Analysis of Vehicle Breakdown Frequency: A Case Study of New South Wales, Australia

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} div.type-section h2 { font-size: 20px; line-height: 26px; font-weight: 300; } div.type-section h3 { margin-left: 15px; margin-bottom: 0px; font-weight: 300; } .journal-tabs .tab-title.active a { } </style> <link rel="stylesheet" href="https://pub.mdpi-res.com/assets/css/slick.css?f38b2db10e01b157?1732286508"> <meta name="title" content="Analysis of Vehicle Breakdown Frequency: A Case Study of New South Wales, Australia"> <meta name="description" content="Traffic incidents such as crashes, vehicle breakdowns, and hazards impact traffic speeds and induce congestion. Recognizing the factors that influence the frequency of these traffic incidents is helpful in proposing countermeasures. There have been several studies on evaluating crash frequencies. However, research on other incident types is sparse. The main objective of this research is to identify critical variables that affect the number of reported vehicle breakdowns. A traffic incident dataset covering 4.5 years (January 2012 to June 2016) in the Australian state of New South Wales (NSW) was arranged in a panel data format, consisting of monthly reported vehicle breakdowns in 28 SA4s (Statistical Area Level 4) in NSW. The impact of different independent variables on the number of breakdowns reported in each month–SA4 observation is captured using a random-effect negative binomial regression model. The results indicate that increases in population density, the number of registered vehicles, the number of public holidays, average temperature, the percentage of heavy vehicles, and percentage of white-collared jobs in an area increase the number of breakdowns. On the other hand, an increase in the percentage of unrestricted driving licenses and families with children, number of school holidays, and average rainfall decrease the breakdown frequency. The insights offered in this study contribute to a complete picture of the relevant factors that can be used by transport authorities, vehicle manufacturers, sellers, roadside assistance companies, and mechanics to better manage the impact of vehicle breakdowns." > <link rel="image_src" href="https://pub.mdpi-res.com/img/journals/sustainability-logo.png?8600e93ff98dbf14" > <meta name="dc.title" content="Analysis of Vehicle Breakdown Frequency: A Case Study of New South Wales, Australia"> <meta name="dc.creator" content="Sai Chand"> <meta name="dc.creator" content="Emily Moylan"> <meta name="dc.creator" content="S. Travis Waller"> <meta name="dc.creator" content="Vinayak Dixit"> <meta name="dc.type" content="Article"> <meta name="dc.source" content="Sustainability 2020, Vol. 12, Page 8244"> <meta name="dc.date" content="2020-10-07"> <meta name ="dc.identifier" content="10.3390/su12198244"> <meta name="dc.publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="dc.rights" content="http://creativecommons.org/licenses/by/3.0/"> <meta name="dc.format" content="application/pdf" > <meta name="dc.language" content="en" > <meta name="dc.description" content="Traffic incidents such as crashes, vehicle breakdowns, and hazards impact traffic speeds and induce congestion. Recognizing the factors that influence the frequency of these traffic incidents is helpful in proposing countermeasures. There have been several studies on evaluating crash frequencies. However, research on other incident types is sparse. The main objective of this research is to identify critical variables that affect the number of reported vehicle breakdowns. A traffic incident dataset covering 4.5 years (January 2012 to June 2016) in the Australian state of New South Wales (NSW) was arranged in a panel data format, consisting of monthly reported vehicle breakdowns in 28 SA4s (Statistical Area Level 4) in NSW. The impact of different independent variables on the number of breakdowns reported in each month–SA4 observation is captured using a random-effect negative binomial regression model. The results indicate that increases in population density, the number of registered vehicles, the number of public holidays, average temperature, the percentage of heavy vehicles, and percentage of white-collared jobs in an area increase the number of breakdowns. On the other hand, an increase in the percentage of unrestricted driving licenses and families with children, number of school holidays, and average rainfall decrease the breakdown frequency. The insights offered in this study contribute to a complete picture of the relevant factors that can be used by transport authorities, vehicle manufacturers, sellers, roadside assistance companies, and mechanics to better manage the impact of vehicle breakdowns." > <meta name="dc.subject" content="breakdowns" > <meta name="dc.subject" content="incidents" > <meta name="dc.subject" content="negative binomial" > <meta name="dc.subject" content="random effects" > <meta name ="prism.issn" content="2071-1050"> <meta name ="prism.publicationName" content="Sustainability"> <meta name ="prism.publicationDate" content="2020-10-07"> <meta name ="prism.volume" content="12"> <meta name ="prism.number" content="19"> <meta name ="prism.section" content="Article" > <meta name ="prism.startingPage" content="8244" > <meta name="citation_issn" content="2071-1050"> <meta name="citation_journal_title" content="Sustainability"> <meta name="citation_publisher" content="Multidisciplinary Digital Publishing Institute"> <meta name="citation_title" content="Analysis of Vehicle Breakdown Frequency: A Case Study of New South Wales, Australia"> <meta name="citation_publication_date" content="2020/1"> <meta name="citation_online_date" content="2020/10/07"> <meta name="citation_volume" content="12"> <meta name="citation_issue" content="19"> <meta name="citation_firstpage" content="8244"> <meta name="citation_author" content="Chand, Sai"> <meta name="citation_author" content="Moylan, Emily"> <meta name="citation_author" content="Waller, S. Travis"> <meta name="citation_author" content="Dixit, Vinayak"> <meta name="citation_doi" content="10.3390/su12198244"> <meta name="citation_id" content="mdpi-su12198244"> <meta name="citation_abstract_html_url" content="https://www.mdpi.com/2071-1050/12/19/8244"> <meta name="citation_pdf_url" content="https://www.mdpi.com/2071-1050/12/19/8244/pdf?version=1602064932"> <link rel="alternate" type="application/pdf" title="PDF Full-Text" href="https://www.mdpi.com/2071-1050/12/19/8244/pdf?version=1602064932"> <meta name="fulltext_pdf" content="https://www.mdpi.com/2071-1050/12/19/8244/pdf?version=1602064932"> <meta name="citation_fulltext_html_url" content="https://www.mdpi.com/2071-1050/12/19/8244/htm"> <link rel="alternate" type="text/html" title="HTML Full-Text" href="https://www.mdpi.com/2071-1050/12/19/8244/htm"> <meta name="fulltext_html" content="https://www.mdpi.com/2071-1050/12/19/8244/htm"> <link rel="alternate" type="text/xml" title="XML Full-Text" href="https://www.mdpi.com/2071-1050/12/19/8244/xml"> <meta name="fulltext_xml" content="https://www.mdpi.com/2071-1050/12/19/8244/xml"> <meta name="citation_xml_url" content="https://www.mdpi.com/2071-1050/12/19/8244/xml"> <meta name="twitter:card" content="summary" /> <meta name="twitter:site" content="@MDPIOpenAccess" /> <meta name="twitter:image" content="https://pub.mdpi-res.com/img/journals/sustainability-logo-social.png?8600e93ff98dbf14" /> <meta property="fb:app_id" content="131189377574"/> <meta property="og:site_name" content="MDPI"/> <meta property="og:type" content="article"/> <meta property="og:url" content="https://www.mdpi.com/2071-1050/12/19/8244" /> <meta property="og:title" content="Analysis of Vehicle Breakdown Frequency: A Case Study of New South Wales, Australia" /> <meta property="og:description" content="Traffic incidents such as crashes, vehicle breakdowns, and hazards impact traffic speeds and induce congestion. Recognizing the factors that influence the frequency of these traffic incidents is helpful in proposing countermeasures. There have been several studies on evaluating crash frequencies. However, research on other incident types is sparse. The main objective of this research is to identify critical variables that affect the number of reported vehicle breakdowns. A traffic incident dataset covering 4.5 years (January 2012 to June 2016) in the Australian state of New South Wales (NSW) was arranged in a panel data format, consisting of monthly reported vehicle breakdowns in 28 SA4s (Statistical Area Level 4) in NSW. The impact of different independent variables on the number of breakdowns reported in each month–SA4 observation is captured using a random-effect negative binomial regression model. The results indicate that increases in population density, the number of registered vehicles, the number of public holidays, average temperature, the percentage of heavy vehicles, and percentage of white-collared jobs in an area increase the number of breakdowns. On the other hand, an increase in the percentage of unrestricted driving licenses and families with children, number of school holidays, and average rainfall decrease the breakdown frequency. The insights offered in this study contribute to a complete picture of the relevant factors that can be used by transport authorities, vehicle manufacturers, sellers, roadside assistance companies, and mechanics to better manage the impact of vehicle breakdowns." /> <meta property="og:image" content="https://pub.mdpi-res.com/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001-550.jpg?1602076212" /> <link rel="alternate" type="application/rss+xml" title="MDPI Publishing - Latest articles" href="https://www.mdpi.com/rss"> <meta name="google-site-verification" content="PxTlsg7z2S00aHroktQd57fxygEjMiNHydKn3txhvwY"> <meta name="facebook-domain-verification" content="mcoq8dtq6sb2hf7z29j8w515jjoof7" /> <script id="Cookiebot" data-cfasync="false" src="https://consent.cookiebot.com/uc.js" data-cbid="51491ddd-fe7a-4425-ab39-69c78c55829f" type="text/javascript" async></script>  <script type="text/plain" data-cookieconsent="statistics"> (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); 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height:6px;"></span> <div></div> <div style="margin: 5px 0 15px 0;" class="hypothesis_container"> <div class="art-affiliations"> <div class="affiliation "> <div class="affiliation-item"><sup>1</sup></div> <div class="affiliation-name ">Research Centre for Integrated Transport Innovation (rCITI), School of Civil and Environmental Engineering, University of New South Wales, Sydney, NSW 2052, Australia</div> </div> <div class="affiliation "> <div class="affiliation-item"><sup>2</sup></div> <div class="affiliation-name ">School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia</div> </div> <div class="affiliation"> <div class="affiliation-item"><sup>*</sup></div> <div class="affiliation-name ">Author to whom correspondence should be addressed. </div> </div> </div> </div> <div class="bib-identity" style="margin-bottom: 10px;"> <em>Sustainability</em> <b>2020</b>, <em>12</em>(19), 8244; <a href="https://doi.org/10.3390/su12198244">https://doi.org/10.3390/su12198244</a> </div> <div class="pubhistory" style="font-weight: bold; padding-bottom: 10px;"> <span style="display: inline-block">Submission received: 8 September 2020</span> / <span style="display: inline-block">Revised: 1 October 2020</span> / <span style="display: inline-block">Accepted: 5 October 2020</span> / <span style="display: inline-block">Published: 7 October 2020</span> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/sustainability/sections/Sustainable_Transportation">Sustainable Transportation</a>)<br/> </div> <div class="highlight-box1"> <div class="download"> <a class="button button--color-inversed button--drop-down" data-dropdown="drop-download-424511" aria-controls="drop-supplementary-424511" aria-expanded="false"> Download <i class="material-icons">keyboard_arrow_down</i> </a> <div id="drop-download-424511" class="f-dropdown label__btn__dropdown label__btn__dropdown--button" data-dropdown-content aria-hidden="true" tabindex="-1"> <a class="UD_ArticlePDF" href="/2071-1050/12/19/8244/pdf?version=1602064932" data-name="Analysis of Vehicle Breakdown Frequency: A Case Study of New South Wales, Australia" data-journal="sustainability">Download PDF</a> <br/> <a id="js-pdf-with-cover-access-captcha" href="#" data-target="/2071-1050/12/19/8244/pdf-with-cover" class="accessCaptcha">Download PDF with Cover</a> <br/> <a id="js-xml-access-captcha" href="#" data-target="/2071-1050/12/19/8244/xml" class="accessCaptcha">Download XML</a> <br/> <a href="/2071-1050/12/19/8244/epub" id="epub_link">Download Epub</a> <br/> </div> <div class="js-browse-figures" style="display: inline-block;"> <a href="#" class="button button--color-inversed margin-bottom-10 openpopupgallery UI_BrowseArticleFigures" data-target='article-popup' data-counterslink = "https://www.mdpi.com/2071-1050/12/19/8244/browse" >Browse Figures</a> </div> <div id="article-popup" class="popupgallery" style="display: inline; line-height: 200%"> <a href="https://pub.mdpi-res.com/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001.png?1602076212" title=" <strong>Figure 1</strong><br/> <p>Map of New South Wales (NSW) with Statistical Area Level 4 (SA4) classification (map of Australia in the inset).</p> "> </a> <a href="https://pub.mdpi-res.com/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g002.png?1602076212" title=" <strong>Figure 2</strong><br/> <p>Comparison of increases in breakdowns on motorways (<b>a</b>) and non-motorways (<b>b</b>).</p> "> </a> </div> <a class="button button--color-inversed" href="/2071-1050/12/19/8244/notes">Versions Notes</a> </div> </div> <div class="responsive-moving-container small hidden" data-id="article-counters" style="margin-top: 15px;"></div> <div class="html-dynamic"> <section> <div class="art-abstract art-abstract-new in-tab hypothesis_container"> <p> <div><section class="html-abstract" id="html-abstract"> <h2 id="html-abstract-title">Abstract</h2><b>:</b> <div class="html-p">Traffic incidents such as crashes, vehicle breakdowns, and hazards impact traffic speeds and induce congestion. Recognizing the factors that influence the frequency of these traffic incidents is helpful in proposing countermeasures. There have been several studies on evaluating crash frequencies. However, research on other incident types is sparse. The main objective of this research is to identify critical variables that affect the number of reported vehicle breakdowns. A traffic incident dataset covering 4.5 years (January 2012 to June 2016) in the Australian state of New South Wales (NSW) was arranged in a panel data format, consisting of monthly reported vehicle breakdowns in 28 SA4s (Statistical Area Level 4) in NSW. The impact of different independent variables on the number of breakdowns reported in each month–SA4 observation is captured using a random-effect negative binomial regression model. The results indicate that increases in population density, the number of registered vehicles, the number of public holidays, average temperature, the percentage of heavy vehicles, and percentage of white-collared jobs in an area increase the number of breakdowns. On the other hand, an increase in the percentage of unrestricted driving licenses and families with children, number of school holidays, and average rainfall decrease the breakdown frequency. The insights offered in this study contribute to a complete picture of the relevant factors that can be used by transport authorities, vehicle manufacturers, sellers, roadside assistance companies, and mechanics to better manage the impact of vehicle breakdowns.</div> </section> <div id="html-keywords"> <div class="html-gwd-group"><div id="html-keywords-title">Keywords: </div><a href="/search?q=breakdowns">breakdowns</a>; <a href="/search?q=incidents">incidents</a>; <a href="/search?q=negative+binomial">negative binomial</a>; <a href="/search?q=random+effects">random effects</a></div> <div> </div> </div> </div> </p> </div> </section> </div> <div class="hypothesis_container"> <ul class="menu html-nav" data-prev-node="#html-quick-links-title"> </ul> <div class="html-body"> <section id='sec1-sustainability-12-08244' type='intro'><h2 data-nested='1'> 1. Introduction</h2><div class='html-p'>Investigating ways to reduce the impacts of road congestion is an increasingly important challenge as vehicle ownership and population increase across the world. Traffic congestion is divided into two categories, namely recurrent and non-recurrent [<a href="#B1-sustainability-12-08244" class="html-bibr">1</a>]. Recurrent congestion is caused by demand chronically exceeding road capacity, and non-recurrent congestion is caused by random events, such as traffic incidents, adverse weather, and hazards [<a href="#B2-sustainability-12-08244" class="html-bibr">2</a>]. Non-recurrent traffic congestion is non-trivial, and it was found to account for up to 60% of total congestion [<a href="#B3-sustainability-12-08244" class="html-bibr">3</a>]. As the critical source of non-recurrent congestion, a traffic incident is defined as a non-recurring event that causes a reduction of roadway capacity or an abnormal increase in demand [<a href="#B4-sustainability-12-08244" class="html-bibr">4</a>]. Crashes, breakdowns, police stops, and hazards are some examples of the non-planned incidents that impact the typical traffic conditions. The sudden and unpredictable nature of these incidents results in unreliable and fluctuating travel times [<a href="#B5-sustainability-12-08244" class="html-bibr">5</a>]. Commuters tend to show varying behaviors, such as risk aversion, risk neutrality, and risk seeking [<a href="#B6-sustainability-12-08244" class="html-bibr">6</a>]. Furthermore, non-recurrent congestion is also found to influence commuters’ departure time, route, and mode choice [<a href="#B7-sustainability-12-08244" class="html-bibr">7</a>].</div><div class='html-p'>The unplanned incidents drastically reduce the performance of a network through increased congestion and unreliability [<a href="#B8-sustainability-12-08244" class="html-bibr">8</a>,<a href="#B9-sustainability-12-08244" class="html-bibr">9</a>]. Furthermore, the primary incidents are likely to provoke secondary incidents, particularly in areas with more vehicular traffic [<a href="#B10-sustainability-12-08244" class="html-bibr">10</a>]. This could be due to driver distraction, more increased congestion than usual, stop-and-go movements, etc. [<a href="#B11-sustainability-12-08244" class="html-bibr">11</a>,<a href="#B12-sustainability-12-08244" class="html-bibr">12</a>]. The secondary crashes are likely to increase by 2.8% for every minute the primary incident is not cleared and continues to be a hazard [<a href="#B13-sustainability-12-08244" class="html-bibr">13</a>]. Identifying the key factors that influence unplanned incidents would allow us to suggest appropriate management strategies to mitigate the damage that road traffic inflicts on the environment [<a href="#B14-sustainability-12-08244" class="html-bibr">14</a>,<a href="#B15-sustainability-12-08244" class="html-bibr">15</a>,<a href="#B16-sustainability-12-08244" class="html-bibr">16</a>].