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category: literaturenote citekey: haodomotoristsselectsafe2025 title: Do motorists select safe routes over efficient routes? An empirical study using travel trajectory data authors: "Hao, Wei; Liu, Fang; Han, Chunyang; Pervez, Amjad; Wang, Kai; Chen, Jie; Tang, Jinjun" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.aap.2025.108090 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2025.108090" zotero_key: BTHD6MNV zotero_storage: SHEX8GMW collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Hao, Wei"
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Accident Analysis and Prevention
journal homepage: www.elsevier.com/locate/aap
Do motorists select safe routes over efficient routes? An empirical study using travel trajectory data
Wei Hao a , Fang Liu a , Chunyang Han b,c,* , Amjad Pervez d , Kai Wang e , Jie Chen f , Jinjun Tang d
- a School of Transportation Engineering, Changsha University of Science and Technology, Changsha 410205, China
- b Faculty of Transportation, Kunming University of Science&Technology, Kunming, Yunnan 650500, China
- c Yunnan Modern Logistics Engineering Research Center, Kunming University of Science&Technology, Kunming, Yunnan 650500, China
- d Smart Transport Key Laboratory of Hunan Province, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China
- e ZTE Corporation, Shenzhen 518057, China
- f Yunnan Infrastructure Investment Co Ltd, Yunnan 650000, China
ARTICLE INFO
Keywords: Safety route choice Motorists Paired scenario comparison Random parameters logit regression Vehicles travel trajectory
ABSTRACT
Studies have highlighted the importance of traffic safety concerns in travelers' mode choices. However, little attention has been given to route choices between safety and efficiency. This study aims to investigate motorists' safety route choice behavior using vehicle trajectory data collected by the Automatic License Plate Recognition (ALPR) system in Changsha, China. A paired scenario comparison (PSC) method is proposed to examine motorists' safety route choice behaviors by contrasting the choices under two scenarios across a large-scale city area. Specifically, four scenarios are considered, including daytime/nighttime, work/non-work, livelihood/non-livelihood, and short-distance/long-distance travel. Motorists' route choice preferences are hypothesized to differ between paired scenarios. Motorists' route choices are depicted by the Group Random Parameters Logit (GRPL) model with a set of route safety and efficiency attributes. Hypotheses are tested through an overall model validation and a series of scenario-specific model validations. Results demonstrate the significance of motorists' priority of the routes with safety attributes (e.g., fewer intersections, wider roads) during nighttime trips or for non-livelihood purposes. However, evidence for work/non-work and trip distance effects remains inconclusive. This study provides empirical support for safety-oriented route planning and navigation systems.
1. Introduction
In the past decades, researchers have extensively studied travel route choice in the literature of behavior interpretation and modeling. Most of these studies have focused on the assumption that travelers make decisions based on least-time–cost criteria or other time-effective factors, such as avoiding congestion and seeking high reliability (Carrion and Levinson, 2013; Moghaddam et al., 2019). However, recent studies have shown that travelers also consider their safety and express concerns about being involved in road crashes while making route decisions (Nordfjærn et al., 2021; Rundmo et al., 2011; Roche-Cerasi et al., 2013; Kummeneje and Rundmo, 2019; Huang et al., 2020; Han et al., 2023).
Rundmo and his co-workers have defined transport risk perception as "subjective evaluations of probability and potential severity of consequences of accidents or security incidents in transport" (Nordfjærn et al., 2021). Their studies provided valuable insights into the role of risk perception in travelers' transport mode selection. They found that travelers who rely more on active modes (walking and cycling) and public transport perceived lower crash risk than those who primarily use private modes (Rundmo et al., 2011; Roche-Cerasi et al., 2013). They further revealed that perceived risk level can vary with the time day and seasons (Kummeneje and Rundmo, 2019). Other studies have confirmed similar findings (Muraleetharan et al., 2005; Tribby et al., 2016; Evans et al., 2022). Although, safety concerns may not always be the primary factor in travelers' decisions compare to time concerns, its potential impact on travel choices cannot be disregarded when interpreting and modeling travelers' behavior.
Recently, there has been an increasing focus on bicyclists' route choices under safety concerns. Studies (Shan and Cherry, 2021) have concluded that bicyclists are willing to take detours to avoid historic
* Corresponding author at: Faculty of Transportation, Kunming University of Science&Technology, Kunming, Yunnan 650500, China. E-mail address: sandiant@foxmail.com (C. Han).
crash locations, and regular bicyclists are more inclined to take longer detours compare to casual bicyclists. Other studies (Weinstein Agrawal et al., 2008; Sener et al., 2009) found that factors related to the built environment and road network attributes, such as the presence of separated bicycling lanes, speed limits and on-street parking characteristics, significantly influence bicyclists' safety concerns. Moreover, some studies (Heinen et al., 2010) found that bicyclists' demographic characteristics, such as gender, age, and biking experience, are correlated with their concerns of route safety. However, very few studies have devoted to specifically investigating the safety route choice behavior of motorists. The findings from above bicyclist studies cannot be directly used to represent the characteristics of motorists' safety route choice behaviors.
Several studies have begun investigating motorists' safety route choices, but the focus has been on modeling the behavior. For instance, Huang et al. (2020) used reliability theory to depict motorists' safety route choice behavior. In this study, motorists are assumed to estimate the safety of a route by perceiving its safety reliability. This safety reliability is mathematically represented by a random value that follows a certain probability distribution. The model was later extended by incorporating a time-distance-based risk measurement (Teng et al., 2022). Han et al. (2023) further upgraded the model to accommodate joint choices related to speed safety and route safety. While previous studies have made significant efforts to behavior modeling, there remains a lack of empirical evidence demonstrating motorists' safety route choice behavior. More important, it is still unclear which factors would significantly affect their safety route choice behavior. Addressing these questions will not only assist traffic operators and managers in comprehensively understanding motorists' route choice behavior and guiding them toward safer routes, but will also contribute to the field of travel behavior modeling, especially in enhancing the precision of safety-oriented choice behavior modeling.
Moreover, most existing literature on safety-concerned travel behavior has relied on conventional survey methods to collect data, such as self-reported stated preference (SP) and revealed preference (RP) surveys (Weinstein Agrawal et al., 2008; Evers et al., 2014; Muraleetharan et al., 2005; Sener et al., 2009; Shah and Cherry, 2021). While these methods are effective for mode choice data collection by directly query respondents' motivations, they are not well-suited for gathering route choices data due to potential bias among travelers between their responses and actual behaviors (Hanley, 1961; Koller et al., 2023; Broach et al., 2012; Carrion and Levinson, 2013; Dhakar and Srinivasan, 2014; Ribeiro et al., 2014; Cools et al., 2024). The difficulty in replicating real-world scenarios is a primary cause of such response biases. Motorists typically make route decisions based on their long-term experience, which is deeply influenced by the features of road infrastructure and traffic conditions. However, in SP surveys, many salient features of a route are sure to be missing in a hypothetical scenario. There is a high possibility of bias among motorists when they are asked to assess route safety in such a hypothetical scenario. Self-report bias is another important cause for the discrepancy between the responses and behaviors. It has been found to correlate with many factors, including social desirability (Hanley, 1961; Francisca, 2008; Caputo, 2015; Krohn et al., 2011), biased memories (Norman et al., 1987), and unconscious uncertainty (Stone and Moskowitz, 2011; Yas¸ar, 2022; Koller et al., 2023).
Automatic License Plate Recognition (ALPR) provides a promising alternative to the self-reported survey. ALPR system can automatically identify vehicles in images or real-time video (Du et al., 2013; Hadavi et al., 2020), and has been used to trace vehicles on the network and reconstruct their trip trajectories. Unlike "hypothesis-based" SP surveys, ALPR provides data that reflects motorists' actual route choices and the state of the real traffic the motorists encounter when selecting routes. This data-driven approach can be viewed as a superior form of the traditional RP survey, as it can collect a wealth of detailed and precision trip level data, such as travel time and distance, origin and destination
pair with link-by-link trajectory, rather than relying on motorists' experiences or recollections. The superiorities in authenticity and accuracy of ALPR data collection method make it a valuable tool for investigating travel behaviors, especially for route choice behavior. This study uses the ALPR data to extract motorists' route choice data. The ALPR data allows to examine motorists' preference of route selection under the hypothetical scenarios. The results could help reveal whether travelers are likely to choose safe routes over efficient routes.
The present study aims to investigate motorists' safety route choice behaviors. The Group Random Parameters Logit (GRPL) model, a type of random parameters route choice model, is employed to depict motorists' route choice behaviors. The strength of the GRPL model lies in its ability to capture individual heterogeneity by accounting for variations in how travelers respond to route attributes due to unobserved factors. This feature is especially important, as it offers a more realistic representation of the diversity in motorists' preferences compared to traditional models. The modeling process follows a three-step approach. First, an overall analysis is conducted using a two-level GRPL model. The first level represents the utility of a route based on safety and efficiency attributes, while the second level captures the influence of contextual (scenario-specific) factors on these attributes. Second, scenario-specific analyses are performed. For each of the four paired scenarios—daytime vs. nighttime, work-related vs. non-work-related, livelihood vs. non-livelihood, and short-distance vs. long-distance—three Random Parameters Logit (RPL) models are estimated: one focusing on safety attributes, one on efficiency attributes, and one hybrid model combining both. Finally, multi-sample cross-validation is conducted to assess the robustness and reliability of the model results.
