Risk factors associated with truck-involved fatal crash severity: Analyzing their impact for different groups of truck drivers

Introduction: Fatal crashes that include at least one fatality of an occupant within 30 days of the crash cause large numbers of injured persons and property losses, especially when a truck is involved. Method: To better understand the underlying effects of truck-driver-related characteristics in fatal crashes, a five-year (from 2012 to 2016) dataset from the Fatality Analysis Reporting System (FARS) was used for analysis. Based on demographic attributes, driving violation behavior, crash histories, and conviction records of truck drivers, a latent class clustering analysis was applied to classify truck drivers into three groups, namely, ‘‘middle-aged and elderly drivers with low risk of driving violations and high historical crash records,” ‘‘drivers with high risk of driving violations and high historical crash records,” and ‘‘middle-aged drivers with no driving violations and conviction records.” Next, equivalent fatalities were used to scale fatal crash severities into three levels. Subsequently, a partial proportional odds (PPO) model for each driver group was developed to identify the risk factors associated with the crash severity. Results' Conclusions: The model estimation results showed that the risk factors, as well as their impacts on different driver groups, were different. Adverse weather conditions, rural areas, curved alignments, tractor-trailer units, heavier weights and various collision manners were significantly associated with the crash severities in all driver groups, whereas driving violation behaviors such as driving under the influence of alcohol or drugs, fatigue, or carelessness were significantly associated with the high-risk group only, and fewer risk factors and minor marginal effects were identified for the low-risk groups. Practical Applications: Corresponding countermeasures for specific truck driver groups are proposed. And drivers with high risk of driving violations and high historical crash records should be more concerned.     

Factors associated with fatal accident involvement among California drivers

The primary objectives of this study were to examine characteristics of drivers involved in fatal accidents and to determine if those drivers could be distinguished from California's general driving population on the basis of prior driving record. A sample of drivers involved in 1970–1971 fatal accidents was analyzed and compared to a sample of drivers from the general driving population during the same time period. Drivers who had been drinking prior to the accident, who were considered at-fault for the accident, or whose accident occurred at night were found to have worse prior driving records than other fatal accident-involved drivers. The results also indicated that, as a whole, drivers involved in fatal accidents had worse violation and/or accident records, as well as different demographic and license characteristics than drivers in the general population. The classification functions derived to predict fatal accidents, however, did not differ greatly from regression equations that have been constructed to predict total accidents. It was therefore concluded that prediction systems keyed to total accidents will, to a large extent, also identify high-risk fatal accident drivers.     

License extensions for clean-record drivers: A 4-year follow-up

Over 4,000,000 of California's 17,000,000 licensed drivers used to come to the California Department of Motor Vehicles (DMV) annually to take written and vision tests in order to renew their driver licenses. In an effort to increase public convenience and reduce costs, extension of the license by mail was implemented for selected groups of drivers with clean records over the life of their previous licenses. Continued implementation of the program was subject to evaluation of its effect on traffic safety. Since clean-record drivers make up about 50% of the renewal population, this program made it possible for some 2,000,000 drivers annually to avoid coming to the DMV for license renewal. Two studies of program safety effects were conducted, one evaluating a 2-year extension (760,000 subjects), and the other a 4-year extension (407,000 subjects). Random assignment to a group offered extension by mail or to a control group undergoing standard renewal testing and procedures was followed by careful tracking of accident and conviction activity. During the 48-month period following mailing of renewal notices or extension offers, the extension group had a slightly higher accident rate than did the in-person renewal group — an increase of 1%, or 13 accidents for every 10,000 extension offers. Although this small increase in accident rate would translate into about 2,500 additional accident involvements per year if applied to the current volume of clean-record drivers eligible for extension, statistical tests of significance indicated that the increase could easily be due to sampling error (p>.10). A supplemental Bayesian analysis resulted in a .24 probability that there was no true increase. The administrative cost savings attributable to the extension program were conservatively estimated to be $3,000,000 per year.     