</div><div class='html-p'>Numerous studies focus on the prediction of crash frequencies, severities, rates, and durations using advanced statistical models [<a href="#B17-sustainability-12-08244" class="html-bibr">17</a>]. For example, Negative Binomial and Poisson models are commonly used for crash frequencies [<a href="#B18-sustainability-12-08244" class="html-bibr">18</a>], Tobit models are used for crash rates [<a href="#B19-sustainability-12-08244" class="html-bibr">19</a>], Multinomial Logit, Ordered Logit, and Ordered Probit models are used for modeling crash severity [<a href="#B20-sustainability-12-08244" class="html-bibr">20</a>], and Hazard-based models are used for crash duration [<a href="#B21-sustainability-12-08244" class="html-bibr">21</a>]. Various data mining and empirical approaches, such as clustering [<a href="#B22-sustainability-12-08244" class="html-bibr">22</a>,<a href="#B23-sustainability-12-08244" class="html-bibr">23</a>], support vector machine [<a href="#B24-sustainability-12-08244" class="html-bibr">24</a>], fuzzy logic [<a href="#B25-sustainability-12-08244" class="html-bibr">25</a>], artificial neural networks [<a href="#B26-sustainability-12-08244" class="html-bibr">26</a>], time-series analysis [<a href="#B27-sustainability-12-08244" class="html-bibr">27</a>,<a href="#B28-sustainability-12-08244" class="html-bibr">28</a>], and genetic algorithms [<a href="#B29-sustainability-12-08244" class="html-bibr">29</a>], have been widely used to identify trends and patterns in large temporal and spatial crash datasets [<a href="#B30-sustainability-12-08244" class="html-bibr">30</a>]. Furthermore, advanced statistical models, such as Random Parameter models, Latent Class models, Bayesian models, and Markov Switching models, are widely used to account for unobserved temporal and spatial heterogeneity [<a href="#B17-sustainability-12-08244" class="html-bibr">17</a>].</div><div class='html-p'>However, research on the prediction of other incident types has been sparse. A contributing factor to this underattention is the lack of comprehensive data regarding other types of incidents, such as breakdowns. These incidents are not well reported to the transport authorities because their safety and property damage repercussions are small compared to those of crashes. However, traffic congestion induced by on-road breakdowns is non-trivial, as noted by Wang et al. (2005) [<a href="#B31-sustainability-12-08244" class="html-bibr">31</a>].</div><div class='html-p'>Vehicle breakdown is a type of unplanned incident where a vehicle fails during operation on a roadway and is forced to stop. There can be many reasons for a vehicle breakdown, such as a flat battery, faulty electrical wiring, fuel pressure problems, tire puncture, driver error, etc. Most breakdowns can be resolved on the spot by self-repairing or calling a mechanic or roadside assistance company. Few breakdowns are so complex as to require towing. Vehicle breakdowns can result in traffic congestion, particularly when the road is partially or fully closed due to obstruction by the broken-down vehicle or the towing equipment. Furthermore, vehicle breakdowns are unusual events, and many drivers are uncertain about how to respond to the failure. This can lead to unsafe behavior and, in some cases, secondary incidents.</div><div class='html-p'>Despite the recent improvements in the quality of automobile designs that have improved safety and security, vehicle breakdowns still happen on roads. In fact, they constitute a major proportion of the road incidents, particularly on freeways [<a href="#B31-sustainability-12-08244" class="html-bibr">31</a>]. There were around 20,000 yearly reported on-road vehicle breakdowns compared to the 27,000 yearly crashes in New South Wales (NSW) between the years 2012 and 2015. Vehicle breakdowns accounted for about 30% of all types of incidents in the state of New South Wales (NSW), Australia, 64% of all incidents on a motorway in the United Kingdom [<a href="#B31-sustainability-12-08244" class="html-bibr">31</a>], and 32% of total incidents on urban freeways in South East Queensland, Australia [<a href="#B32-sustainability-12-08244" class="html-bibr">32</a>]. As noted, there are only a handful of studies on vehicle breakdowns.</div><div class='html-p'>However, the total number of on-road breakdowns could be even higher because of under-reporting, including breakdowns that occur on local streets or can be easily relocated to a side street or parking lot. The relevant transport authorities may not be notified of such breakdowns, but they are also less likely to contribute significantly to congestion. On the other hand, on controlled-access highways, tunnels, and bridges, vehicle failure often requires the driver to stop the vehicle in a driving lane or a dedicated breakdown bay. Stopping of vehicles on such roadways contributes significantly to congestion, and these breakdowns are reported immediately to the concerned authorities for rapid response and clearance.</div><div class='html-p'>Vehicle breakdowns are non-trivial in number and significantly impact traffic congestion. However, the literature has not yet explored the factors behind vehicle breakdowns at a macro-level. The current study addresses the gap in the literature thanks to a more comprehensive, long-baseline dataset of unplanned incidents that includes on-road breakdowns across the state of NSW, Australia. The main objectives of the study are to investigate the impacts of various variables, including socioeconomic attributes, weather, heavy vehicles, exposure, and temporal attributes, on vehicle breakdown frequency.</div></section><section id='sec2-sustainability-12-08244' type=''><h2 data-nested='1'> 2. Study Area and Data Description</h2><section id='sec2dot1-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 2.1. Study Area</h4><div class='html-p'>New South Wales (NSW), with an estimated population of 7.5 million, is the most populous state in Australia. Sydney, Newcastle, and Wollongong are the three largest cities in the state, accounting for almost 70% of the population of NSW. In order to curb congestion and improve safety, state transport authorities employ various forms of Intelligent Transportation System (ITS) infrastructures, such as Variable Message Signs (VMS), Variable Speed Limit Signs (VSLS), and Vehicle Detection Systems, to manage demand and safety on major roads. Crash fatalities have been declining over the last decade; however, incidents of different types and magnitudes continue to increase [<a href="#B33-sustainability-12-08244" class="html-bibr">33</a>].</div><div class='html-p'>Statistical Area Level 4 (SA4) is the largest spatial unit defined under the Australian Statistical Geography Standard (ASGS). NSW is comprised of 28 SA4s, and each SA4 has a population of at least 100,000 (<a href="#sustainability-12-08244-f001" class="html-fig">Figure 1</a>). The SA4 classification was used in this study to model vehicle breakdowns. According to the Household Travel Survey of Sydney [<a href="#B34-sustainability-12-08244" class="html-bibr">34</a>], most trips are short ones and are mainly for non-work purposes, such as education, shopping, socializing, and entertainment. In addition, the survey also showed that 76% of trips were less than 10 km. Although the average distance of commuting travel (usually the longest trip for a traveler) was around 15 km, it only accounted for approximately 15% of the total number of trips. Therefore, most of the trips happen within the SA4. Therefore, the SA4 aggregation is acceptable for the study, which provides a nexus between the sociodemographic, weather, and infrastructure attributes of the statistical areas and the vehicle breakdowns.</div></section><section id='sec2dot2-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 2.2. Data Description</h4><div class='html-p'>For this study, historical incident data for 4.5 years, i.e., from the 1st of January 2012 to the 30th of June 2016, were obtained for New South Wales, Australia. The dataset includes information on time, location, duration, incident type, incident detection mechanism, incident severity, and a description of the nature of the incident. The dataset contains over 320,000 records of unplanned incidents, including accidents, breakdowns, hazards, police stops, towing, and fires. There are 90,159 records of reported on-road vehicle breakdowns in the dataset. The average breakdown duration is 43 min, the standard deviation is 80 min, and the median value is 24 min. An interesting observation from the dataset is that the breakdowns that occur near the Central Business District (CBD) and urbanized areas tend to have lower durations than the ones that occur in other locations.</div><div class='html-p'>Using basic text filtering of the description field, it was observed that 50.8% of breakdowns involved light vehicles (cars, vans, light commercial vehicles, motorcycles, and taxis), 24.8% involved heavy vehicles (buses, trucks, and tankers), and the remaining observations did not specify the vehicle type. According to the Australian Bureau of Statistics (ABS), light vehicles account for 96.6% of the total registered vehicles in NSW, whereas heavy vehicles account for only 3.4% [<a href="#B35-sustainability-12-08244" class="html-bibr">35</a>]. Furthermore, the total vehicle-kilometers traveled (VKT) by heavy vehicles made up 8.3% of the total kilometers traveled in NSW during a one-year period starting from July 2015. These statistics indicate that despite the low proportionality of heavy vehicles, they are prone to more on-road breakdowns than regular passenger vehicles.</div><div class='html-p'>Less than 0.3% of the records mentioned fuel or petrol in the text description, so running out of fuel is not a major cause of breakdowns. Furthermore, 24.8% of breakdowns occurred on freeways, 48.6% occurred on non-freeways, and the rest did not identify a primary street for the breakdown location. However, freeways contribute to just 0.54% of the road length in NSW [<a href="#B36-sustainability-12-08244" class="html-bibr">36</a>,<a href="#B37-sustainability-12-08244" class="html-bibr">37</a>]. One potential reason for the higher proportion of breakdowns on freeways compared to the road length is the efficient detection of traffic incidents on motorways [<a href="#B38-sustainability-12-08244" class="html-bibr">38</a>].