The study seeks to answer two questions: 1) Do motorists select safe routes over efficient routes? and 2) Which factors significantly impact motorists' safety route choice behaviors? To achieve this, a large-scale vehicle routing traces dataset collected by the ALPR system in Changsha city, China, is used. A series of route-specified factors that have been found to associate with motorists' safety route choices in previous studies is selected to model the route safety. The random parameters Logit (RPL) model is adopted as the behavior modeling approach. Moreover, a Paired Scenario Comparison (PSC) method is proposed to examine motorists' safety route choice behaviors by assuming their choices to be different between two paired scenarios.
The remainder of this paper is organized as follows. Section 2 summarizes and discusses the relevant studies. Section 3 develops the research hypotheses. Section 4 introduces the collected ALPR data and presents its processing for trajectory reconstruction. Section 5 describes the RPL model with its specification and introduces the research strategy. The results are presented and discussed in Section 6. Section 7 concludes the study and discusses its limitations and future directions.
2. Literature review
2.1. Route choice criterion
Most existing studies on route choice often assume that travelers prioritize the shortest time or distance when choosing the optimal routes. However, numerous empirical studies have demonstrated the significance of time reliability in travelers' route choice behavior. For example, Jackson and Jucker (1982) conducted a SP survey for 214 Stanford University employees. They highlighted that participants might favor more time-reliable routes, even if those routes have longer expected travel times. Abdel-Aty et al. (1997) adopted two SP methods and collected route preference data from 707 commuters. The results also supported the above conclusion by showing the importance of time reliability in route preferences.
However, studies have found the limitations of the SP survey techniques in route choice data collection. For example, Carrion and Levinson (2013) argued that in SP surveys, the lack of realism in the hypothetical route selection scenarios could cause discrepancies
between participants' responses and their actual choices. They also noted that the self-reported SP survey cannot collect the data on variables that require field measurements. To overcome the limitations, device-aided survey methods were implemented to collect trip data, such as GPS-aided methods (Dhakar and Srinivasan, 2014; Chen et al., 2017) and ALPR-based methods (Chen et al., 2013; Arefkhani and Shafahi, 2023). These methods provide real trip data that reflect individual's accurate route choices, thus avoiding the influence of human error in self-reporting.
Studies (Shah and Cherry, 2021) have revealed that travelers consider more than just time efficiency or cost-effectiveness in route choices; health, environmental friendliness, and safety are equally crucial considerations. Active travelers (i.e., cyclists and pedestrians) are the groups who prioritize health and environment-related factors. For example, Kim and Gong (2023) surveyed 164 residents in Daegu, South Korea, and found that most respondents preferred healthier walking routes over the shortest options. Gaker et al. (2010, 2011) conducted two investigations using data collected from 312 undergraduate students at the University of California. They demonstrated that participants are willing to adjust routes to reduce emissions.
Several earlier studies have attempted to explore safety-concerned route choices among pedestrians (Weinstein Agrawal et al., 2008; Evers et al., 2014). Evidence indicates that pedestrians are more likely to select routes perceived as safer. Traffic safety emerges as a key determinant influencing their risk perception (Evers et al., 2014; Tribby et al., 2016). Some pedestrians prioritize safety over the shortest distance (Weinstein Agrawal et al., 2008). Notably, safety concerns could vary with the time of day (Tribby et al., 2016) and across seasons (Muraleetharan et al., 2005). Recent studies have also examined bicyclists' route safety concerns (Sener et al., 2009; Broach et al., 2012; Chen et al., 2017). Shah and Cherry (2021) found that some bicyclists also give prioritization to the routes that they perceived as safer. Studies indicated that built environment features, including posted speed limits (Chen et al., 2017), street lighting (Chen et al., 2017), bicycle facility type (Broach et al., 2012; Chen et al., 2017), and separated bicycle lanes on bridges (Broach et al., 2012), and motor traffic characteristics, such as traffic volume and traffic composition (Broach et al., 2012; Sener et al., 2009), impact bicyclists' route choices.
2.2. Route choice modeling for safety
Discrete choice models rooted in random utility maximization theory have been extensively employed to depict travel route choice behaviors (Frejinger and Zimmermann. 2021). The multinomial logit (MNL) model proposed by McFadden (1974) is the simplest among these models. However, studies unveiled the inability of the MNL model to capture route similarities within network configurations (Prashker and Bekhor, 2004). To address this, Cascetta et al. (1996) proposed the C-Logit model, introducing a commonality factor to gauge route similarity. Ben-Akiva and Bierlaire (1999) developed a path-size model to account for the between-route similarity problem. The path-size is a correction term similar to the commonality factor, but the logit model containing the path-size term outperforms the C-Logit model for the fitting results (Prato and Bekhor, 2006). Another limitation of the MNL model is that it does not account for the possible correlations between path utilities in the stochastic part of the utility function. To address this, solutions like the paired combinatorial logit model (Pravinvongvuth and Chen, 2005), the cross-nested logit model (Vovsha and Bekhor, 1998), and the random parameters Logit (RPL) models (Bekhor et al., 2002) were proposed. Among these models, the RPL model better captures the heterogeneities in the data (Prato, 2009). Therefore, in the present study, the path-size RPL model is adopted for safe-route choice modeling.
The advancements in empirical investigations on travelers' route choice criteria prompt the development of behavior modeling research. Earlier studies constructed the models based on the assumption of timeminimization choice criteria (Wardrop, 1952). However, as the significance of traveler's time reliability concern emerged, researchers began to develop models that depict travel time reliability (variability) perception during route selection (Uchida and Iida, 1993; Lo et al., 2006). The concept of travel time budget (TTB) introduced by Lo et al. (2006) has gained widespread acceptance in the realm of travel time reliability behavior modeling (Shao et al., 2006; Siu and Lo, 2006). Further, Chen and Zhou (2010) proposed the mean-excess travel time (METE) equilibrium model, an extension of the TTB model, considering travelers' perception of unreliability stemming from travel time variability.
Recent studies in route choice modeling have begun to address safety-driven travel decisions (Li and Huang, 2019; Huang et al., 2020; Han et al., 2023). However, modeling travelers' safety route choice behavior is challenging. Li and Huang (2019) quantified road safety conditions with specific values derived from historical crash frequency data. However, given that road safety varies over time, a single value might not be appropriate for quantification (Mannering and Bhat, 2014). Huang et al. (2020) employed the value-at-risk measure to define travelers' perception of road safety, defining safety level as a probability distribution (i.e., route safety reliability) rather than a specific value. Han et al. (2023) extended the safety-reliability route choice model by considering travelers' concerns about safe speed and the corresponding choices.
2.3. Traveler risk perception
Previous research has identified a diverse array of factors associated with travelers' risk perception, which can be broadly categorized into three groups: travelers' characteristics, road attributes, and environmental conditions. Table 1 and presents a comprehensive overview of these factors.
Among the traveler characteristics, age, gender and driving experience are the motorist's characteristics reported to affect the risk perception. Notably, driving experiments assessing en-route risk perception have highlighted distinctions between age groups. Younger drivers exhibit slower response times to risk compared to mid-age drivers but are faster than older drivers (Quimby and Watts, 1981; Feng et al., 2018). In the pre-trip planning stage, older drivers tend to make more cautious choices when anticipating potential risks than their younger counterparts (Underwood et al., 2005). In terms of gender, literatures have reached a common conclusion that female drivers are less prone to risk than male travelers in driving behavior, since male drivers' perception of their susceptibility to the risk is higher than female drivers (Davidson and Freudemberg, 1996; Bine et al., 2006; Rosenbloom and Beigel, 2011; Salducco et al., 2022; Zhao et al., 2025; Meng et al., 2025). Moreover, studies reported that experienced drivers had significantly faster and more accurate risk detection abilities than novice drivers (Isler et al., 2009; Crundall et al., 2012), and are adept at recognizing potential risks (Evans et al., 2020). This might explain the observation that less experienced drivers tend to perceive traffic risk as lower than their more experienced counterparts (Evans et al., 2020, 2022).
Road- and traffic-related attributes have been found to have significant influence on travelers' risk perception. For example, many studies have reported the effect of road line type (curves) and road width on risk perception (Kanellaidis and Dimitropoulos, 1994; Charlton et al., 2014; Evans et al., 2020). Charlton et al. (2014) conducted three risk rating experiments and found that road curves and width are the factors affecting participants' judgements of driving risk. This finding supports the earlier studies that found the presence of curves (Kanellaidis and Dimitropoulos, 1994) and narrow roads (Watts and Quimby, 1980) associate with higher risk perceptions. Moreover, Charlton and Starkey (2016) found that the risk ratings had a significant correlation with the type of centerlines, especially under high traffic volume conditions. Payyanadan et al. (2017) examined the driving challenges facing older
Table 1 A summary of variables that affect drivers' traffic risk perception.