Traffic safety impacts of the Home Instruction/ Point Reduction Incentive (HI/PRI) program

The California Department of Motor Vehicles (DMV) implemented and evaluated a pilot driver improvement program involving the withholding (“masking”) from public inspection of one conviction from the driving record of qualifying drivers. To qualify for masking, the driver had to complete and return a mailed, self-administered test and remain free of traffic convictions and accidents for a period of 6 months after selection into the program. This Home Instruction/Point Reduction Incentive (HI/PRI) countermeasure was developed in two distinct versions: the Speed HI/PRI was designed for multiple violators of the 55 Maximum Speed Law (MSL), and the Negligent Operator (Neg-Op) HI/PRI was designed for drivers classified as negligent operators based on their traffic conviction record. Both HI/PRI countermeasures covered the safety and energy-saving advantages of 55-MSL compliance; the Neg-Op HI/PRI included general traffic safety material as well. The multiple 55-MSL violators were assigned at random to either the Speed HI/PRI or a no-contact comparison group. The negligent operators were assigned at random to one of four conditions: the Neg-Op HI/PRI, the existing DMV group educational meeting, a modified group meeting incorporating 55-MSL issues, or a no-contact comparison group. The Speed HI/ PRI and Neg-Op HI/PRI were each estimated to be cost-beneficial on the basis of accidents prevented. In addition, the Neg-Op HI/PRI had a larger estimated effect on accidents and lower cost than the group meeting countermeasures, which were also cost-beneficial. The coverage of 55-MSL issues in the group meeting did not appear to influence its effect in reducing either accidents or convictions. All of the countermeasures appeared to reduce subsequent convictions.     

Culpable versus non-culpable traffic accidents; what is wrong with this picture?

INTRODUCTION: It is often implicitly or explicitly assumed in traffic accident research that drivers with accidents designated as non-culpable are a random sample from the population. However, this assumption is dependent upon differences in the criterion used for culpability. If drivers are erroneously categorized by assuming randomness, results could be grossly misleading. METHOD: The assumption of randomness leads to two predictions: first, no correlation should exist between culpable and non-culpable crashes; and second, the accident groups should differ on the variables known to be associated with accidents, such as amount of driving experience. These predictions were tested in two samples of bus drivers. RESULTS: It was found that in a sample with a harsh criterion (70% culpable accidents) for crash responsibility, the drivers with non-culpable accidents had the features expected, namely, they were more experienced for example, while in a sample with a lenient criterion (50 % culpable), this was not so. DISCUSSION: It was concluded that similar studies to the present one would need to be undertaken to establish exactly what percentage of drivers in a given population should be assigned culpable accidents, and construct a criterion that yields this ratio. Otherwise, the theoretical assumptions of randomness and non-responsibility will probably be violated to some degree. IMPACT ON INDUSTRY: Many estimates of risk of crash involvement may have been wrong. Given the potential for erroneous criteria, a number of studies may make invalid assumptions from their data.     

Driver license renewal by mail in California

Drivers under the age of 70 whose prior 4-year accident and conviction records showed no entries when examined 2 months prior to the date of expiration of their driver licenses were randomly assigned to either a group that renewed licenses in the normal manner or a group that was offered the opportunity to receive a 4-year license extension by mail. A related experiment involved comparing clean-record drivers of any age who were given a 2-year extension with a group of drivers required to renew in person. Examination of driver records 18 and 28 months subsequent to extension uncovered no deleterious effects of the program, while savings of roughly 3 million dollars annually are expected. Findings are tentative, however, until 4-year data can be collected. The report concludes that the extension program has been successful, that multiple extensions should be authorized and evaluated for drivers with continuing clean records, and that the present exclusion of drivers 70 and above does not appear to be defensible.     

Evaluating the speed camera sites selection criteria in the UK

Introduction: Speed cameras have been implemented to improve road safety over recent decades in the UK. Although the safety impacts of the speed camera have been estimated thoroughly, the criteria for selecting camera sites have rarely been studied. This paper evaluates the current speed camera sites selection criteria in the UK based on safety performance. Method: A total of 332 speed cameras and 2,513 control sites with road traffic accident data are observed from 2002 to 2010. Propensity score matching method and empirical Bayes method are employed and compared to estimate the safety effects of speed cameras under different scenarios. Results: First, the main characteristics of speed cameras meeting and not meeting the selection criteria are identified. The results indicate that the proximity to school zones and residential neighborhoods, as well as population density, are the main considerations when selecting speed camera sites. Then the official criteria used for selecting camera sites are evaluated, including site length (a stretch of road that has a fixed speed camera or has had one in the past), previous accident history, and risk value (a numerical scale of the risk level). The results suggest that a site length of 500 m should be used to achieve the optimum safety effects of speed cameras. Furthermore, speed cameras are most effective in reducing crashes when the requirement of minimum number of historical killed and seriously injured collisions (KSIs) is met. In terms of the risk value, it is found that the speed cameras can obtain optimal effectiveness with a risk value greater than or equal to 30, rather than the recommended risk value of 22.     

