dynamics.", "language": "english", "position": {"atoms": [{"position_id": 581, "txt": " Notably, traffic volume and maximum temperature emerged as significant predictors of fatal crashes, while seasonal harmonic terms further enhanced model accuracy by effectively capturing temporal dynamics.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 28, "edu_l1_label": "IOS"}, {"txt": " The Bayesian estimation framework employed facilitates robust inference and the analysis of posterior predictive distributions, affirming the Negative Binomial GSARIMAX model’s superior fit and forecasting capabilities.", "language": "english", "position": {"atoms": [{"position_id": 582, "txt": " The Bayesian estimation framework employed facilitates robust inference and the analysis of posterior predictive distributions, affirming the Negative Binomial GSARIMAX model’s superior fit and forecasting capabilities.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 29, "edu_l1_label": "IOS"}, {"txt": " These findings underscore the model’s potential advantages over conventional Gaussian statistical methods, particularly in handling low temporal resolution and large spatial datasets.", "language": "english", "position": {"atoms": [{"position_id": 583, "txt": " These findings underscore the model’s potential advantages over conventional Gaussian statistical methods, particularly in handling low temporal resolution and large spatial datasets.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 30, "edu_l1_label": "IOS"}, {"txt": " Moreover, dynamic models incorporating exogenous variables demonstrated enhanced predictive performance, highlighting the importance of integrating diverse factors in crash analysis.", "language": "english", "position": {"atoms": [{"position_id": 584, "txt": " Moreover, dynamic models incorporating exogenous variables demonstrated enhanced predictive performance, highlighting the importance of integrating diverse factors in crash analysis.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[5]/div[2]/div[2]/div/div"}]}, "tags": [], "label": "abstract", "web_segment_id": 19, "global_sentence_id": 31, "edu_l1_label": "IOS"}, {"txt": " This study not only advances the methodological landscape for traffic crash analysis but also provides actionable insights for policymakers and safety authorities.", "language": "english", "position": {"atoms": [{"position_id": 585, "txt": " This study not only advances the methodological landscape for traffic crash analysis but also provides actionable insights for policymakers and safety 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"edu_l1_label": "BOS"}, {"txt": "Road traffic crashes remain a significant public health concern globally, with the World Health Organization (WHO) reporting in 2021 that approximately 3,260 individuals lose their lives each day due to this issue (World Health Organization, 2023).", "language": "english", "position": {"atoms": [{"position_id": 591, "txt": "Road traffic crashes remain a significant public health concern globally, with the World Health Organization (WHO) reporting in 2021 that approximately 3,260 individuals lose their lives each day due to this issue (World Health Organization, 2023).", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[1]"}]}, "tags": [], "label": "content", "web_segment_id": 21, "global_sentence_id": 36, "edu_l1_label": "IOS"}, {"txt": " These crashes account for approximately 1.35 million fatalities annually, with over 90 % occurring in low- and middle-income countries (LMICs) (Geneva:", "language": "english", 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"position": {"atoms": [{"position_id": 606, "txt": "While significant strides have been made in the realm of crash trend prediction and time series modeling, a predominant focus on monthly or annual data has occurred, thus overlooking the dynamic nature of daily fatal crash occurrences.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[3]"}]}, "tags": [], "label": "content", "web_segment_id": 23, "global_sentence_id": 49, "edu_l1_label": "IOS"}, {"txt": " Furthermore, there has been limited research integrating exogenous variables such as traffic volume and weather conditions into daily fatal crash prediction models.", "language": "english", "position": {"atoms": [{"position_id": 607, "txt": " Furthermore, there has been limited research integrating exogenous variables such as traffic volume and weather conditions into daily fatal crash prediction models.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[3]"}]}, "tags": [], "label": "content", "web_segment_id": 23, "global_sentence_id": 50, "edu_l1_label": "IOS"}, {"txt": " This study aims to address these gaps by employing advanced time series models.", "language": "english", "position": {"atoms": [{"position_id": 608, "txt": " This study aims to address these gaps by employing advanced time series models.