</div><div class='html-p'>The individual breakdown records were arranged in a panel data format, consisting of monthly reported vehicle breakdowns in 28 SA4s in NSW. Data about the weather, holidays, socioeconomic attributes, and other relevant variables were collated from various sources for the model estimation. Only the relevant variables were included in the final model. However, the descriptive statistics of all the potential variables are shown in <a href="#sustainability-12-08244-t001" class="html-table">Table 1</a>. The dependent variable, i.e., the frequency of vehicle breakdowns, ranges from 0 to 416. Furthermore, the variance of the number of breakdowns per month is greater than the observed mean, indicating a potential over-dispersion and suggesting the use of a negative binomial model.</div></section></section><section id='sec3-sustainability-12-08244' type='methods'><h2 data-nested='1'> 3. Methodology</h2><div class='html-p'>To date, the literature has not addressed the impact of various factors on vehicle breakdown frequency. However, there have been several studies in the recent past on macro-level safety models, where spatially aggregated accidents are modeled against area-wide variables. These studies have employed various aggregation levels, such as census tracts, traffic analysis zones, counties, cities, states, and countries [<a href="#B39-sustainability-12-08244" class="html-bibr">39</a>,<a href="#B40-sustainability-12-08244" class="html-bibr">40</a>]. Attributes of these spatial aggregations, such as population, density, income, land use characteristics, environmental variables, traffic characteristics, trip generation rates, road density, etc., are typically used to model crashes.</div><div class='html-p'>Panel datasets are widely used in the macro-level safety models to observe the effect of spatiotemporal variations of the explanatory variables on crash frequencies [<a href="#B40-sustainability-12-08244" class="html-bibr">40</a>,<a href="#B41-sustainability-12-08244" class="html-bibr">41</a>,<a href="#B42-sustainability-12-08244" class="html-bibr">42</a>]. The crash counts in a region (city, state, country, etc.) will be correlated over time because the unobserved effects associated with a specific region will remain the same over time [<a href="#B43-sustainability-12-08244" class="html-bibr">43</a>]. Similarly, there can be correlation over space because regions that are nearby may share unobserved effects. These correlations violate the assumptions of ordinary least squares regression and misestimate the errors on the model coefficients. To account for these correlations, random-effect (RE) and random-parameter (RP) models are considered [<a href="#B40-sustainability-12-08244" class="html-bibr">40</a>,<a href="#B44-sustainability-12-08244" class="html-bibr">44</a>,<a href="#B45-sustainability-12-08244" class="html-bibr">45</a>,<a href="#B46-sustainability-12-08244" class="html-bibr">46</a>]. In the case of the RE model, the common unobserved effects are assumed to be distributed across the spatial and temporal units according to some distribution, and shared unobserved effects are assumed to be uncorrelated with explanatory variables [<a href="#B43-sustainability-12-08244" class="html-bibr">43</a>]. Therefore, the intercept term is represented by a distribution in RE models. In the case of RP models, each estimable parameter (including the intercept) of the model can vary across observations in the dataset. In this regard, the RP model can be considered as a more flexible extension of the RE model.</div><div class='html-p'>While RP models account for unobserved heterogeneity and offer a better fit than fixed-parameter models, they are time-consuming and complex to estimate due to the simulation-based likelihood estimation. Furthermore, the analyst is required to select the random parameters and their appropriate distribution. The RP approach may not necessarily improve predictability, and for studies with many explanatory variables, using an RP approach can be computationally intensive due to simulation-based Halton sequences, which are subject to errors in specification because the modeler needs to select the variables with distributed parameters and non-parsimonious because of the many parameters to be estimated [<a href="#B18-sustainability-12-08244" class="html-bibr">18</a>,<a href="#B41-sustainability-12-08244" class="html-bibr">41</a>,<a href="#B47-sustainability-12-08244" class="html-bibr">47</a>,<a href="#B48-sustainability-12-08244" class="html-bibr">48</a>]. Therefore, in the current study, a random-effect negative binomial model (RENB) is developed to model vehicle breakdowns.</div><div class='html-p'>Poisson and negative binomial (NB) models are the most generally espoused approaches for count data modeling. The NB model can handle over-dispersed count data and assumes that counts are independent for an entity for any time. The form of the RENB model is:<div class='html-disp-formula-info' id='FD1-sustainability-12-08244'> <div class='f'> <math display='block'><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mrow> <mo>(</mo> <mrow> <mi>β</mi> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <mo> </mo> <msub> <mi>φ</mi> <mi>i</mi> </msub> <mo> </mo> <mo>+</mo> <mo> </mo> <msub> <mi>ε</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </msup> <mo>,</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(1)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> represents the expected number of breakdowns in a SA4 <span class='html-italic'>i</span> in month <span class='html-italic'>t</span>; <math display='inline'><semantics> <mrow> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> is a vector of explanatory variables; <math display='inline'><semantics> <mi>β</mi> </semantics></math> is a vector of estimable parameters; <math display='inline'><semantics> <mrow> <msub> <mi>ε</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> represents the error term for the <span class='html-italic'>i</span>th SA4 at time <span class='html-italic'>t</span>; <math display='inline'><semantics> <mrow> <msub> <mi>φ</mi> <mi>i</mi> </msub> </mrow> </semantics></math> is the unknown intercept term of segment <span class='html-italic'>i</span>, which varies with the individual and time such that <math display='inline'><semantics> <mrow> <msup> <mi>e</mi> <mrow> <msub> <mi>φ</mi> <mi>i</mi> </msub> </mrow> </msup> </mrow> </semantics></math> follows a gamma distribution with mean 1 and variance <span class='html-italic'>α</span>. To illustrate the variation of the SA4 effect over time, the associated dispersion parameters are not supposed to be constant.</div><div class='html-p'>It should be noted that any generalized linear model (GLM), such as a Poisson or a negative binomial regression with a fixed dispersion parameter with random effects, is part of the broader class of generalized linear mixed models (GLMM). The model given in (1) is a specific version using the canonical log link function, but one can use other link functions, such as logit, probit, and complementary log-log [<a href="#B49-sustainability-12-08244" class="html-bibr">49</a>,<a href="#B50-sustainability-12-08244" class="html-bibr">50</a>].</div><div class='html-p'>It is noted that 1/<math display='inline'><semantics> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> </mrow> </semantics></math> = <span class='html-italic'>α<sub>i</sub></span>, the over-dispersion parameter in the NB model. Furthermore, it is assumed that <math display='inline'><semantics> <mrow> <mfrac> <mrow> <msub> <mi>θ</mi> <mi>i</mi> </msub> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>θ</mi> <mi>i</mi> </msub> </mrow> </mfrac> </mrow> </semantics></math> or <math display='inline'><semantics> <mrow> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mi>α</mi> <mi>i</mi> </mrow> </mfrac> </mrow> </semantics></math> follows a beta distribution with parameters <span class='html-italic'>a</span> and <span class='html-italic'>b</span>. All the parameters (<span class='html-italic'>a</span>, <span class='html-italic'>b</span>, and <math display='inline'><semantics> <mrow> <mi>β</mi> <mo stretchy="false">)</mo> <mo> </mo> </mrow> </semantics></math> are estimated by maximum likelihood techniques [<a href="#B51-sustainability-12-08244" class="html-bibr">51</a>]. This approach of the RENB model estimation has been used in several studies of crash modeling [<a href="#B52-sustainability-12-08244" class="html-bibr">52</a>,<a href="#B53-sustainability-12-08244" class="html-bibr">53</a>,<a href="#B54-sustainability-12-08244" class="html-bibr">54</a>]. The joint probability density function can be written for an RENB model as follows:<div class='html-disp-formula-info' id='FD2-sustainability-12-08244'> <div class='f'> <math display='block'><semantics> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>|</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mo> </mo> <mfrac> <mrow> <mi>Γ</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> </mrow> <mo>)</mo> </mrow> <mi>Γ</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <msub> <mstyle mathsize="90%" displaystyle="true"> <mo>∑</mo> </mstyle> <mi>T</mi> </msub> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mi>Γ</mi> <mrow> <mo>(</mo> <mrow> <mi>b</mi> <mo>+</mo> <msub> <mstyle mathsize="90%" displaystyle="true"> <mo>∑</mo> </mstyle> <mi>T</mi> </msub> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Γ</mi> <mrow> <mo>(</mo> <mi>a</mi> <mo>)</mo> </mrow> <mi>Γ</mi> <mrow> <mo>(</mo> <mi>b</mi> <mo>)</mo> </mrow> <mi>Γ</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>+</mo> <msub> <mstyle mathsize="90%" displaystyle="true"> <mo>∑</mo> </mstyle> <mi>T</mi> </msub> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <msub> <mstyle mathsize="90%" displaystyle="true"> <mo>∑</mo> </mstyle> <mi>T</mi> </msub> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </mfrac> <msub> <mstyle mathsize="90%" displaystyle="true"> <mo>∏</mo> </mstyle> <mi>T</mi> </msub> <mfrac> <mrow> <mi>Γ</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mi>Γ</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>λ</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>Γ</mi> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mfrac> <mo> </mo> <mo>,</mo> </mrow> </semantics></math> </div> <div class='l'> <label >(2)</label> </div> </div> where <math display='inline'><semantics> <mrow> <msub> <mi>y</mi> <mrow> <mi>i</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> represents the observed number of breakdowns in SA4 <span class='html-italic'>i</span> in month <span class='html-italic'>t; T</span> is the number of statistical segments.