Accident rates of drivers with bioptic telescopic lenses

The major purpose of this study was to determine the accident rate of drivers with bioptic telescopic lenses (“bioptic drivers”) in California. The bioptic driver group consisted of 229 drivers, while a randomly selected comparison sample consisted of 21,064 drivers. The 2-year total and fatal/injury accident rates of the bioptic group were normalized to the age/sex distribution of the comparison sample. Normalized accident rates for bioptic drivers were significantly greater than the corresponding rates for comparison drivers. The study also included an analysis of the driving records of bioptic drivers prior and subsequent to acquisition of telescopic lenses and an analysis of total and fatal/injury accidents for bioptic and comparison drivers with valid licenses only. It was recommended that California continue to license bioptic drivers, but with greater use of license restrictions and more stringent post-licensing control.     

Severity of accidents with hazardous materials A comparison between transportation and fixed installations

A review of accident case histories relevant to hazardous materials has been performed. From the literature, 1793 accident case histories involving hazardous materials were identified, most of them from the period 1960–1988. Of these 1793 accidents, 39% happened during transportation. In 682 accidents the consequences included fatalities, and of these 27% involved the transportation of hazardous materials. The accumulated frequency-fatality curves (so-called fN curves) have been constructed and are close to straight lines with a slope of –1, indicating that the probability of having an accident with, for instance, more than one hundred fatalities is approximately ten times lower than the probability of having an accident with more than ten fatalities. The accidents were grouped according to transportation type, and the difference between the various groups was tested using a standard χ² approach. No significant difference between fixed installations and transportation was found for accidents having consequences above three fatalities. Differences were found between Western Europe and North America and the rest of the world. Once an accident has happened, it seems to have more severe effects outside Western Europe and North America, both for transportation accidents and fixed installations. Comparison of fN curves for Western Europe and North America from different time periods did not show significant differences, indicating that once an accident has happened, it has the same probability of escalating now, as it had 20 years ago.     

Investigating the self-reported behavior of drivers and their attitudes to traffic violations

IntroductionDriving behavior theoretical models consider attitudes as an important determinant of driver behavior. Moreover, the association between the self-reported tendency to commit violations and accident involvement is widely recognized. This research investigates drivers’ self-reported behavior and attitudes to risky behaviors related to the traffic violations of speeding, drink-driving, and cell phone use using cluster analysis.MethodA sample of 601 Greek drivers participating at the SARTRE 4 pan-European survey is utilized. The analysis identified three clusters of drivers. Drivers in Cluster 1 commit traffic violations more often; drivers in Cluster 2 favor traffic violation countermeasures while having moderate views toward compliance with traffic rules; and drivers in Cluster 3 strongly support traffic violation countermeasures and also have strong views toward compliance with traffic rules. Risky behaviors and related attitudes that differentiate the three distinct groups of drivers (clusters) were determined.ResultsThe findings indicate that differences in attitudes and behaviors may be attributed to factors such as age, gender, and area of residence. The research findings also provided some insight about the current level of drivers’ attitudes to traffic violations, especially those that negatively affect traffic safety. The pattern of their views on violations may form the basis of risk behavior-related interventions tailored to the identified groups, aiming at informing, educating, and raising the awareness of the public.Impact on IndustryAgencies focused on safety interventions could exploit this information in designing and implementing education campaigns, enforcement programs and in defining relevant priorities.     