| Variables | Findings |
|---|---|
| Driver characteristics | |
| Age | Older drivers were significantly less accurate and slower at-risk perception than younger drivers (Quimby and Watts, 1981; Underwood et al., 2005; Feng et al., 2018). |
| Gender | Female travelers are less prone to risk than male travelers (Davidson and Freudemberg, 1996; Bine et al., 2006; Rosenbloom and Beigel, 2011; Salducco et al., 2022). |
| Driving experience | Experienced drivers had significantly faster and more accurate risk detection compared to novice drivers (Isler et al., 2009; Crundall et al., 2012). |
| Road and Traffic Attributes | |
| Road line type | Curves were the most frequently mentioned road feature in participant reports that caused the increase in risk ratings (Watts and Quimby, 1980; Kanellaidis and Dimitropoulos, 1994; Charlton et al., 2014; Evans et al., 2020; Starkey and Charlton, |
| Road width | 2020). Narrower roads increase the risk rating of drivers on the road (Watts and Quimby, 1980; Charlton et al., 2014). |
| Median type | There was a significant correlation between the median type and driver's risk perception (Charlton and Starkey, 2016). |
| Intersection density | Dense intersections increase the risk rating of drivers on the road (Basu et al., 2022). |
| Left turn and U-turn | Background survey supports senior drivers think left turns and U-turns have a higher risk |
| Speed limit | (Payyanadan et al., 2017). Lower speeds limits are associated with higher safety levels (Sener et al., 2009; Chen et al., 2017). |
| Traffic state | Interact with road factors to influence travelers' risk perception. Increase in risk perception is associated with higher traffic volume or speed. |
| Environmental conditions Road surface conditions (wet or dry associated with weather conditions) |
Wet road conditions increase the drivers' perceived risk of accidents. Drivers perceive higher risks when driving on snow-covered roads (Muraleetharan et al., 2005; Kilpel¨ ainen and Summala, 2007). |
| Visibility | Poor visibility often increases a drivers' risk rating on the road (Evans et al., 2020, 2022). |
motorists and found that older drivers avoided left turns, U-turns, and uncontrolled intersections because of more difficulty and risky for driving. Basu et al. (2022) investigated the influence of intersection density on drivers' risk perception by conducting a driving simulation experiment. The results indicated a positive correlation between intersection density and drivers' perceived risk in rural roads. Several empirical studies also demonstrated the effects of speed limits on travelers' risk perception by using SP surveys (Sener et al., 2009; Chen et al., 2017). Rankavat and Tiwari (2016) reveal that road and traffic features interact to influence how pedestrians perceive traffic safety. For example, they found that roads with fewer number of lanes and lower traffic speed is safer as perceived by pedestrians. However, they trend to perceive high risk when the traffic is congested (traffic volume increases).
Environmental conditions, including roadway surface conditions (dry or wet) and visibility (day or night), were found to impact travelers' risk perceptions. Kilpelainen ¨ and Summala (2007) conducted a study in Finland using a questionnaire to explore adverse weather effects on motorists' behavior. The results indicated that perceptions of crash risk
heightened with increased slipperiness risk due to adverse weather. Similarly, Hjelkrem and Ryeng (2016) explored the influence of environmental factors on risk perception using the behavior observation data collected on a rural road in Norway. They found that drivers perceived higher crash risk when driving on snow-covered roads than on dry roads. Regarding visibility, Evans et al. (2020) presented the participants with day-night video clips at various locations, allowing them to rate traffic risk. The results suggested that risk ratings were higher for nighttime than daytime at most locations due to reduced visibility and challenges in identifying potential risks. Their subsequent study (Evans et al. 2022) has similar findings, with participants reporting higher perceived risks during nighttime than daytime.
3. PSC method
The primary objective of this study is to examine whether motorists select routes that are safer rather than routes that are more travel efficient, and, if so, which factors influence their safety route choice behavior. However, it is difficult to reach the conclusion directly from the route choice data. A feasible way is to compare whether people behave differently under varying circumstances that may influence their choices.
According to the idea above, this study introduced a paired scenario comparison (PSC) method. In this method, several hypothetical paired scenarios are devised, where each pair has a significant distinction in one circumstantial factor that has been found to have effect on travelers' trade-offs between safety and efficiency. The motorists are assumed to prioritize travel safety and tend to select safer routes in one of each paired scenario, while emphasizing travel efficiency and select quicker routes in the other. Route safety and efficiency are quantified using the road- and traffic-related factors that have been found to be associated with travel safety and efficiency.
To test the proposed hypotheses, this study follows an approach that is inspired by Kim (2022) who investigated taxi drivers' learning curves and tested given hypotheses by checking the statistical significance of variables' coefficients in two learning curve regression models depicting the relationship between drivers' experiences and performances. In the present study, an overall test is performed first where drivers' route choice is described by using a two-layer Group Random Parameters Logit (GRPL) model. The model represents the structure that individual (level-1 model with the variables representing route safety and efficiency) involves in scenarios (level-2 model with scenario-specified variables). The hypotheses could be proven correct if corresponding scenario variable in level-2 model has statistically significant effect on the safety variable in level-1 model.
Subsequently, to ensure the reliability of conclusion, a Scenariospecific Test is conducted to double-test the proposed hypotheses. In this test, for each scenario, a safety Random Parameters Logit (RPL) model and an efficiency RPL model are developed, respectively, using the selected route safety and efficiency variables to fit motorists' route choices. The hypotheses can be tested by comparing the predictions of the safety models and efficiency models between two paired scenarios. The hypothesis would be substantiated if the safety (or efficiency) model predicts the route choices more accurately than the efficiency (or safety) model in the safety (or efficiency-concerned) route choice scenarios.
In the final step, a multi-sample cross-validation is employed to validate further the results obtained in the former steps. The safety and efficiency models are recalibrated across ten distinct subsamples which are meticulously selected to include a balanced mix of daytime and nighttime trips, as well as commuting and non-commuting travel. By employing 10-fold cross-validation, we can further ensure the reliability of the conclusion of the test described in the above paragraph. If the observed accuracy trends across the ten subsamples align with the findings of the former Scenario-specific test, it affirms the robustness and validity of the conclusions.
It is worth mentioning that the overall test is a comprehensive,
holistic assessment that evaluates the validity of the proposed hypotheses by examining the statistical significance of the model parameters across the entire sample set. In contrast, the scenario-specific test, complemented by subsequent multi-sample cross-validation, is an indepth examination that assesses hypothesis validity on a per-scenario basis, focusing on the predictive accuracy of the models. These two stages not only differ in terms of sample scope but also in their evaluative methodologies. Importantly, the scenario-specific test and multisample cross-validation serve as a logical extension and refinement of the initial global evaluation provided by the overall test.
It is also worthwhile to discuss the advantages of this method. As introduced in the literature section, while the traditional questionnairebased survey methods enable investigators to directly query motorists' route choices, these methods come with several inherent limitations: 1) The first limitation is what is known as self-reported bias. The respondents may not always respond in alignment with their actual behaviors. This phenomenon has been found in many previous studies (Francisca, 2008; Krohn et al., 2011; Ribeiro et al., 2014; Caputo, 2015; Cools et al., 2024; Koller et al., 2023). A primary reason for this misalignment is Social Desirability Bias, which has been extensively studied in earlier research (Hanley, 1961; Francisca, 2008; Krohn et al., 2011). Respondents may provide answers that they believe are socially acceptable or expected, rather than reflecting their true preferences. For example, motorists may report prioritizing safety highly in surveys, yet their actual route choices may contradict this claim. 2) The second limitation is that survey-based methods struggle to replicate real-world scenarios. Travel safety is related to a wide range of factors. Capturing this complexity in a survey is inherently challenging because it requires simplifying or abstracting real-world conditions into hypothetical scenarios that may not fully resonate with respondents. Furthermore, unlike the factors such as travel time and fuel cost which have established social consensus-based measures, safety is an abstract concept that varies among individuals. Motorists may perceive travel traffic safety differently based on their past experiences, risk tolerance, and psychological state. In a questionnaire-based survey, it is difficult to ensure that all respondents interpret safety-related questions in the same way.
The PSC method leverages a large-scale behavioral dataset, capturing real-world route choices made by motorists under diverse conditions. This real-world, large dataset enables the study to avoid the pitfalls of traditional self-reported data. Observed behavior data provides an direct way and a reliable basis for understanding the choice behavior, compared to relying on questionnaire measures to speculate about future behaviors. Additionally, the scale of the dataset ensures statistical reliability and generalizability of the findings. This is particularly important given the complexity and variability of route choice behaviors across individuals and contexts. Moreover, the proposed PSC method involves comparing route choices across similar yet distinct real-world scenarios. This approach allows us to isolate the influence of specific factors (i.e. safety) on route selection while controlling for other variables. Thus, the proposed PSC approach provides a more reliable means of inferring safety route choice behaviors compared to traditional questionnaire-based survey methods.
4. Hypotheses
The elaboration on the scenarios and corresponding hypotheses proposed in this study are provided below:
(1) Hypothesis 1 (Day-night Risk Choice Difference, Dn-RCD)
It is widely acknowledged that visibility is reduced during nighttime compared to daytime. In transportation, studies have demonstrated that drivers' ability to identify risks is diminished at night (Asadamraji et al., 2019). Evans et al. (2020, 2022) further investigated the effect of differing day-night visibility on drivers' risk perception and awareness. Their findings suggested that drivers exhibit increased caution when driving at night due to visibility limitations. While these investigations primarily focus on on-route safety concerns, it is reasonable to infer that during pre-trip planning, due to reduced visibility, motorists are more prone to select the routes that are safer than other routes when driving at nighttime than in the daytime. Thus, the first hypothesis of this study can be formulated as follows: Motorists at nighttime are more inclined to select safe routes than at daytime.