</div><div class='html-p'>As noted by Shankar et al. (1998), the main advantage of this RENB approach is that the over-dispersion parameter is not constrained to be constant across SA4s, as it is in the case of the cross-sectional negative binomial regression [<a href="#B53-sustainability-12-08244" class="html-bibr">53</a>]. Moreover, a unique characteristic of this formulation is that within-group effects can be allowed to vary over time, even when the exogenous vector of attributes is constant, thereby better accounting for unobserved heterogeneity.</div><div class='html-p'>Before estimating the RENB model, a simple multiple linear regression model was estimated by including all the potential independent variables. The variance inflation factors (VIFs) were calculated and the variables with VIFs exceeding 10 were omitted. This was done to address the problem of multicollinearity [<a href="#B55-sustainability-12-08244" class="html-bibr">55</a>].</div><div class='html-p'>Then, for the RENB model, a reverse stepwise approach was used to explore model specification. First, all the variables of interest (identified from the VIF procedure) were included in the model fitting. To address multicollinearity and lack of parsimony, the least significant variables (critical <span class='html-italic'>p</span> = 0.10 in this study) were sequentially dropped. Furthermore, the goodness-of-fit measures, such as the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), were evaluated at each step.</div></section><section id='sec4-sustainability-12-08244' type='results'><h2 data-nested='1'> 4. Results</h2><div class='html-p'>The results of the final model, including coefficients, standard errors, z-values, and elasticities (only for the continuous variables) of the significant variables, are shown in <a href="#sustainability-12-08244-t002" class="html-table">Table 2</a>. In addition, the log-likelihood, AIC, and BIC values are presented. The positive sign of the coefficient indicates that as the variable increases, the number of breakdowns increases. The elasticity indicates the percent change (+ sign indicates increase and − sign indicates decrease) in the number of breakdowns for a 1% increase in the continuous variable when all other variables are held constant.</div></section><section id='sec5-sustainability-12-08244' type='discussion'><h2 data-nested='1'> 5. Discussion</h2><div class='html-p'>The results of the RENB model shown in <a href="#sustainability-12-08244-t002" class="html-table">Table 2</a> offer some interesting insights into the contributing factors and their directions.</div><section id='sec5dot1-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 5.1. Temporal Variables</h4><div class='html-p'>Four dummy variables for the year were included in the model to compare with the base year, i.e., 2012. The breakdowns in all the years show a significant increase (see the z-values) compared to the base year, with the most recent year being the highest. This relationship can be partly attributed to a decline in vehicle maintenance skills among drivers and growth in fragile technological components in the vehicles. According to the Royal Automobile Club (RAC) of Britain, owners are less likely to read their vehicle manuals than in the past, and a quarter of breakdown call-outs could be prevented if the owners consulted the manual [<a href="#B56-sustainability-12-08244" class="html-bibr">56</a>].</div><div class='html-p'>Additionally, some technologies, such as DVD systems, keyless electronic ignitions, music players, and satellite navigation, put more strain on battery life, thereby resulting in battery-related vehicle breakdowns. Furthermore, according to the American Automobile Association (AAA), low-profile tires used in the latest vehicles are highly damage-prone and contribute to breakdowns through flat tires [<a href="#B57-sustainability-12-08244" class="html-bibr">57</a>]. Another potential reason for the increase in the number of reported breakdowns could be accredited to the increased deployment of ITSs across NSW, particularly cameras on motorways, which detect the incidents that might not otherwise have been recorded [<a href="#B38-sustainability-12-08244" class="html-bibr">38</a>]. This is evident from <a href="#sustainability-12-08244-f002" class="html-fig">Figure 2</a>a, showing a steep rise in the number of breakdowns on motorways as compared to a stable pattern of breakdowns on non-motorways (<a href="#sustainability-12-08244-f002" class="html-fig">Figure 2</a>b) over the same period. As camera technology becomes more pervasive, the increased reporting of breakdowns is expected for non-motorways as well, and may be suggested in the increase in non-motorway breakdowns from mid-2015.</div></section><section id='sec5dot2-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 5.2. Exposure Variables</h4><div class='html-p'>Population density is an indicator of congestion. Vehicles decelerate and accelerate more often in highly congested areas. These driving patterns put more strain on the vehicle, resulting in an increased expectation of brake failure or engine overheating. The model results support this hypothesis. The elasticity indicates that as the logarithm of population density increases by 1%, the total number of breakdowns in NSW increases by 1.33% when the remaining variables are equal to the original values.</div><div class='html-p'>The number of registered vehicles in SA4 acts as a proxy for vehicle use, which might also be measured as vehicle-kilometers traveled. Increased vehicle use is expected to increase chances of a breakdown due to the amount of time spent driving and wear and tear on the vehicle. In addition, the sheer fact that there are more cars in an SA4 could also result in the higher number of breakdowns. The model results indicate that a 1% increase in the number of registered vehicles could lead to a 1.40% increase in the number of on-road breakdowns.</div></section><section id='sec5dot3-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 5.3. Socioeconomic Variables</h4><div class='html-p'>The percentage of families with children aged less than 15 shows a negative effect on the number of breakdowns. A 1% increase in such families could reduce the expected breakdowns by 2.87% when all the other variables are equal. This could potentially be due to the extra caution and care taken by the parents (drivers). Additionally, families are more likely to purchase vehicle makes and models known to be safe and reliable, which could impact the prevalence of vehicle breakdowns.</div><div class='html-p'>The increasing proportion of managers and professionals in a region shows a positive impact on breakdowns. These categories of people typically maintain a busy lifestyle with more work-related responsibilities and decreased capacity for vehicle maintenance. AAA states that 35% of Americans have delayed or skipped service or repairs that were recommended by a mechanic, and a significant number of breakdowns each year could be prevented with basic vehicle maintenance [<a href="#B57-sustainability-12-08244" class="html-bibr">57</a>]. A related explanation is that managers and professionals have higher incomes, which might facilitate the purchase of new, technology-laden vehicles. However, according to the AAA and RAC, newer models are more prone to breakdowns, since they rely heavily on fragile electronic components [<a href="#B56-sustainability-12-08244" class="html-bibr">56</a>,<a href="#B57-sustainability-12-08244" class="html-bibr">57</a>]. Furthermore, the combination of technology-laden vehicles and higher mileage (because of the propensity of higher-income earners to travel long distances and make more trips) could lead to a greater number of breakdowns.</div><div class='html-p'>There are four categories of driving licenses. However, the number of people with unrestricted licenses is significantly more than any other license type (see <a href="#sustainability-12-08244-t001" class="html-table">Table 1</a>). Only the unrestricted licenses were included in the model. As may be seen in <a href="#sustainability-12-08244-t002" class="html-table">Table 2</a>, the increased percentage of unrestricted driving licenses results in a reduction of breakdowns. Unrestricted drivers are likely to be more experienced in both vehicle maintenance and operation and, due to being older on average, are more able to afford the costs associated with a reliable car and timely service and maintenance.</div></section><section id='sec5dot4-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 5.4. Heavy Vehicles</h4><div class='html-p'>A 1% increase in the percentage of heavy vehicles registered in a region is observed to have a 0.24% rise of breakdown frequency. One contribution is the damage and deterioration caused by heavy vehicles to the roads, which, in turn, could result in more breakdowns. A second contributing reason is that a single heavy vehicle might be used by different drivers, who may not develop sufficient familiarity with the vehicle to monitor changes and address concerns before they evolve into failures. The maintenance strategy is typically post-active for commercial vehicles, such as trucks (primarily) and buses (to an extent), which means that a fault is fixed only after it has occurred [<a href="#B58-sustainability-12-08244" class="html-bibr">58</a>]. One countermeasure for addressing the congestion caused by breakdowns is to support the adoption of predictive maintenance by heavy vehicle operators, i.e., forecasting that there is a need for maintenance before a vehicle breaks down. Some preventive maintenance recommendations include annual battery testing after it reaches three years of age, monthly tire pressure checks, filling the tank when the fuel level is below 1/4, inspecting battery terminals for corrosion, and multipoint inspections at a repair shop before a long road trip [<a href="#B57-sustainability-12-08244" class="html-bibr">57</a>].