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class=anchor-text-container><span class=anchor-text><img alt="Accident Analysis & Prevention"class=publication-cover-image src=https://ars.els-cdn.com/content/image/1-s2.0-S0001457525X00026-cov200h.gif></span></span></a></div></div><div class=PageDivider></div><h1 class="Head u-font-serif u-h2 u-margin-s-ver"id=screen-reader-main-title><span class=title-text>Modelling low temporal, large spatial data of fatal crashes: An application of negative binomial GSARIMAX time series</span></h1><div class=Banner id=banner><div class="wrapper truncated"><div aria-live=polite></div><div class=AuthorGroups><div class=author-group id=author-group><span class=sr-only>Author links open overlay panel</span><button class="button-link button-link-secondary button-link-underline"data-sd-ui-side-panel-opener=true data-xocs-content-id=au005 data-xocs-content-type=author type=button><span class=button-link-text-container><span class=button-link-text><span class=react-xocs-alternative-link><span 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class=u-margin-s-bottom id=p0015>Data includes 2,920 days of crashes, traffic volume, and weather conditions.</div></span><li class=react-xocs-list-item><span class=list-label>•</span><span><div class=u-margin-s-bottom id=p0020>Achieved low MARE (<10%) in models with large spatial and low temporal data.</div></span><li class=react-xocs-list-item><span class=list-label>•</span><span><div class=u-margin-s-bottom id=p0025>GSARIMA outperforms Gaussian by 15% in modeling seasonal crash data.</div></span></ul></div></div></div><div class="abstract author"id=ab010><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">Abstract</h2><div id=as010><div class=u-margin-s-bottom id=sp0010>Road traffic injuries represent a critical public health concern, particularly in developing nations such as Iran, where the incidence of fatal crashes is escalating. Addressing this issue effectively requires sophisticated analytical methodologies to elucidate and mitigate the multifaceted factors contributing to traffic fatalities. 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. 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. 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. Model performance was rigorously evaluated using Deviance Information Criterion (DIC) and Mean Absolute Relative Error (MARE) metrics, alongside out-of-sample predictive accuracy assessments. 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. 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. 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. These findings underscore the model’s potential advantages over conventional Gaussian statistical methods, particularly in handling low temporal resolution and large spatial datasets. Moreover, dynamic models incorporating exogenous variables demonstrated enhanced predictive performance, highlighting the importance of integrating diverse factors in crash analysis. This study not only advances the methodological landscape for traffic crash analysis but also provides actionable insights for policymakers and safety authorities. By identifying key determinants of fatal crashes and accounting for seasonal variations, the Negative Binomial GSARIMAX model serves as a valuable tool for informing targeted interventions aimed at reducing traffic fatalities. Future research should extend this approach by incorporating additional environmental and behavioral variables and conducting comparative analyses across multiple provinces to capture a broader spectrum of influencing conditions.</div></div></div></div></div><div id=preview-section-introduction><div class=PageDivider></div><div class="Introduction u-font-serif u-margin-l-ver"><h2 class="u-h4 u-margin-s-bottom">Introduction</h2><section id=s0005><div class=u-margin-s-bottom id=p0040>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). These crashes account for approximately 1.35 million fatalities annually, with over 90 % occurring in low- and middle-income countries (LMICs) (Geneva: World Health Organization, 2018). The economic consequences are similarly substantial, costing LMICs 1–2 % of their gross national product and exceeding $100 billion annually (Jacobs et al., 2000). Projections indicate that road traffic injuries will become the seventh leading cause of death by 2030, underscoring the urgent need for appropriate countermeasures to reduce fatal crashes, especially in LMICs (World Health Organization, 2015, Geneva: World Health Organization, 2018, Wegman et al., 2017). In Iran, the annual motor vehicle crash death rate of 20.5 per 100,000 population exceeds the global average of 18.2, despite the implementation of a Road Safety Strategic Plan aimed at addressing this issue (WHO, 2018). With a population of 85 million and over 30 million motorized vehicles, road crashes in the country impose substantial economic costs, estimated at 2.19 % of the national GDP (Rezaei et al., 2014). Beyond the immediate economic consequences, road traffic crashes result in significant emotional trauma, psychological effects, and permanent disabilities.</div><div class=u-margin-s-bottom id=p0045>Reducing motor vehicle fatalities is crucial due to their profound societal impact. By analyzing patterns and preventive measures over time, it is possible to evaluate policy effectiveness in improving road safety and address this pressing issue. The development of effective traffic safety policies is contingent upon the accurate forecasting of future trends in motor vehicle crashes. This process is heavily dependent upon the utilization of suitable methodologies.</div><div class=u-margin-s-bottom id=p0050>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. Furthermore, there has been limited research integrating exogenous variables such as traffic volume and weather conditions into daily fatal crash prediction models. This study aims to address these gaps by employing advanced time series models.