An examination of the characteristics and traffic risks of drivers suspended/revoked for different reasons

PROBLEM: Prior research has demonstrated that suspended/revoked drivers pose a significant traffic risk, but until now little has been known about whether, and if so how, this risk varies as a function of the reason for suspension/revocation. METHOD: This study classifies suspended/revoked drivers into subgroups based on their reason for suspension/revocation, and then develops demographic and driving record profiles for each group. Separate driving record profiles are developed for the following traffic safety indicators, measured 3 years prior to the suspension/revocation action: (a) total crashes, (b) fatal/injury crashes, (c) total traffic convictions, and (d) total incidents (crashes + convictions). RESULTS: The findings clearly show that: (a) suspended/revoked drivers are a heterogeneous group, both demographically and in their driving behavior; (b) some suspended drivers, such as those suspended/revoked for a non-driving offense, have low traffic risks that are not much higher than those of validly-licensed drivers, and; (c) all suspended groups have elevated crash and conviction rates, compared to validly-licensed drivers. DISCUSSION: The implications of these findings for current laws and policies targeting suspended/revoked drivers are discussed, and recommendations for improving these laws/policies are presented. IMPACT ON INDUSTRY: None.     

对“安全驾驶适应性测验”的可行性研究

重点对“安全驾驶适应性测验”的信度和效度进行了研究和检验。通过对３１０ 名汽车驾驶员的答卷资料所处理结果表明：事故群驾驶员和非事故群驾驶员的心理品质差异主要表现在观察能力,判断能力,推断能力,辨别能力,思维的灵活性,注意的广度与稳定性,个性方面的安全驾驶态度,情绪的稳定性及是否过分自信等方面。另外,对年龄、文化程度、驾驶经验与事故率之间关系的考查表明,年龄与事故率之间的相关程度是十分显著的。说明该测验对于识别事故群驾驶员和非事故群驾驶员具有一定的区分性和预测性。     

Factors and challenges of driving reduction and cessation: A systematic review and meta-synthesis of qualitative studies on self-regulation

Introduction: Older adults are at a greater risk of injury and death in a motor-vehicle accident. While the ability to drive safely can be challenging with aging, the concept of self-regulation and associated support system have attracted more attention in recent years, especially in developed countries. This review describes the mechanism and summarizes the potential factors that influenced self-regulation of driving amongst older adults to provide new insights into a broader framework for transportation and safe mobility. Methods: We systematically searched 12 online databases for qualitative studies exploring the experiences of older adults aged 60 years and above on their decision to self-regulate their driving. Thematic synthesis was performed to identify elements influencing driving reduction and cessation. The confidence profile of each findings from the meta-synthesis was appraised using the Confidence in the Evidence from Reviews of Qualitative research (CERQual) tool. Results: A total of 17 studies representing views of 712 older adults from four countries were included. Three major themes were identified with each representing a transition phase that can either facilitate or hinder older drivers from ceasing completely or reducing their driving, when transitioning from pre-decision phase to post-cessation phase. Conclusions: Our findings suggest that there is a mismatch between the current traffic collation prevention measures, such as age-specific mandatory license renewal system and travel needs of older adults. As such, it is time for the authorities, researchers, and public from various fields and perspectives to collaborate, sustain, and improve safety and mobility in older adults. Practical applications: Adequate regulations and guidelines from the medical community and legal authorities are warranted to assist older adults and caregivers. Social support (e.g., feedback, assurance, or transportation support) from family members, friends, and healthcare professionals are crucial for a smooth transition. Provision of alternative transportations in rural areas are needed and future interventions should focus on engaging and educating older adults to consider alternative transportation modes for mobility. Age-specific mandatory license renewal procedure can be useful in screening for at-risk groups.     

Developing and testing a hazard prediction task for novice drivers: A novel application of naturalistic driving videos

Introduction: Novice drivers’ inability to appropriately anticipate and respond to hazards has been implicated in their elevated crash risk. Our goal was to develop a driving hazard prediction task using naturalistic videos from the U.S. context that could distinguish between novice and experienced drivers. Method: Using the query builder from the SHRP 2 InSight Data Access Website, we identified a sample of 1034 videos for further review. Task criteria reduced these to 30 videos of near-crash events that were split into event and non-event segments and were used to develop the driving hazard prediction task (task). Participants, aged 16–20 years-old (22 novice and 19 experienced drivers) completed the task during which they watched event and non-event videos and were asked, “How likely was the driver of this car to get into a crash?” after each video. Overall ratings for hazardousness were calculated for experienced and novice drivers as well as a group difference score for hazardousness. Results: All participants rated event videos as more hazardous than non-event videos, but there was no main effect of group. Rather, there was a significant EventbyGroup interaction in which there were no group differences in hazard ratings for non-event videos, but experienced drivers rated event videos as more hazardous than novice drivers. Specific characteristics of the event videos, such as the hazard development period, were related to differences between novice and experienced drivers’ hazardousness ratings. Conclusion: To the best of our knowledge, this is the first use of naturalistic driving videos from an existing database as experimental stimuli. We found that the task discriminated between novice and experienced drivers’ ratings of hazardousness. This distinction suggests naturalistic driving videos may be viable stimuli for experimental studies. Practical Applications: The application of naturalistic driving video database for experimental research may hold promise.     