</div></section><section id='sec5dot5-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 5.5. Weather Variables</h4><div class='html-p'>NSW is typically warm, with summer temperatures reaching 40 °C. Increased breakdowns are observed in the dataset with increasing temperature. This can be explained by the overheating of engines and increased use of air conditioners. In contrast, more breakdowns are observed during cold weather in the UK, where heaters are used more often, thus placing extra strain on the vehicle’s battery [<a href="#B56-sustainability-12-08244" class="html-bibr">56</a>].</div><div class='html-p'>Rainfall has an adverse effect on the number of breakdowns. This could be due to the reduction in speeds and careful driving by motorists on wet pavements to avoid driving on potholes [<a href="#B59-sustainability-12-08244" class="html-bibr">59</a>]. Furthermore, adverse weather deters travelers, decreasing vehicle-kilometers traveled (exposure) and, therefore, the expected frequency of breakdowns. However, rainfall also accelerates road damage, such as potholes, which might result in increased breakdowns. Additionally, the amount of rain over a month will operate on the frequency of breakdowns with different mechanisms than the presence of rain at the time of the breakdown, so it is important to consider the relevance of the explanation to the units of observation used in this model. The impact of weather on breakdowns is complex and is ripe for further study.</div></section><section id='sec5dot6-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 5.6. Holidays and Other Variables</h4><div class='html-p'>Congestion is reduced during the school recess, with some commuters going on a vacation and some making fewer trips than usual due to caretaking responsibilities. This reduces the overall VKT exposure and, ultimately, the frequency of breakdowns. Moreover, people going for road trips during school holidays might assess the vehicle’s condition to ensure comfort and safety. These factors impact breakdown frequency, as evidenced by the negative sign of the parameter. An additional school holiday every month could reduce the total breakdowns by 0.70% when the other variables do not change.</div><div class='html-p'>However, the number of public holidays was found to have a positive effect on breakdowns. The range of public holidays was narrower (minimum = 0 and maximum = 3) than the number of days of school holidays in any month in the dataset (minimum = 0 and maximum = 18). One explanation is that many residents take advantage of public holidays by staying at home and leaving their vehicle stationary. An RAC study found that more breakdowns occur during Monday morning peak hours, as commuters return to their cars after leaving them stationary for the weekend [<a href="#B56-sustainability-12-08244" class="html-bibr">56</a>]. Public holidays may fill the same role as a weekend, causing vehicles to go unused for one or more days and resulting in an increase in breakdowns when the vehicles are called into action again.</div></section><section id='sec5dot7-sustainability-12-08244' type=''><h4 class='html-italic' data-nested='2'> 5.7. Insignificant and Correlated Variables Not Considered in the Final Model</h4><div class='html-p'>The variables indicating the percentage of vehicles by fuel type (petrol, diesel, and LPG) were found to be strongly correlated with other variables and, thus, had to be omitted in the final model. For example, LPG vehicles were positively correlated with population density. The majority of taxis in NSW use LPG, and there will be more taxis registered and operating in high-density areas. Furthermore, heavy vehicles use diesel-operated engines, and strong positive correlation occurs between these variables.</div><div class='html-p'>Furthermore, the percentage of vehicles by age was omitted because of correlation issues. For example, new vehicles are negatively correlated with heavy vehicles and old vehicles are negatively correlated with population density.</div><div class='html-p'>The information on the percentage of people born overseas or percentage of people who speak a language other than English at their homes was collected to test hypotheses related to the role of migrant status. Immigrants may be unfamiliar with the geography of NSW or may be less connected to social networks. These attributes might cause these drivers to exercise additional caution by checking and maintaining their vehicles regularly. However, they were insignificant and, also, as one would expect, highly correlated with each other. Furthermore, they were individually correlated with population density because high-density areas are associated with diverse populations.</div><div class='html-p'>The income and percentage of income earners were highly correlated with the percentage of managers and professionals. Furthermore, the percentage of young adults was negatively correlated with the percentage of unrestricted driving licenses and also the percentage of managers and professionals. The fraction of managers and professionals offers better explanatory power in the model as well as better interpretability, since this information captures a complex set of attributes surrounding income, career factors, and lifestyle.</div></section></section><section id='sec6-sustainability-12-08244' type=''><h2 data-nested='1'> 6. Suggestions to Reduce Breakdowns</h2><div class='html-p'>As cities grow in size, the average vehicle kilometers travelled increase. This leaves drivers spending an increasing fraction of their time either driving or working, leaving less time available for discretionary activities, such as vehicle monitoring and maintenance. Furthermore, changing automobile technology increases the reluctance among motorists to undertake vehicle maintenance themselves, as the technology has become more electronic and complex. One intervention to manage the impact of breakdowns on congestion is to educate drivers about vehicle maintenance procedures and also encourage them to read the vehicle manuals thoroughly. Another intervention is to initiate questions regarding routine maintenance and minor repair procedures during the vehicle registration process. This strategy takes advantage of the existing interaction between vehicle owners and the local transport authority in order to investigate and internalize the costs associated with preventable breakdowns. This proactive approach could reduce the breakdown frequency and durations, and could also reduce the unnecessary call-outs to roadside assistance companies.</div><div class='html-p'>One factor touched upon in these model results is the potential contribution of vehicle reliability. Some vehicle attributes, such as newer models with vulnerable electronic components, reduce the reliability of the vehicle. On the other hand, some vehicle makes and models have earned reputations for reliability. Providing information on breakdown frequency and magnitude is a valuable step towards educating purchasers about the potential risks associated with each vehicle—in the same way that vehicle manufacturers must report on the fuel economy of their products, they could be required to identify each model’s vulnerability to breakdown. This kind of reporting is supported with the growing availability of relevant data, including big data analysis techniques and improved ITS deployment.</div></section><section id='sec7-sustainability-12-08244' type='conclusions'><h2 data-nested='1'> 7. Conclusions and Future Work</h2><div class='html-p'>Non-recurrent congestion that is caused by sudden and unpredictable occurrence of crashes, breakdowns, hazards, and adverse weather is non-trivial, and, in fact, constitutes a signficant proportion of total congestion delay. Numerous past studies have focused mainly on a single type of incident, i.e., crashes in terms of their duration, frequency, severity, and rate. Only a handful of studies have evaluated other types of incidents, which is likely due to the lack of availability of data at a large scale. In this context, the current study has been set up with an objective to understand the factors impacting vehicle breakdown frequency at a macro-level. This research was possible thanks to a large dataset of traffic incidents comprising 90,159 records over a period of 4.5 years (from January 2012 to June 2016) in the state of New South Wales, Australia.This study provides insight on various factors contributing towards regional-level breakdowns, and various interventions are suggested for the management of breakdowns and congestion. The results from this study can be employed by transport authorities, roadside assistance companies, automobile manufacturers, and mechanics to manage their involvement in on-road vehicle breakdowns. The scope of the study can be extended by including information on roadway characteristics and driving habits of the people at the SA4 level and also by better accounting for unobserved heterogeneity. The electric vehicle market is trivial in Australia, and so its impacts on breakdown frequency have not been studied in this paper.</div></section> </div> <div class="html-back"> <section class='html-notes'><h2 >Author Contributions</h2><div class='html-p'>Conceptualization, S.C. and E.M.; methodology, S.C.; software, S.C.; validation, S.C.; formal analysis, S.C.; investigation, S.C. and E.M.; resources, E.M., S.T.W. and V.D.; data curation, S.C. and E.M.; writing—original draft preparation, S.C.; writing—review and editing, S.C., E.M., S.T.W. and V.D.; visualization, S.C.; funding acquisition, S.C. All authors have read and agreed to the published version of the manuscript.