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[3]"}]}, "tags": [], "label": "content", "web_segment_id": 23, "global_sentence_id": 51, "edu_l1_label": "IOS"}, {"txt": "The study's objectives include evaluating the performance of the GSARIMAX model using Bayesian estimation in order to obtain robust inference in predicting daily fatal crash trends and investigating a dynamic model incorporating exogenous daily factors such as traffic volume and weather conditions on the seasonality and autocorrelation of the model, thus enhancing future crash trend predictions.", "language": "english", "position": {"atoms": [{"position_id": 610, "txt": "The study's objectives include evaluating the performance of the GSARIMAX model using Bayesian estimation in order to obtain robust inference in predicting daily fatal crash trends and investigating a dynamic model incorporating exogenous daily factors such as traffic volume and weather conditions on the seasonality and autocorrelation of the model, thus enhancing future crash trend predictions.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[4]"}]}, "tags": [], "label": "content", "web_segment_id": 24, "global_sentence_id": 52, "edu_l1_label": "IOS"}, {"txt": " Additionally, comparing the Gaussian SARIMAX model with the negative binominal GSARIMAX model and examining their behavior and accuracy on discrete data are crucial aspects of this research.", "language": "english", "position": {"atoms": [{"position_id": 611, "txt": " Additionally, comparing the Gaussian SARIMAX model with the negative binominal GSARIMAX model and examining their behavior and accuracy on discrete data are crucial aspects of this research.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[4]"}]}, "tags": [], "label": "content", "web_segment_id": 24, "global_sentence_id": 53, "edu_l1_label": "IOS"}, {"txt": "The rest of the paper is structured as follows:", "language": "english", "position": {"atoms": [{"position_id": 613, "txt": "The rest of the paper is structured as follows:", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[5]"}]}, "tags": [], "label": "content", "web_segment_id": 25, "global_sentence_id": 54, "edu_l1_label": "IOS"}, {"txt": " Section 2 provides a thorough review of the extant literature, emphasizing prior studies and identifying existing research gaps.", "language": "english", "position": {"atoms": [{"position_id": 614, "txt": " Section 2 provides a thorough review of the extant literature, emphasizing prior studies and identifying existing research gaps.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[5]"}]}, "tags": [], "label": "content", "web_segment_id": 25, "global_sentence_id": 55, "edu_l1_label": "IOS"}, {"txt": " Section 3 details the data sources utilized and the composition of the dataset.", "language": "english", "position": {"atoms": [{"position_id": 615, "txt": " Section 3 details the data sources utilized and the composition of the dataset.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[5]"}]}, "tags": [], "label": "content", "web_segment_id": 25, "global_sentence_id": 56, "edu_l1_label": "IOS"}, {"txt": " Section 4 outlines the methods employed, incorporating the Gaussian SARIMAX and GSARIMAX models.", "language": "english", "position": {"atoms": [{"position_id": 616, "txt": " Section 4 outlines the methods employed, incorporating the Gaussian SARIMAX and GSARIMAX models.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[5]"}]}, "tags": [], "label": "content", "web_segment_id": 25, "global_sentence_id": 57, "edu_l1_label": "IOS"}, {"txt": " Section 5 presents the discussion and results obtained after fitting the models to the data.", "language": "english", "position": {"atoms": [{"position_id": 617, "txt": " Section 5 presents the discussion and results obtained after fitting the models to the data.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[5]"}]}, "tags": [], "label": "content", "web_segment_id": 25, "global_sentence_id": 58, "edu_l1_label": "IOS"}, {"txt": " Finally, Section 6 presents the conclusions, recommendations, and limitations of the study.", "language": "english", "position": {"atoms": [{"position_id": 618, "txt": " Finally, Section 6 presents the conclusions, recommendations, and limitations of the study.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[6]/div[2]/section/div[5]"}]}, "tags": [], "label": "content", "web_segment_id": 25, "global_sentence_id": 59, "edu_l1_label": "IOS"}, {"txt": "Section snippets", "language": "english", "position": {"atoms": [{"position_id": 620, "txt": "Section snippets", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/h2"}]}, "tags": ["h2"], "label": "title1", "web_segment_id": 26, "global_sentence_id": 60, "edu_l1_label": "BOS"}, {"txt": "Literature review", "language": "english", "position": {"atoms": [{"position_id": 622, "txt": "Literature review", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[1]/section/h2"}]}, "tags": ["h2"], "label": "title1", "web_segment_id": 27, "global_sentence_id": 61, "edu_l1_label": "BOS"}, {"txt": "Examining policy implications can benefit from employing time series analysis, a method used at a broader scale 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loop detectors.", "language": "english", "position": {"atoms": [{"position_id": 631, "txt": " Additionally, the cumulative daily traffic volume on Iran's intercity highways is compiled from daily reports provided by the Ministry of Roads and Urban Development (MRUD), utilizing data collected by 2604 nationwide highway loop detectors.