</div><div class=u-margin-s-bottom id=p0055>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. 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.</div><div class=u-margin-s-bottom id=p0060>The rest of the paper is structured as follows: Section 2 provides a thorough review of the extant literature, emphasizing prior studies and identifying existing research gaps. Section 3 details the data sources utilized and the composition of the dataset. Section 4 outlines the methods employed, incorporating the Gaussian SARIMAX and GSARIMAX models. Section 5 presents the discussion and results obtained after fitting the models to the data. Finally, Section 6 presents the conclusions, recommendations, and limitations of the study.</div></section></div></div><div id=preview-section-snippets><div class=PageDivider></div><div class="Snippets u-font-serif"><h2 class="u-h4 u-margin-l-ver">Section snippets</h2><section><section id=s0010><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">Literature review</h2><div class=u-margin-s-bottom id=p0065>Examining policy implications can benefit from employing time series analysis, a method used at a broader scale (Kisely and Lawrence, 2015, Pun et al., 2013). Meanwhile, at a more detailed level, methods like temporal and spatio-temporal multivariate random-parameters Tobit models are available (Zeng et al., 2018, Zeng et al., 2019). However, it should be noted that the efficacy of these methodologies in adequately addressing the impact of serial correlation in long-time series count data is</div></section></section><section><section id=s0015><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">Data</h2><div class=u-margin-s-bottom id=p0120>The study examined daily crash data from Iran's intercity highways, sourced from the records of the National Traffic Police (NAJA). 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. In addition, the weather data, encompassing minimum and maximum temperatures, average wind speed, and wind direction, were</div></section></section><section><section id=s0020><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">Method</h2><div class=u-margin-s-bottom id=p0145>In this section, the statistical analyses performed on the data are detailed in time domain. It begins with an overview of time series modeling, followed by description models and identifying metrics for model assessing. The flowchart of model is shown in Fig. 3. In the following subsections, all details will be introduced.</div></section></section><section><section id=s0035><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">Result and discussion</h2><div class=u-margin-s-bottom id=p0245>An overview of the aggregate time series decomposition of the fatal crashes (Fig. 4) illustrates a general long-term decreasing trend in the average data level. 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. Therefore, to address the non-stationarity in variance in Gaussian SARIMA modeling, the Box-Cox transformation was applied.</div><div class=u-margin-s-bottom id=p0250>The Box-Cox transformation emerged as a crucial</div></section></section><section><section id=s0040><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">Conclusion</h2><div class=u-margin-s-bottom id=p0375>The escalating prevalence of road traffic injuries, especially in developing nations like Iran, underscores the urgent necessity for effective interventions. Addressing this critical issue mandates the deployment of precise analytical methodologies to dissect and mitigate the multifaceted factors contributing to fatal crashes. This study successfully introduced the Negative Binomial Generalized Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (GSARIMAX) model as a</div></section></section><section><section id=s0050><h2 class="section-title u-h4 u-margin-l-top u-margin-xs-bottom">CRediT authorship contribution statement</h2><div class=u-margin-s-bottom id=p0405><strong>Sara Ghalehnovi:</strong> Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. <strong>Abolfazl Mohammadzadeh Moghaddam:</strong> Writing – review & editing, Writing – original draft, Supervision, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. <strong>Seyed Iman Mohammadpour:</strong> Writing – review & editing, Validation, Software, Methodology, Formal analysis, Data curation,</div></section></section><section><section id=coi005><h2 class="u-h4 u-margin-l-top u-margin-xs-bottom"id=st075>Declaration of competing interest</h2><div class=u-margin-s-bottom id=p0410>The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.</div></section></section><section><section id=ak005><h2 class="u-h4 u-margin-l-top u-margin-xs-bottom"id=st080>Acknowledgment</h2><div class=u-margin-s-bottom id=p0415>The authors would like to express their profound gratitude to Ferdowsi University of Mashhad for providing grant number 3/58712.</div></section></section></div></div><div class="related-content-links u-display-none-from-md"><button class="button-link button-link-primary button-link-small"type=button><span class=button-link-text-container><span class=button-link-text>Recommended articles</span></span></button></div><div class=Tail></div><div id=preview-section-references><div class="paginatedReferences u-font-serif"><div class=PageDivider></div><header><h2 class="u-h4 u-margin-l-ver"><span>References</span><span> (65)</span></h2></header><ul><li class="bib-reference u-margin-s-bottom"><span class=u-font-sans><span class="author u-font-sans"><span>M. </span>Abdel-Aty</span><em> et al.</em></span><h3 class=title>Analysis and prediction of traffic fatalities resulting from angle collisions including the effect of vehicles’ configuration and compatibility</h3><span class="host u-clr-grey6 u-font-sans"><div class=series><h3 class=title>Accid. 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