(2) Hypothesis 2 (Trip-purpose Route Choice Difference, Tp-RCD) Studies on travel choice reveal that trip purpose is one of the most significant factors influencing travelers' route choices (Ramaekers et al., 2013; Moghaddam et al., 2019). Commuter and non-commuter exhibit different preferences when it comes to route selection. For example, commuting cyclists are more inclined to select time-efficient routes to avoid potential delays, while recreational cyclists prioritize routes with scenic views and recreational facilities (Sener et al., 2009). Similarly, motorists have been observed to be more concerned about arriving late during their commuting trips compare to non-commuting journeys. In a multi-scenario experiment conducted by Moghaddam et al. (2019), participating motorists even expressed a willingness to choose toll roads for work-related trips to ensure punctuality. Ramaekers et al. (2013) investigated the route choice of motorists in Flanders, Belgium, revealing that commuters are more likely to prioritize the quickest routes with less deviation than non-commuters.
Although direct evidence linking trip purpose to safety route selection is lacking, the behavioral difference between commuters and noncommuters in their considerations of travel timelines implies a plausible link between trip purpose and safety route selection: Motorists are more likely to select route with safer attributes for a non-commuting trip than a commuting trip.
(3) Hypothesis 3 (Professional-nonprofessional Route Choice Difference, Pn-RCD)
Safety attitudes and driving behaviors are different between professional and nonprofessional drivers. Many questionnaire-based studies have investigated the difference in driving behaviors between taxi and private car drivers (Peltzer and Renner, 2003; Rosenbloom and Shahar, 2007). The taxi drivers in these studies tended to comply less with traffic laws and regulations than other driver groups. Unlike private car use, which primarily focuses on personal mobility, taxi driving is profitdriven, motivating drivers to maximize earnings within limited timeframes (Zhang et al., 2006). Consequently, this financial incentive may elevate their risk propensity and inclination to take chances, leading to potential violations of traffic rules (Dorn et al. 2010). Several empirical investigations provided similar conclusions. For instance, Xu et al. (2014) compared the traffic conflict data collected from taxis and private cars at sixteen signalized intersections, revealing that taxi drivers were 2.37 times more inclined to engage in risky behaviors and consequently more prone to conflicts than other drivers. Chin and Huang (2009) conducted a comprehensive analysis of taxi-related crashes using six years of crash data, identifying risk-taking behaviors among taxi drivers, such as failing to maintain proper vigilance, neglecting right-ofway rules, and disregarding traffic signals, as the primary contributors to taxi-related crashes.
Given the insights from these studies, it is reasonable to posit that private car motorists might prioritize safety more than taxi drivers when making route decisions. These considerations lay the foundation for the formulation of the third hypothesis: Private-car motorists are more prone to selecting safe route than taxi motorists.
(4) Hypothesis 4 (Trip-distance Route Choice Difference, Td-RCD)
It has been established that travelers' considerations when choosing routes can vary based on the length of the trip (Sener et al., 2009; Li et al., 2016; Kang and Fricker, 2018; Deng et al., 2020). For instance, Deng et al. (2020), analyzed the vehicle GPS trajectory data in Xi'an, China, and found that as the travel distance increases, motorists tend to select routes with a higher proportion of freeways or highways for their perceived time-effectiveness while avoiding circuitous routes with several intersections. It indicates that motorists tend to pursue higher travel efficiency when trip distance increases. Similarly, Sener et al. (2009) investigated bicyclists' route choices while considering trip distance. They concluded that bicyclists commuting longer distances were inclined to travel on routes with less traffic and moderate speed limit, while those with shorter commutes were less sensitive to traffic volume but favored routes with lower speed limits. Kang and Fricker (2018) investigate bicyclists' route choice behavior and provide stronger evidence of the trade-off between travel distance and safety. They find that the participant bicyclists tend to increase their route safety concern when perceived risk is high. More important is that these bicyclists become more likely to trade off increased distance for decreased perceived risk.
The phenomenon revealed by above two bicyclist behavior studies may also occur among motorists, suggesting that trip length could also influence motorists' safety route choices. Thus, the fourth hypothesis is formulated as follows: Motorists tend to select safer routes for a shortdistance trip but are more prone to efficient routes for a long-distance trip.
5. Data processing
5.1. Trajectory reconstruction
5.1.1. ALPR data collection
The ALPR system, which combines advanced image processing, pattern recognition, and remote data access technologies, has been widely used in many cities for the tasks of regional traffic management, such as road network state discrimination, vehicle characteristics recognition, and vehicle travel trajectory reconstruction. The ALPR system provides large-scale vehicle trip data with accurate, detailed and disaggregated travel information, allowing the studies to reconstruct vehicles' trajectories, and investigate motorists' safety-concern route choice behaviors.
In this study, the ALPR data were collected at 88 road sites in Changsha City, China, from July 1st to July 28th, 2019 (28 days). Fig. 1 shows the road network configurations, and the spatial distribution of ALPR cameras across the study area. The network comprises of 102 intersections, with 84 (82.4 %) equipped with cameras (indicated by red nodes in the figure). As shown in Table 2, each data observation contains essential information, including "Plate Number (CLPZ)", "Timestamp (JLSJ)", "Intersection ID (LKBH)", "Lane Number (CDBH)", and "Driving Direction (XSFX)". It is worth noting that for confidentiality purpose, parts of the number on each plate had been converted using a specific code before we obtained the data. "Time stamp" and "Intersection ID" specify when and where the vehicle was detected on the network. "Lane Number" and "Driving Direction" indicate the lane and the direction of travelling on the segment.
5.1.2. Data cleaning
As the influences of the factors, such as illumination condition, blockage, and random shadow, on the performance of plate recognition, some of the records in the ALPR data appear missing or erroneous information. In addition, the vehicles stopping at intersections could easily lead to repetitive recognition of the ALPR system. Therefore, a data cleaning process has to be conducted before reconstructing the travel trajectory.
The first step is to remove the erroneous data form the dataset. The erroneous data are defined as the records where the time stamp is beyond the range from 0:00 to 24:00, or the site latitude and longitude are out of region of the study area. In the second step, the data with repetitive records or missing records are excluded from the dataset. The repetitive data are records of the same vehicle with the identical time stamps, or consecutive records of the same vehicle with the time interval within a specified threshold. According to Yu et al. (2018), this study uses a threshold of 5 s to identify the repetitive data.
Moreover, motorist's unfamiliarity with road network would influence their route choice. These records are likely to introduce bias to the model estimations. Thus, it is important to make sure that the recorded vehicles are possessed by the local residents and be frequently used. As a result, the records of non-local (those with the plates registered in other cities) and inactive vehicles (those appearing on average less than three times1 per week) were also removed from the dataset.
5.1.3. Particle filter algorithm
a
A complete vehicle travel trajectory is defined as the path followed by a vehicle moving from an origin node to a destination node within a road network (Chen et al., 2017; Cui et al., 2017; Huang et al., 2019). Using ALPR data, the trajectories were described based on the sequence of intersections traversed during a trip. A specific time interval was employed to distinguish between two closely spaced trips. If the time gap between the previous and the next intersection's timestamp records surpassed a predetermined threshold value, the two intersections were considered as the origin and destination (O-D) of separate trip. The threshold value was calculated using the following equation (Yu et al., 2018):
$$Ba = \frac{\sum{z=1}^{N_a^c} T_z^a}{N_y^c} + t # \tag{1}$$
where *Ta z*is the travel time of vehicle z spends on link a; *Nv a*is the total number of vehicles passing through link a in one day; t is an additional term representing the maximum intersection light time circle (Yu et al., 2018), which is 253 s in the selected area. This study uses 5 min as the additional waiting time.
To address missing trajectory segment, the Particle Filter (PF)-based Trajectory Reconstruction method proposed by Feng et al. (2015) was employed. PF is a nonlinear filtering algorithm that uses Monte Carlo random sampling and Bayesian filter to approximate the posterior density probability of a system. PF outperforms traditional (e.g. Kalman filter) in handling nonlinear and non-Gaussian complex systems, such as the traffic system. The PF-based trajectory reconstruction algorithm has three major steps, including initialize the particle set, importance sampling, and output the true trajectories. More details can be found in Feng et al. (2015). The final dataset comprised 17,466,750 trips extracted from 151,017 vehicles, each with a complete trajectory.
Furthermore, for the large-scale network, it would take considerable computational time to consider all the routes between O-D pairs. In the real cases, the number of routes frequently chosen by the motorists may be limited. Inspired by two route choice set generation methods, including the k-shortest and constrained enumeration, this study selects the k-most-frequently used routes for each of the selected O-D pair to construct the alternative route set. Sadeghian et al. (2006) and Xu et al., (2024) found that the number of travelers' preferred routes typically ranges from 2 to 5. Accordingly, this study selects the five most frequently used routes to build the choice dataset.
5.2. Trip classification
Given the proposed four hypothetical paired scenarios in Section 3, the task is to assign trajectories to appropriate scenario. For Hypotheses 1 and 4, the differentiation is relatively straightforward based on the time stamps and O-D distances information. Trips between 5:15 am to 19:50 pm are categorized as daytime trips, while the rest are nighttime trips. In this study, short trips are defined as the distance below the median of all the trip distances.
In Hypothesis 2, the classification of trip trajectories into commuting
1 This study uses a threshold of "three times" to screen for inactive motorists, as the dataset shows that 16.87% motorists travel less than or equal three times per week, and 29.33% (beyond 25%) motorists travel less than or equal four times. According to Adult Physical Inactivity Outside of Work (2022) from U.S. Centers for Disease Control and Prevention (CDC), an average of 15%-25% of the Americans are inactive population.
Fig. 1. Spatial distribution of ALPR cameras in the study area.