Influence of personality traits on aberrant driving behaviors: A comparison of Japanese,Chinese, and Vietnamese drivers

Introduction: This study aims to explore the influence of Big Five personality traits in combination with various socio-demographic factors and experiences of accident involvement on aberrant driving behaviors. The study also compares the effects of the level of development (i.e., developed or developing) of three countries on the personality traits and driving behaviors. Method: The four-factor Driver Behavior Questionnaire was used to collect data on aberrant driving behaviors, while a short version of the 10-item Big Five Inventory was used to collect data on personality traits. Responses were collected from Japan (1,250 responses), China (1,250), and Vietnam (1,000). A latent variable model was applied after controlling data in each category (e.g., age). Results: This study revealed that respondents who experienced accidents in the past and scored higher on Agreeableness were less likely to commit aggressive violations in Japan, China, and Vietnam. Further, Japanese and Vietnamese female drivers who scored high on Conscientiousness were found to be less likely to commit ordinary violations. Neuroticism was positively correlated with aggressive violations only in the case of Vietnamese drivers, irrespective of the history of accident involvement. Conclusions: Drivers with particular personality types that are linked with aberrant driving behavior may need to receive additional training on behavior management. Practical Applications: This study may help road traffic policymakers predict future driving behaviors of Vietnamese and Chinese drivers based on those of Chinese and Japanese drivers, respectively, and act accordingly.     

汽车驾驶员行车事故神经行为学方法研究的多因素分析

采用世界卫生组织“神经行为核心测试组合”（ＷＨＯ．ＮＣＴＢ），对１２５名汽车驾驶员进行了神经行为功能测试，并对测试结果及方法作了进一步的一元和多元回归分析。结果表明：事故组与无事故组驾驶员在神经行为功能方面存在显著差异。神经行为功能测试总分与年龄和事故次数是显著负相关，与学龄呈显著正相关。在ＮＣＴＢ各分测验中，简单反应时、目标追踪和提转捷度三项测验得分对总分贡献率较大，为最敏感指标。揭示在驾驶员行车事故的预防及职业选择和培训中，应考虑年龄因素和文化水平，并选择敏感指标进行神经行为功能测试，以预防和减少交通事故的发生。     

Continued trends in older driver crash involvement rates in the United States: Data through 2017–2018

Introduction: With the growing older adult population due to the aging baby-boom cohort, there was concern that increases in fatal motor-vehicle crashes would follow. Yet, previous analyses showed this to be untrue. The purpose of this study was to examine current trends to determine if previous declines have persisted or risen with the recent increase in fatalities nationwide. Methods: Trends among drivers ages 70 and older were compared with drivers 35–54 for U.S. passenger vehicle fatal crash involvements per 100,000 licensed drivers from 1997 to 2018, fatal and all police-reported crash involvements per vehicle miles traveled using the 1995, 2001, 2009, and 2017 National Household Travel Surveys, and driver deaths per 1,000 crashes. Results: Since the mid-1990s, fatal crashes per licensed driver trended downward, with greater declines for drivers ages 70 and older than for middle-aged drivers (43% vs. 21%). Fatal crash rates per 100,000 licensed drivers and police-reported crash rates per mile traveled for drivers ages 70–79 are now less than those for drivers ages 35–54, but their fatal crash rates per mile traveled and risk of dying in a crash remain higher as they drive fewer miles. As the economy improved over the past decade, fatal crash rates increased substantially for middle-aged drivers but decreased or remained stable among older driver age groups. Conclusions: Fatal crash involvements for adults ages 70 and older has recently increased, but they remain down from their 1997 peak, even as the number of licensed older drivers and the miles they drive have increased. Health improvements likely contributed to long-term reductions in fatal crash rates. As older drivers adopt vehicles with improved crashworthiness and safety features, crash survivability will improve. Practical Application: Older adults should feel confident that their independent mobility needs pose less risk than previously expected.     