</div></section><section class='html-notes'><h2 >Funding</h2><div class='html-p'>This research received no external funding.</div></section><section id='html-ack' class='html-ack'><h2 >Acknowledgments</h2><div class='html-p'>The authors thank the three anonymous reviewers and the Editor for their thorough comments and feedback which improved the quality of the manuscript.</div></section><section class='html-notes'><h2 >Conflicts of Interest</h2><div class='html-p'>The authors declare no conflict of interest.</div></section><section id='html-references_list'><h2>References</h2><ol class='html-xx'><li id='B1-sustainability-12-08244' class='html-x' data-content='1.'>Nair, D.J.; Gilles, F.; Chand, S.; Saxena, N.; Dixit, V. Characterizing multicity urban traffic conditions using crowdsourced data. <span class='html-italic'>PLoS ONE</span> <b>2019</b>, <span class='html-italic'>14</span>, e0212845. 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href="#fig_body_display_sustainability-12-08244-f001"> <img alt="Sustainability 12 08244 g001 550" data-large="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001.png" data-original="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001.png" data-lsrc="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2071-1050/12/19/8244/display" href="#fig_body_display_sustainability-12-08244-f001"></a> </div> </div> <div class="html-fig_description"> <b>Figure 1.</b> Map of New South Wales (NSW) with Statistical Area Level 4 (SA4) classification (map of Australia in the inset).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sustainability-12-08244-f001" > <div class="html-caption" > <b>Figure 1.</b> Map of New South Wales (NSW) with Statistical Area Level 4 (SA4) classification (map of Australia in the inset).</div> <div class="html-img"><img alt="Sustainability 12 08244 g001" data-large="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001.png" data-original="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001.png" data-lsrc="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g001.png" /></div> </div><div class="html-fig-wrap" id="sustainability-12-08244-f002"> <div class='html-fig_img'> <div class="html-figpopup html-figpopup-link" data-counterslinkmanual = "https://www.mdpi.com/2071-1050/12/19/8244/display" href="#fig_body_display_sustainability-12-08244-f002"> <img alt="Sustainability 12 08244 g002 550" data-large="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g002.png" data-original="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g002.png" data-lsrc="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g002-550.jpg" /> <a class="html-expand html-figpopup" data-counterslinkmanual = "https://www.mdpi.com/2071-1050/12/19/8244/display" href="#fig_body_display_sustainability-12-08244-f002"></a> </div> </div> <div class="html-fig_description"> <b>Figure 2.</b> Comparison of increases in breakdowns on motorways (<b>a</b>) and non-motorways (<b>b</b>).  </div> </div> <div class="html-fig_show mfp-hide" id ="fig_body_display_sustainability-12-08244-f002" > <div class="html-caption" > <b>Figure 2.</b> Comparison of increases in breakdowns on motorways (<b>a</b>) and non-motorways (<b>b</b>).</div> <div class="html-img"><img alt="Sustainability 12 08244 g002" data-large="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g002.png" data-original="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g002.png" data-lsrc="/sustainability/sustainability-12-08244/article_deploy/html/images/sustainability-12-08244-g002.png" /></div> </div><div class="html-table-wrap" id="sustainability-12-08244-t001"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2071-1050/12/19/8244/display" href='#table_body_display_sustainability-12-08244-t001'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2071-1050/12/19/8244/display" href="#table_body_display_sustainability-12-08244-t001"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 1.</b> Descriptive statistics of all the considered variables. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sustainability-12-08244-t001" > <div class="html-caption" ><b>Table 1.</b> Descriptive statistics of all the considered variables.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Variable</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Freq.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Mean</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Std. Dev.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Min.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Max.</th></tr></thead><tbody ><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Dependent variable:</b><br>Frequency of breakdowns</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Monthly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >416</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Exposure variables</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Logarithm of population density (per sq. km.)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI *</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.70</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.88</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−1.04</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.5</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Total registered vehicles (in 10,000)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.17</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >34.81</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Socioeconomic variables</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Income (in 10,000 AUD)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.45</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.46</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.74</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of income earners</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >51.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.47</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >43.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >59.00</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of managers and professionals</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >35.26</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >23.30</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >57.50</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of families with children aged less than 15 years</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >47.54</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >35.05</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >57.41</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of young adults (aged 19–29)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >13.39</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >25.00</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of people born overseas</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >28.06</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >14.31</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >11.80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >52.40</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of people who speak language other than English at home</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >TI</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >18.06</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.66</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >59.10</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Vehicle characteristics</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of vehicles aged less than 5 years</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >24.99</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.52</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.00</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >38.91</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of vehicles aged between 5 and 10 years</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >28.60</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.48</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >24.14</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >34.88</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of vehicles aged greater than 5 years</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >46.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.44</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >33.23</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >57.50</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of heavy vehicles</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.50</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.58</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.27</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of vehicles operated by petrol</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >80.81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >64.