Table 2 Summary of the datasets.
| Column number |
Explanation | Example Sample |
|---|---|---|
| CLPZ | Vehicle license plate number (the first character is the provincial capital and the second number is for the city; these are followed by four numbers and letters which were converted into codes) |
"Xiang X 1010X…" |
| CLLX | Types of license plate number (01 or 02; 01 is for large vehicles and 02 is for small vehicles) |
01 |
| JLSJ | The time the vehicles pass the test point | 2019/3/14 10:33 |
| LKBH | Location (Intersection) number (from 1 to 88) | 01 |
| CDBH | Lane number (1, 2, or 3, beginning with the center line from left to right) |
02 |
| XSFX | Driving direction | South to North |
or non-commuting purposes is achieved using a method proposed by Chen et al. (2018). The approach involves dividing the network into 42 grids, each with a size of 1 km × 1 km. The Point of Interest (POI) data is then used to identified the trip purposes. The data contains the physical coordinators (xi,yi) of the basic unit of taking activities for the travelers. The POIs are classified into nine categories (as shown in Table 3) to correlate the points to the potential human activities. The trips are then divided into either commuting or non-commuting by considering the purpose and duration of the trip.
Hypothesis 3 necessitates the segmentation of trajectory data into two categories: taxi trips and private-car trips. The prerequisite involves
Table 3 POI categories in network grids.
| No. | Categories | No. | Categories |
|---|---|---|---|
| 1 | Arts and entertainment | 2 | College and university |
| 3 | Dining | 4 | Nightlife spot |
| 5 | Outdoors and recreation | 6 | Professional and other places |
| 7 | Residence | 8 | Shop and service |
| 9 | Travel and transport |
identifying whether the vehicle is for private or commercial use. To achieve this, the present study adopts the method proposed by Jiang et al. (2021) for vehicle identification. The classification is on the basis of two key indicators: the frequency of daily trips and the mean total daily on-road travel time. In this study, 10 trips and 1.5 h per day are selected as the threshold values. Vehicles surpassing the predefined thresholds for both indicators are classified as commercial, while those falling below are considered private.
In total, 11,317 taxis and 139,700 private vehicles were identified, generating 5,413,987 trips and 12,052,763 trips, respectively. Among the taxi trips sample, 2,052,048 (37.90 %) trips occurred during nighttime, while 3,361,939 (62.10 %) were in the daytime. Further classification reveals 687,479 (12.70 %) work-related trips and 4,726,508 (87.30 %) non-work trips. Moreover, 3,588,103 (66.27 %) short-distance trips and 1,825,884 (33.73 %) long-distance trips were identified. In the private-car trips sample, there were 2,475,914 (20.54 %) nighttime trips and 9,576,849 (79.46 %) daytime trips. Also, 1,431,858 (11.88 %) trips were work-related, and 10,620,905 (88.12 %) were non-work-related. Notably, 8,671,835 (71.95 %) short-distance trips and 3,380,928 (28.05 %) long-distance trips were extracted from the private-car sample.
5.3. Route attributes extraction
Measuring route safety and efficiency is the fundamental aspect of this study. Previous studies (Charlton et al., 2014; Charlton and Starkey, 2016) have demonstrated that route travel safety and efficiency attributes are associated with the road, traffic and environmental factors (Chen et al., 2017). An important consideration is that some of the variables in Table 1 have dual effect of being both safety-related and efficiency-related. To address potential overlap effects, this study follows three progressive principles for attribute selection. First, attributes are chosen based on data availability. For instance, environmental and road pavement conditions during the trips and motorists' demographics are excluded due to the lack of accessible data for this study. The second principle is dominance-based selection, where attributes are classified according to the findings that are most prominent in existing research
(Xiao et al., 2023; Dong and Chang, 2023; Hossain and Rahman, 2023). For example, median type is considered a safety-related attribute, as its strong correlation with driving safety has been well-documented in previous studies (Charlton and Starkey, 2016). The third principle is the effect-refinement approach, which focuses on attributes that must be included but are subject to controversy regarding their effects. For example, regarding the route intersection attribute, turning maneuvers (such as left or U-turns) are selected as safety indicators, while intersection density is used to represent route efficiency. By refining the attributes into dimensions that are specific in effects on route safety or efficiency, this approach averts the possible interpretive ambiguity in result and discussion sections.
5.3.1. Route safety attributes
Section 2.3 has highlighted several factors that are associate with rode travel safety. The present study selects three of these factors including the percentage of left turns and U-turns, road width, and median types to quantify route travel safety. Moreover, a comprehensive indicator is derived from these factors to represent the overall route safety level.
Left-turn and U-turn movements (LU) at intersections are associated with higher risks compared to straight and right turns (Payyanadan et al., 2017). Therefore, in this study, the route safety attribute concerning left- and U-turns is quantified using the percentage of these maneuvers in relation to the total turns within a given route, which is calculated as follows:
$$LU{i} = \frac{N{L-Turn} + N{U-Turn}}{N{i}^{t}} #$$ (2)
where NL− Turn and NU− Turn are the number of left turns and U-turns of route i; and *Nt i*is the total number of turns in route i.
Numerous studies (Evans et al., 2020; Evans et al., 2022) have
established the correlations between road width (RW) and driving safety. To account for the varying number of lanes on different segments of a route, the impact of road width on safety at the route level is quantified by summing the weighted numbers of lanes across all the segment links within the route, which is expressed as:
$$RW{i} = \sum{a=1}^{N{i}^{s}} w{a}^{i} \cdot rw_{a} #$$ (3)
where ra is the number of lanes of segment link a; *Ns i*is the total number of segment links on route i; *wi a*denotes the weight of the segment link a, which is calculated using the link length *l a*divided by route length Li, wi a = l i a/Li; rwa is the number of lanes on segment link a.
Concerning median types, the roads within the network commonly feature six distinct median types: dashed yellow centerline markings (type 1); single yellow lines (type 2); double yellow lines (type 3); steel guard fence (type 4); green median strip (type 5); and concrete barrier (type 6). Examples of each median countermeasure are shown in Fig. 2. Previous studies on median crash risk (Charlton and Starkey, 2016) have ranked the risk levels of these six median types as: type1 = type2 = type3 = 3 > type4 = 2 > type5 = type6 = 1. Thus, the route-level median risk (MR) can be calculated by this three-level criterion as:
$$MRi = \sum{a=1}^{N_a^i} w_a^i \cdot c r_a # \tag{4}$$
where mra is the risk level of the median type of segment link a.
Furthermore, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) (Hwang and Yoon, 1981) was used to evaluate the route's safety level, providing the Safety Indicator (SI) of the route. The value is calculated through a combination of the three aforementioned factors. The detailed calculation steps are provided in Appendix I.
5.3.2. Route efficiency attributes
The factors influencing route travel efficiency have long been
Fig. 2. The six median treatments selected for modeling.
examined extensively in the literature. Route length is seen as the most direct factor influencing travel efficiency (MacEachren, 1980; Chen et al., 2001; Papinski and Scott, 2011; Vreeswijk et al., 2013); however, its effect on route choice is typically mediated by interactions with traffic-related factors, such as flow density and speed (Chen et al., 2001; Vreeswijk et al., 2013). Moreover, some early study conducted by Sadalla and Staplin (1980) and Staplin and Sadalla (1981) have revealed a strong positive relationship between travel time and the number of intersections along travel route. Routes with more intersections are less efficient because of the extra waiting or stopping time at intersections (Wu et al., 2009; Pavithra et al., 2013). In addition to the road-related factors, traffic flow characteristics is another important indicator for travel efficiency (Tu et al., 2007; Tawfik et al., 2010; Ringhand and Vollrath, 2019; Ramming, 2002). Very few travelers would choose the routes with congested traffic (Tu et al., 2007; Ringhand and Vollrath, 2019) or slower travel speed (Dia and Panwai, 2007; Tawfik et al., 2010) for their journeys. Thus, this study utilizes four factors including route length (LE), the number of intersections (NI), route average travel time (TT) and traffic volume (RV) to account for route travel efficiency.
For an alternative route, the number of intersections on it and its length are fixed values and were easily ascertainable. Whereas the average travel time and traffic flow of the route are time-varying values and were computed using the ALPR data. The values of two time-varying factors were estimated first for each segment link of a route during a onehour interval. These link-level estimations were then aggregated to provide the route-level estimation. The average travel time for a link was calculated by taking the average travel times of all vehicles within an hour, while the total number of these vehicles determined the link flow. For the segments lacking sensors, the average travel time was estimated using the free-flow speed vfree (Yu et al, 2018). The equation for route average travel time is provided as follows:
$$TT{in} = \sum\nolimits{\alpha = 1}^{Ni^c} tt{\alpha}, \alpha \in i, i \in C_n #$$ (5)
where tta is the average travel time of segment link a such that:
$$tta = \begin{cases} \frac{\sum{j \in J_a} \Delta tj}{\eta{J_a}} & \text{for the segments with ALPR cameras} \ \frac{la^l}{\nu{free}^a} & \text{for the segments without ALPR cameras} \end{cases} ; \tag{6}$$
where vfree is 15 km/h for peak hours and 30 km/h for non-peak hours; Δtj is the interval between two adjacent times recorded in the upstream and downstream intersections of segment link a for *j*th vehicle; Ja is the set contains all vehicles passing through link a; and nJa is the total number of vehicles in set Ja. The route traffic volume is:
$$RF{in} = \sum{a=1}^{N{i}^{s}} w{a}^{i} f l{a}, a \in i, i \in C{n} #$$ (7)
Table 4 Variables and operational definition.
| Variables | Operational Description | Range* | Mean | Variance |
|---|---|---|---|---|
| Route Safety attributes | ||||
| SIin | Safety indicator of route i. | [0, 1] | 0.516 | 0.033 |
| LUin | Percentage of left turns and U-turns of route i. |
[0, 1] | 0.369 | 0.050 |
| RWin | Width indicator of route i. | [0, 1] | 0.569 | 0.046 |
| MRin | Risk level of median type of route i. | [0, 1] | 0.541 | 0.019 |
| Route Efficiency attributes | ||||
| NIin | Number of intersections of route i. | [0, 1] | 0.379 | 0.041 |
| TTin | Travel time on route i. | [0, 1] | 0.199 | 0.015 |
| LEin | Length of route i. | [0, 1] | 0.354 | 0.039 |
| RVin | Traffic flow on route i. | [0, 1] | 0.404 | 0.031 |
*Normalized values.
where fla is the traffic volume of segment link a. Table 4 presents a summary of the factors considered in this study.