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[2]/section/div"}]}, "tags": [], "label": "content", "web_segment_id": 30, "global_sentence_id": 67, "edu_l1_label": "IOS"}, {"txt": " In addition, the weather data, encompassing minimum and maximum temperatures, average wind speed, and wind direction, were", "language": "english", "position": {"atoms": [{"position_id": 632, "txt": " In addition, the weather data, encompassing minimum and maximum temperatures, average wind speed, and wind direction, were", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[2]/section/div"}]}, "tags": [], "label": "content", "web_segment_id": 30, "global_sentence_id": 68, "edu_l1_label": "IOS"}, {"txt": "Method", "language": "english", "position": {"atoms": [{"position_id": 634, "txt": "Method", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[3]/section/h2"}]}, "tags": ["h2"], "label": "title1", "web_segment_id": 31, "global_sentence_id": 69, "edu_l1_label": "BOS"}, {"txt": "In this section, the statistical analyses performed on the data are detailed in time domain.", "language": "english", "position": {"atoms": [{"position_id": 636, "txt": "In this section, the statistical analyses performed on the data are detailed in time domain.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[3]/section/div"}]}, "tags": [], "label": "content", "web_segment_id": 32, "global_sentence_id": 70, "edu_l1_label": "IOS"}, {"txt": " It begins with an overview of time series modeling, followed by description models and identifying 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In the following subsections, all details will be introduced.", "language": "english", "position": {"atoms": [{"position_id": 639, "txt": " 3. In the following subsections, all details will be introduced.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[3]/section/div"}]}, "tags": [], "label": "content", "web_segment_id": 32, "global_sentence_id": 73, "edu_l1_label": "IOS"}, {"txt": "Result and discussion", "language": "english", "position": {"atoms": [{"position_id": 641, "txt": "Result and discussion", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[4]/section/h2"}]}, "tags": ["h2"], "label": "title1", "web_segment_id": 33, "global_sentence_id": 74, "edu_l1_label": "BOS"}, {"txt": "An overview of the aggregate time series decomposition of the fatal crashes (Fig.", "language": "english", "position": {"atoms": [{"position_id": 643, "txt": "An overview of the aggregate time series decomposition of the fatal crashes (Fig.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[4]/section/div[1]"}]}, "tags": [], "label": "content", "web_segment_id": 34, "global_sentence_id": 75, "edu_l1_label": "IOS"}, {"txt": " 4) illustrates a general long-term decreasing trend in the average data level.", "language": "english", "position": {"atoms": [{"position_id": 644, "txt": " 4) illustrates a general long-term decreasing trend in the average data level.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[4]/section/div[1]"}]}, "tags": [], "label": "content", "web_segment_id": 34, "global_sentence_id": 76, "edu_l1_label": "IOS"}, {"txt": " Moreover, it suggests non-stationarity in variance, which seems to escalate alongside the mean of the data, and the existence of seasonality within the dataset.", "language": "english", "position": {"atoms": [{"position_id": 645, "txt": " Moreover, it suggests non-stationarity in variance, which seems to escalate alongside the mean of the data, and the existence of seasonality within the dataset.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[4]/section/div[1]"}]}, "tags": [], "label": "content", "web_segment_id": 34, "global_sentence_id": 77, "edu_l1_label": "IOS"}, {"txt": " Therefore, to address the non-stationarity in variance in Gaussian SARIMA modeling, the Box-Cox transformation was applied.", "language": "english", "position": {"atoms": [{"position_id": 646, "txt": " Therefore, to address the non-stationarity in variance in Gaussian SARIMA modeling, the Box-Cox transformation was applied.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[7]/div[2]/section[4]/section/div[1]"}]}, "tags": [], "label": "content", "web_segment_id": 34, "global_sentence_id": 78, "edu_l1_label": "IOS"}, {"txt": "The Box-Cox transformation emerged as a crucial", "language": "english", "position": {"atoms": [{"position_id": 648, "txt": "The Box-Cox transformation emerged as a crucial", "x": 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.", "language": "english", "position": {"atoms": [{"position_id": 1039, "txt": "© 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.", "x": "/html/body/div[1]/div/div/div/div/div[2]/div[2]/article/div[13]/span"}]}, "tags": [], "label": "O", "web_segment_id": 151, "global_sentence_id": 255, "edu_l1_label": "EDU_O"}], "type": "WEB"}
# Modelling low temporal, large spatial data of fatal crashes: An application of negative binomial GSARIMAX time series
## Highlights
### •GSARIMA models daily fatal crashes using 8 years (2014-2022) of Iran's data.
### •Compared Negative Binomial GSARIMA vs. Gaussian GSARIMA for 2,920 crash counts.
### •Data includes 2,920 days of crashes, traffic volume, and weather conditions.
### •Achieved low MARE (<10%) in models with large spatial and low temporal data.
### •GSARIMA outperforms Gaussian by 15% in modeling seasonal crash data.
## Abstract
## Introduction
## Section snippets
### Literature review
### Data
### Method
### Result and discussion
## Conclusion