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >91.25</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of vehicles operated by diesel</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.40</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.20</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >35.38</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of vehicles operated by Liquefied Petroleum Gas (LPG)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Yearly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.02</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.80</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.11</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.22</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Weather variables</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average temperature (°C)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Monthly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >17.63</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >27.95</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average rainfall (cm)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Monthly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.14</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.95</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >16.47</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Driver licenses</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of drivers with learners’ licenses</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Quarterly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.22</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.41</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.46</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >9.32</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of drivers with P1 licenses</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Quarterly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.92</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.92</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.30</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of drivers with P2 licenses</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Quarterly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.24</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.13</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.64</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.91</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of drivers with unrestricted licenses</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Quarterly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >86.62</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.74</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >79.77</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >89.98</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' ><b>Other variables</b></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Number of school holidays</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Monthly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >18</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Number of public holidays</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Monthly</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3</td></tr></tbody> </table> <div class='html-table_foot html-p'><div class='html-p' style='text-indent:0em;'><span class='html-fn-content'>* TI—Time invariant.</span></div><div style='clear:both;'></div></div> </div><div class="html-table-wrap" id="sustainability-12-08244-t002"> <div class="html-table_wrap_td" > <div class="html-tablepopup html-tablepopup-link" data-counterslinkmanual = "https://www.mdpi.com/2071-1050/12/19/8244/display" href='#table_body_display_sustainability-12-08244-t002'> <img alt="Table" data-lsrc="https://www.mdpi.com/img/table.png" /> <a class="html-expand html-tablepopup" data-counterslinkmanual = "https://www.mdpi.com/2071-1050/12/19/8244/display" href="#table_body_display_sustainability-12-08244-t002"></a> </div> </div> <div class="html-table_wrap_discription"> <b>Table 2.</b> Random-effect negative binomial (RENB) model results for total vehicle breakdowns. </div> </div> <div class="html-table_show mfp-hide " id ="table_body_display_sustainability-12-08244-t002" > <div class="html-caption" ><b>Table 2.</b> Random-effect negative binomial (RENB) model results for total vehicle breakdowns.</div> <table > <thead ><tr ><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Variable</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Coefficient</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Std. Err.</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >z</th><th align='center' valign='middle' style='border-top:solid thin;border-bottom:solid thin' class='html-align-center' >Elasticity (% Change)</th></tr></thead><tbody ><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Year 2012</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Fixed</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Year 2013</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.167</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.016</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10.41</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Year 2014</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.131</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.020</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.67</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Year 2015</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.157</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.024</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.57</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Year 2016</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.218</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.031</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >7.02</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Logarithm of population density (per sq. km.)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.191</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.045</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.26</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.33</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Total registered vehicles (in 10,000)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.068</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.012</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.65</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.40</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average temperature (°C)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.009</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.001</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >6.35</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.17</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Average rainfall (cm)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.017</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.003</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−6.25</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.14</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of managers and professionals</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.051</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.010</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.18</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.17</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of families with children aged less than 15 years</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.062</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.016</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−3.81</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−2.87</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of heavy vehicles</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.083</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.028</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.01</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.24</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Percentage of drivers with unrestricted licenses</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.074</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.027</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−2.75</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−6.21</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Number of school holidays</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.007</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.001</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−6.09</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−0.70 *</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Number of public holidays</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.016</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >0.007</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.29</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.60 *</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Intercept</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >8.611</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >2.737</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >3.15</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >-</td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Parameter, <span class='html-italic'>a</span></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >5.241</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.578</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Parameter, <span class='html-italic'>b</span></td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >4.137</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >1.288</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Log-likelihood</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >−5150</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Akaike Information Criterion (AIC)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10,333</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr><tr ><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >Bayesian Information Criterion (BIC)</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' >10,424</td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td><td align='center' valign='middle' style='border-bottom:solid thin' class='html-align-center' > </td></tr></tbody> </table> <div class='html-table_foot html-p'><div class='html-p' style='text-indent:0em;'><span class='html-fn-content'>* The percentage of change in total breakdowns with an increase of one holiday.</span></div><div style='clear:both;'></div></div> </div></section> <section id="html-copyright"><br>© 2020 by the authors. Licensee MDPI, Basel, Switzerland. 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