6. Route choice models
In practice, travelers do not have perfect knowledge of network conditions. The incomplete information causes a distinction between traveler's perception of travel cost and the actual cost. Daganzo and Sheffi (1977) assume that travelers are random utility maximizers: an individual make a choice between the alternatives that are associated with a random utility. In random utility theory, route choice is assumed as a probability; the utility of route i(i ∈ Cm, Cm is the set of routes between O-D pair m) for individual n is defined as a random component associated with the travel cost as:
$$U{inm} = V{inm} + \varepsilon_{inm} # \tag{8}$$
where Vinm is deterministic utility, and εinm is random utility with E(εinm) = 0 that represents the traveler's perception error.
6.1. Multinomial Logit model
Discrete choice model, grounded on the random utility theory, provide a methodology to describe individual's choice between a discrete number of available routes. The routes are assumed to associated with a random utility, and a traveler chooses to pursue utility maximization. The Multinomial Logit (MNL) model has been widely used to analyze route choice behaviors due to its simplicity and low computational cost. In the model, the deterministic term Vinm (deterministic utility) is given by Vinm = βi ʹXinm, in which Xinm is the vector of explanatory variables (i. e., route attributes), and *βi*is the coefficient matrix representing travelers' tests for route i; the random terms εinm are independently and identically distributed Gumbel variates. The model assumes that travelers are more likely to choose the route with the highest utility. The probability of route i being selected is:
$$P{inm} = \Pr(U{inm} > U_{jnm}, \forall j \in C_m, j \neq i) = \frac{\exp(\betai X{inm})}{\sum_{j \in C_m} \exp(\betaj X{inm})} #$$
$$(9)$$
6.2. C-logit model
In the MNL model, the assumption of utility independence may not hold true since there are similarities among available routes (e.g. overlapping links of two routes). (Prashker and Bekhor, 2004). To address this issue, Cascetta et al. (1996) proposed the C-logit model to account for the similarities between overlapping routes by adding a commonality factor in the systematic part of the utility function (Equ. 8). Then, in the C-logit model, the selection probability of route i is stated as follows:
$$P{inm} = \frac{\exp(V{inm} + \beta{CF} \bullet CF{inm})}{\sum_{j \in Cm} \exp(V{jnm} + \beta{CF} \bullet CF{jnm})} #$$
$$\tag{10}$$
where, CFinm (i ∈ Cm) is a commonality factor of route i between O-D pair m. The commonality factor can be considered as a measure of the perception of route i as an alternative for a traveler. Thus, it reduces the utility of the overlapping routes and provide a better fitting to the realistic route choices. The commonly used functional form is as follows. For more details of other forms of the commonality factor functions, see Cascetta et al. (1996).
$$CFi = ln \sum{i \in Cm} \left( \frac{L{ij}}{\sqrt{L_i L_j}} \right)^{\gamma} #$$ (11)
where Lij is the length of overlapping links of route i and j. γ is the parameter to be estimated.
6.3. Path-size Logit model
The path size-logit (PSL) model proposed by Ben-Akiva and Ramming (1998) is other popular method to mitigate the possible effect of route utility dependence arising from route similarities in model estimation. The model incorporates a correction term that penalizes routes sharing links with other routes. Correspondingly, the deterministic term of route i (∀i ∈ Cm) is Vinm + kim, where kim ≤ 0 is the correction term. In the PSL, kim is usually defined as kim = βPSIn(PSim), where βPS ≥ 0 is the path size scaling parameter, and PSim ∈ [0, 1] is the path size term of route i, which is expressed as:
$$PS{lm} = \sum{a=1}^{N_l^2} \left(\frac{l_a^i}{Li}\right) \frac{1}{\sum{j \in Cm} I{aj}}, \forall i \in C_m #$$ (10)
where *Ns i*is the total number of segment links on route i; *l i a*is the length of link a in route i; Li is the length of route i; *Ia,j*value equals to 1 if link a is in route j(∀j ∈ Cm, j ∕= i) and 0 otherwise. In this case, the probability that route i is chosen is:
$$P{inm} = \frac{exp(V{inm} + \beta{PS}In(PS{im}))}{\sum_{j \in Cm} exp(V{jnm} + \beta{PS}In(PS{jm}))} #$$ (10)
6.4. Grouped random parameter logit model
In the models mentioned above, assumption of utility independence is also challenged by individual heterogeneity, where travelers' responses to specific route attributes might differ due to unobserved factors or uncollected data (Li et al., 2016). To deal with this problem, the Random Parameter Path-size Logit model (RPL), also known as the mixed logit model, was developed. The RPL model considers that some or all taste coefficients in *βi*vary across individuals and follow certain distributions, as expressed by:
$$\beta{inm} = \Theta \mathbf{Z}{inm} + \mathbf{v}_{inm} # \tag{11}$$
where Zinm is a vector containing factors that may explain the heterogeneity in *βi*, Θ represents the corresponding parameter matrix; and vinm is a randomly distributed term that portrays unobserved heterogeneity throughout the observations. This formation allows for random tastes variation that is flexible enough to account for unobserved heterogeneities [Han et al., 2018; 2021; Ding et al., 2024(1); 2024(2)].
The Grouped random parameter logit model (GRPL) is a spatial form of RPL model, which assumes that travelers' taste parameters *βi*differ among higher-level groups but remain consistent within each group. The variation can be specified by group factors as: βikm = ΘWkm + σkm, where k(k = 1, ⋯, K) is a group indictor referring to the *k*th group in higher-level. The model contains all the selected factors, allowing for simultaneous estimation. Consequently, the probability that the motorist n selects route i in set m can be described by allowing the vector βinm with a constant density function Prob (βinm = β) = f(β|φ):
$$P{lmm} = \int \frac{exp(\beta{lmm}/\mathbf{X}{lmm})}{\sum{\beta \in Cm} exp(\beta{lmm}/\mathbf{X}_{lmm})} f(\beta|\varphi) d\beta #$$ (12)
where φ refers to the vector of parameters (mean and variance) of the density function.
6.5. Model specifications
This study aims to empirically investigate the role of safety in motorists' route choices. To achieve this goal, a three-step approach based on the PSC method is employed, which is as follows:
(1) Step 1: Overall test
In the first step, overall test was conducted to examine the variable
effects. The hypotheses in Section 3 suggests that individual choices can vary depending on the scenarios in which the choices are made. This implies a hierarchical structure in the trip data, where a choice is associated with (or made within) a particular scenario. Consequently, a two-level GRPL was developed in this section.
The first level of the GRPL model depicts the utility of route i in set m for motorist n under scenario k with taste variables as:
$$U{iknm} = \beta{ikm,0} + \beta{ikm,1} SI{iknm} + \beta{ikm,2} NI{iknm} + \beta{ikm,3} TT{iknm} + \beta{ikm,4} RV{iknm} + \beta{ikm,5} ln(PS{iknm}) + \varepsilon_{iknm}$$
$$(13)$$
where βikm,q(q = 1, ⋯5) are motorists' tastes on the q th route attribute. The second level of the model captures the effects of scenario factors on the tastes. Specifically, the tastes parameters related to SI and route efficiency attributes NI and TT are assumed to be random and variable across different scenarios. This variability is described by a linear relationship expressed as:
$$\begin{split} \beta{ikm,q} &= \alpha{i,q0} + \alpha{i,q1} \text{Visibility}{km} + \alpha{i,q2} \text{Purpose}{km} + \alpha{i,q3} \text{Occupation}{km} \ &+ \alpha{i,q4} \text{LE-B}{km} + \epsilon_{ikm,q} \end{split} \tag{14}$$
where the scenario attributes Visibilitykm, Purposekm, Occup*a*tionkm, and LE-Bkm (LE-B is an conversion of LE in which the values are bivariate representing short trip and long trip) are both bivariate variables referring to scenario attributes (i.e., nighttime/commuting/ taxi driver/ long-distance = 1); *αi,q*0 is the fixed value of taste βikm,q, and αi,qp(p = 1, ⋯4) are the level-2 coefficient for m th scenario factor. Variables RV, LE, and PS are assumed to be fixed (i.e., βikm,q = *αi,q*0, q = 4 and 5). It is important to highlight that when the level-2 explanatory variables are excluded from the model, the model becomes a Null level-2 Group Random Parameters Logit (N-GRPL) model (i.e., βikm,q = αi,q0 + ∊ikm,q). Conversely, when the model includes the variables as described in Eq. (13), it is typically referred as Slopes-as-outcomes Group Random Parameters Logit (S-GRPL) model (Han et al., 2018, 2021).