Behavior and lifestyle characteristics of male Kuwaiti drivers

Introduction: The high traffic accident risk among young drivers is a well-known and well-documented fact in most countries. Lifestyle has proven to affect driving behavior as well as accident risk. This study covers the lifestyle component of the problems related to young male Kuwaiti drivers’ accident risk. Methods: The purpose of the study is to measure the relationship between lifestyle and accident risk. Lifestyle is measured through a questionnaire, where 302 male Kuwaiti drivers (mean age = 28 years; range 25-35 years) answer 39 questions related to behavioral and social factors, road conditions, police enforcement, and life satisfaction. They also report their involvement in accidents and traffic violations. Results: The questionnaire's validity and reliability (Cronbach's alpha = 0.7) were achieved. Principal component analysis reduced the 39 items on the questionnaire to 5 factors. Inadequate police enforcement is strongly correlated (r = 0.862) to accident risk and traffic violations and is thus considered the best predictor of traffic accidents in Kuwait. Impact on Industry: As driving-related incidents (on-the-job and off-the-job) are a significant source of fatalities and lost-work-days, the study points to the importance of considering cultural factors in the design of comprehensive safety programs for industry.     

Driver distraction by digital billboards? Structural equation modeling based on naturalistic driving study data: A case study of Iran

Introduction: Digital billboards (DBs) are a competing factor for attracting drivers’ attention; evidence shows that DBs may cause crashes and vehicle conflicts because they catch drivers’ attention. Because of the complexity of a system that includes road conditions, driver features, and environmental factors, it is simply not possible to identify relationships between these factors. Thus, the present study was conducted to provide a well-organized procedure to analyze the effects of DBs on drivers’ behavior and measure factors responsible for drivers’ distraction in Babol, Iran, as a case study. Method: Corresponding data were collected through a Naturalistic Driving Study (NDS) of 78 participants when facing DBs (1,326 samples). These data were analyzed by applying structural equation modeling (SEM) to concurrently recognize relationships between endogenous and exogenous variables. Human, environmental, and road factors were determined as exogenous latent variables in a model to evaluate their influences on drivers’ distraction as an endogenous variable. Results: The results showed that road, environmental, and human factors reciprocally interact with drivers’ distraction, although the estimated coefficient of human factors was more of a factor than that of the other groups. Furthermore, younger drivers, beginner drivers, and male drivers (as human factors); night and unclear weather like a rainy day (as environmental factors); and installing DBs at complicated traffic positions like near-intersections (as road factors) were determined to be the main factors that increase the possibility of drivers’ distraction. Finally, model assessment was suggested using the goodness-of-fit indices.     

Investigating lane change behaviors and difficulties for senior drivers using naturalistic driving data

Introduction: Lane changes can be a complicated maneuver occurring a dynamic environment requiring the integration of many streams of information. Older drivers may struggle with lane changes which may elevate crash risk. Methods: Real-world lane change behaviors were examined using the Second Strategic Highway Research Program Naturalistic Driving Study database. A total of 393 lane changes were observed for two age groups: middle-aged (30–49), and older (70+) drivers. Results: Older drivers were highly likely to fail to execute an over-the-shoulder glance prior to initiation of a lane change (in 98% of left lane changes and 92% for right lane changes). Older drivers also showed higher rates of OTS glance errors at any point during the lane change in 95% of left lane changes and 86% of right-lane changes. Additionally, older drivers frequently failed to activate the turn signal prior to lane change initiation (60% of lane changes for right changes and 59% for left lane changes). Of the older drivers that made side mirror glances, many occurred after the initiation of the maneuver (46% of left lane changes and 58% of right lane changes) suggesting glances were occurring while changing lanes. Conclusions: Results for older drivers showed that many key glances (particularly side mirror checks) and turn signal actuations observed in the current study occurred after the initiation of the lane change, ostensibly when this action may be too late to gather relevant information and avoid a conflict. Practical Applications: Knowledge of glance patterns during lane changes for older drivers can help older drivers maintain travel mobility as they age. Either through training to reinforce OTS and side mirror glances, or supplemental devices like convex mirrors or oversized rearview mirrors, older drivers can reduce high-risk lane change maneuvers and help older drivers to maintain their mobility and independence longer.