A preliminary assessment of the effect of safety on route choices can be carried out by examining the significance of the taste coefficient βik,q. Similarly, the significances and values of the level-2 coefficients would be employed to test the hypotheses outlined in Section 3, illustrating how the effects differ across various scenarios (Kim, 2022).
(2) Step 2: Scenarios testing
In the PSC method (see detailed introduction in Section 3), the key to proving the existence of motorists' safety route choices is to either demonstrate that they prone to select safer routes in the "safety-concern scenarios", or to provide evidence that they prioritize effective routes in the "efficiency-concern scenarios". To this end, in this step, three RPL models are developed to predict the route choices for each of the four paired scenarios, including the day and night pair, commuting and noncommuting pair, profession and non-profession pair, and long-distance trip and short-distance trip pair. The first model exclusively encompasses the variables related to rode safety attributes, including LU, RW and MR. The fixed utility is as follows:
$$V{inm}^{s} = \beta{im,1}^{s} \cdot LU{inm} + \beta{im,2}^{s} \cdot RW{inm} + \beta{im,3}^{s} \cdot CR_{inm} #$$
$$\tag{15}$$
The second model focuses on route travel efficiency and includes only the variables, NI, TT and LE:
$$V{inm}^{e} = \beta{im,1}^{e} \cdot NI{inm} + \beta{im,2}^{e} \cdot TT{inm} + \beta{im,3}^{e} \cdot LE_{inm} #$$
$$\tag{16}$$
The third is a hybrid, encompasses all the aforementioned variables. In these three models, the determination of which variables should be treated as random (i.e., β* im,q = α* i,q0 + v* inm,q) is determined by the model fitting performance measured by McFadden Pseudo *R*2. Subsequently, a comparative analysis of predictive accuracy is conducted between the
safety and efficiency models across four paired scenarios to test the hypotheses outlined in Section 3. Specifically, the aim is to observe whether the safety (or efficiency) models consistently outperform the efficiency (or safety) models in predicting route choices within scenarios prioritizing safety (or efficiency) concerns over efficiency (or safety). The evaluation of model prediction accuracy is conducted using the following equation:
$$Accuracy = \frac{N^T}{N^T + N^F}$$ (17)
where *NT*is the number of route choices that are predicted correctly; and *NF*is the number of route choices that are predicted wrongly.
(3) Step 3: Multi-sample cross-validation
This step attempts to further validate the results obtained in step 2. To ensure that the observed outcomes are not mere coincidences, the safety, efficiency and hybrid RPL models will be recalibrated across multiple subsamples. For this validation process, ten subsamples are created, each comprising 30,000 private-car trip and 30,000 taxi trips, extracted from the overall dataset. Each subsample contains sufficient records of trips under the day and night trip scenarios, and commuting and non-commuting scenarios. The predictive accuracy of the three models can be assessed by 10-fold cross-validation. If the trends in prediction accuracy between the two scenarios of each pair consistently align with the results from step 2 across the ten samples, it will confirm the validity of the conclusions.
7. Results and discussions
7.1. Overall test
A subset of twenty O-D pairs with the highest traffic volume was selected to generate the subsample set for the overall test. The subset consists of 267,458 (34.67 % of the total trajectory dataset) trips that occurred between the selected O-D pairs. To perform a comprehensive comparative analysis, four distinct models, including the MNL model, PSL model, N-GRPL model and S-GRPL model, were developed. The data fitting performance of the four models is presented in Table 5, while the parameter estimation results for each model are displayed in Table 6.
7.1.1. Model comparisons
As shown in Table 5, models with path-size correction (i.e., PSL, N-GRPL, and S-GRPL) have higher values of McFadden Pseudo *R*2 and the lower values of AIC compared to the model without path-size correction (i.e., MNL model). The result aligns with previous studies' findings (Dhakar and Srinivasan, 2014; Tang et al., 2019), demonstrating the significance of accounting for link overlapping effects in route choice modeling.
Moreover, both GRPL models (i.e., N-GRPL and S-GRPL) exhibit higher McFadden Pseudo *R*2 values and lower AIC values compared to the other two models (i.e., PSL and MNL models). This observation supports the findings from other choice modeling studies (Han et al.,
Table 5 Model fitting performance comparison.
| MNL | PSL | N-GRPL | S-GRPL | |
|---|---|---|---|---|
| Number of observations |
267,458 | 267,458 | 267,458 | 267,458 |
| McFadden Pseudo R^2 |
0.27 | 0.41 | 0.63 | 0.64 |
| Log-likelihood at estimates |
− 490,058.41 | − 393,628.80 | − 157,701.09 | ¡156,605.02 |
| AIC | 980,126.81 | 787,269.36 | 315,428.2 | 313,260.00 |
| AIC/N | 0.73 | 0.59 | 1.18 | 1.17 |
2018; Li et al., 2023), highlighting the relevance of accounting for the cross-scenario variation in motorists' route attribute preferences and emphasizing the need to consider this heterogeneity when modeling their choices.
A more detailed comparison between the two GRPL models indicates the outperformance of the S-GRPL model in terms of model goodness-offit. This can be attributed to the fact that the S-HPRL model incorporates variables of scenario characteristics in the second level, which could help to explain part of the heterogeneity caused by the scenario effects and thus improve the model fitting performance.
7.1.2. Factors effects
Table 6 presents the estimated parameters of the four models. It can be observed from the table that the coefficients of SF are uniformly positive and statistically significant at a 99 % confidence level across all four models. This indicates that route safety substantially influences motorists' route choices. On average, routes with higher safety indicators are more attractive to motorists than those with lower safety performance. The findings support the overall hypothesis of the present study that motorists consider safety into account when making their route choices.
Examining the level-2 variables of the S-GRPL model, the coefficients of scenario factors of SI, Visibility (*α*11), Purpose (*α*12), Occupation (*α*13) and LE-B (*α*14), are all statistically significant at a 99 % level, which confirms their effects on motorists' safety route choice behaviors. Specifically, Visibility (nighttime = 1) and LE-B (long = 1) are positively associated with the safety route choices. It indicates that motorists traveling at nighttime or long-distance are more incline to select route with safer attributes than those that travel during daytime or shortdistance. The findings support the Dn-RCD hypothesis (Hypothesis 1), but contradict the Td-RCD hypothesis (Hypothesis 4), posing that prioritize route safety more for short-distance trips. Purpose (commuting = 1) and Occupation (taxi = 1) show a negative relationship with SI, implying that commuting motorists or taxi drivers are less likely to choose safety routes when compared to non-commuting motorist or private-car drivers. Consequently, the overall test results support the acceptance of the Tp-RCD hypothesis (Hypothesis 2) and Pn-RCD hypothesis (Hypothesis 3).
Regarding the four efficiency variables in Table 6, the two random coefficients NI (*α*20) and TT (*α*30) are negative and statistically significant at a 99 % confidence level, suggesting that motorists incline to select routes with fewer intersections and shorter travel times. The results align with the expectations that motorists seek prompt destination arrival. More importantly, the four level-2 coefficients pertaining to the efficiency variable TT are all significant at a 99 % confidence level. Among these, three variables, including Visibility (nighttime = 1), Purpose (commuting = 1), and LE-B (long = 1), demonstrate contrasting effects to those observed with SI. This indicates that factors, such as nighttime, commuting purpose, and short-distance mitigate the effect of TT on route utility, indicating that motorists who drive under above scenarios tend to show less inclination to select quicker routes. The results indicate the model's reliability and provide further support for the validity of the proposed Hypothesis 1 and 2 from an opposite perspective. Considering the two fixed level-1 coefficients, *α*40 (RV) has a significant positive sign, indicating that motorists tend to use the routes with heavier traffic flow, which might initially appear counterintuitive. However, this result could be attributed to the fact that routes with higher traffic flow means it is more appealing to motorists. The decrease in motorists' tendency due to traffic volume usually occurs only when the volume surpasses a certain threshold, leading to unpleasant experiences like traffic congestion.
Up to this point, the four proposed hypotheses have been preliminarily tested using the S-GRPL model. Except for the Td-RCD (Hypothesis 4), the data has supported the other three hypotheses. Based on the preliminary analysis results, an initial conclusion can be drawn that there is a likelihood that motorists will be more prone to select safety
Table 6 Model estimation of N-GRPL model and S-GRPL model.
| Variable | MNL | PSL | N-GRPL | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Est. coeff. |
Std. Error |
t-Stat | Est. coeff. |
Std. Error |
t-Stat | Est. coeff. |
Std. Error |
t-Stat | Est. coeff. |
Std. Error |
t-Stat | |
| Level-1 fixed effects | ||||||||||||
| α10(SI) | 1.62*** | 0.03 | 51.38 | 1.83*** | 0.03 | 57.19 | 1.63*** | 0.04 | 39.10 | 0.52*** | 0.09 | 6.05 |
| α20(NI) | − 0.59*** | 0.13 | − 4.67 | − 0.86*** | 0.13 | 6.72 | − 6.12*** | 0.28 | − 21.70 | − 5.79*** | 0.36 | − 16.09 |
| α30(TT) | − 0.58*** | 0.09 | − 6.71 | − 0.74*** | 0.09 | − 8.44 | − 3.85*** | 0.14 | − 27.79 | − 4.73*** | 0.25 | − 18.82 |
| α40(RV) | 4.89*** | 0.07 | 66.70 | 3.66*** | 0.08 | 47.14 | 3.78*** | 0.08 | 46.38 | 3.91*** | 0.08 | 46.59 |
| α50(PS) | − | − | − | − 1.33*** | 0.03 | − 47.04 | − 0.80*** | 0.03 | − 25.60 | − 0.89*** | 0.03 | − 27.47 |
| ASC1 | 2.59*** | 0.02 | 129.89 | 2.55*** | 0.02 | 127.87 | 2.39*** | 0.02 | 115.31 | 2.44*** | 0.02 | 115.36 |
| ASC2 | 1.65*** | 0.02 | 85.28 | 1.65*** | 0.02 | 85.31 | 1.66*** | 0.02 | 81.31 | 1.69*** | 0.02 | 80.66 |
| ASC3 | 0.60*** | 0.02 | 29.39 | 0.61*** | 0.02 | 29.95 | 0.66*** | 0.02 | 30.81 | 0.74*** | 0.02 | 33.51 |
| ASC4 | 0.23*** | 0.02 | 10.43 | 0.30*** | 0.02 | 13.58 | 0.27*** | 0.02 | 11.72 | 0.30*** | 0.02 | 12.75 |
| Level-2 fixed effects | ||||||||||||
| α11(SI, visibility, nighttime = 1) |
− | − | − | 0.86*** | 0.07 | 12.33 | ||||||
| α12(SI, purpose, commuting = 1) |
− | − | − | − 1.44*** | 0.10 | − 14.00 | ||||||
| α13(SI, occupation, taxi = 1) |
− | − | − | − 0.26*** | 0.08 | − 3.29 | ||||||
| α14(SI, LE-B, long = 1) | 1.19*** | 0.07 | 16.49 | |||||||||
| α21(NI, visibility) | − | − | − | 0.03 | 0.16 | 0.16 | ||||||
| α22(NI, purpose) | − | − | − | − 4.63*** | 0.21 | − 21.97 | ||||||
| α23(NI, occupation) | − | − | − | 0.66*** | 0.15 | 4.50 | ||||||
| α24(NI, distance) | − 3.33*** | 0.15 | − 22.16 | |||||||||
| α31(TT, visibility) | − | − | − | 1.82*** | 0.19 | 9.40 | ||||||
| α32(TT, purpose) | − | − | − | − 1.86*** | 0.21 | − 8.84 | ||||||
| α33(TT, occupation) | − | − | − | 0.70*** | 0.17 | 4.10 | ||||||
| α34(TT, distance) | 1.72*** | 0.19 | 8.94 | |||||||||
| Level-2 random effects | ||||||||||||
| φ1(SI) | 1.51*** | 0.13 | 11.46 | 1.61*** | 0.12 | 13.24 | ||||||
| φ2(NI) | 7.26*** | 0.18 | 40.47 | 9.13*** | 0.19 | 47.72 | ||||||
| φ3(TT) | 5.18*** | 0.17 | 29.81 | 4.16*** | 0.20 | 20.46 |
Note: ***, **, * = Significance at 1 % level, 5 % level, and 10 %; ASC is the dummy variable for each alternative route; SI = Safety Indictor, NI = Number of Intersection, TT = Travel Time, RV = Route Flow, LE-B = Route Length (biverate), PS = Ln (path-size).
routes instead of efficiency routes, and this likelihood depends on factors such as time of day, trip purpose, and whether the trip is for livelihood or private mobility.
Moreover, although trip distance also plays a crucial role, the testing results contradict the assumption of the Td-RCD hypothesis (Hypothesis 4). To establish a more reliable conclusion, the following section will further examine the hypotheses by assessing the prediction accuracy of the safety and efficiency route choice models.
7.2. Scenario testing
7.2.1. Single sample testing
Two subsamples, each consisting of 30,000 private car trips and 30,000 taxi trips, are randomly extracted from the dataset. The subsample covers all the eight travel scenarios outlined in Section 3, including day and night, commuting and non-commuting, taxi and private-car, and short- and long-distance scenarios. Three types of RPL route choice models, including safety model, efficiency model, and hybrid model, are developed to fit the two subsamples and predict the choices. Subsequently, the predictive performance of the models is evaluated using Eq. (25).
The predictive accuracy of the six models is shown in Fig. 3. As shown in the figure, the histograms in the first row reveal a consist trend: compare to the safety models, the efficiency models exhibit better performance of route choice predictions for both the daytime private-car trips and daytime taxi trips. However, this trend shifts when considering the nighttime trips. More importantly, the superiority of the safety model becomes more pronounced (more than three times higher, 77.2/ 24 = 3.27) when predicting nighttime private trips. The finding indicates that the route safety attributes better capture route choices during nighttime, particularly for private trips. The result supports the
Dn-RCD hypothesis (Hypothesis 1) and Pn-RCD hypothesis (Hypothesis 3), suggesting that motorists are more safety-route-prone when driving at night, especially when the trips are for private mobility purposes rather than livelihood needs.
The histograms in the second row of Fig. 3 reveal a consistent trend of the models' predictive discrepancy between commuting and noncommuting scenarios: the efficiency models outperform the safety models in predictive accuracy. When predicting taxi trips, the efficiency models remain superior to the safety models. The results indicate that trip purpose might not a significant factor affecting motorists' selections between safety routes and efficiency routes. Thus, the result fails to support the Tp-RCD hypothesis (Hypothesis 2).
A clear trend emerges when examining the short- and long-distance scenarios illustrated in the histograms at the bottom row of Fig. 3. Notably, the superiority of the two short-distance safety models in terms of predictive accuracy is evident. Specifically, the short-distance safety model outperforms the long-distance safety model by over 1.6 times (79.4/48.7 = 1.63) in predicting choices for private trips. This margin decreases to 1.28 (73.1/57.3 = 1.28) in the context of taxi trips. Conversely, as anticipated, the two efficiency models consistently outperform the safety models in predicting choices for long-distance trips. This advantage is slightly more pronounced when predicting taxi trips (a ratio of 66.1/53.9 = 1.23 for private trips compared to 74.6/ 69.2 = 1.08 for livelihood trips). These findings suggest that route safety attributes are more effective in predicting motorists' route choices for short-distance trips, particularly those involving private cars. Thus, from the perspective of model prediction, the results support the proposed Td-RCD hypothesis (Hypothesis 4) and indicate the acceptability of the Pn-RCD hypothesis (Hypothesis 3) in both the short- and long-distance scenarios.
Furthermore, Fig. 3 also provides the insight into the predictive
Fig. 3. Comparison between the safety and efficiency models in different scenarios.
accuracy of the hybrid models across various scenarios. As shown in the figure, the hybrid model outperforms the other two models, suggesting that incorporating route safety attributes with traditional route efficiency attributes enhance the accuracy of the choice prediction across all scenarios.
Table 7 illustrates the parameters estimation result for the two hybrid models, focusing on fixed effect estimation of each variable. The table shows that, safety and efficiency variables are statistically significant at a 99 % confidence level. Specifically, considering the safety variables, LU and RW show negative and positive relationship with route utility for the two different groups of motorists. The findings align with the common understanding that the motorists prefer routes with fewer left- and U-turning movements and broader roads. However, MR relationship with route utility is more complicated. When considering taxi
Table 7 Model estimation of the hybrid model.
| Variable name | Private-car trips | | | Taxi trips | | | | |------------------------|-------------------|--------|-------------|------------|--------|-------------|--| | | Estimation | Std E. | t-value | Estimation | Std E. | t-value | | | Safety variable | | | | | | | | | LU | − 1.13*** | 0.06 | − 17.67 | − 1.07*** | 0.07 | − 16.18 | | | RW | 2.65*** | 0.16 | 16.09 | 3.69*** | 0.16 | 23.48 | | | MR | 0.84*** | 0.15 | 5.68 | − 0.29** | 0.14 | − 2.12 | | | Efficiency variable | | | | | | | | | LE | − 8.38*** | 0.90 | − 9.31 | − 9.21*** | 0.78 | − 11.77 | | | NI | − 31.76*** | 0.40 | − 79.71 | − 30.76*** | 0.46 | − 66.28 | | | TT | − 6.20*** | 0.32 | − 19.15 | − 5.86*** | 0.41 | − 14.25 | | | Others | | | | | | | | | PS | − 2.05*** | | − 22.73 | − 2.83*** | 0.08 | − 34.82 | | | Model fitting | | | | | | | | | Number of observations | | | 30,000 | | | 30,000 | | | McFadden Pseudo Rho^2 | | | 0.62 | | | 0.52 | | | Log-likelihood | | | − 18,587.35 | | | − 23,206.14 | |
Note: ***, **, * = significance at 1 % level, 5 % level, and 10 %; LU = Percentage of left turns and U turns, RW = Route width, MR = Route-level median risk; LE = Route length; NI = Number of intersections; TT = Travel Time, PS = Ln (path-size).
trips, MR is negatively related to motorists' route utility, but this relationship becomes positive for private-car trips. The unexpected relationship suggests that its performance may be influenced by confounding factors not accounted for in the models. Further investigations using more comprehensive data could shed light on these discrepancies.
The effects of the efficiency variables on route utility remain consistent across both models. All the three selected variables exhibit negative effects, indicating that route utility diminishes with increased route length, more intersections, and longer route travel time. This outcome aligns with the common sense, reflecting motorists' preference for shorter routes with fewer stops due to intersection traffic lights and shorter travel time.
7.2.2. Cross-sample verification
The three models (safety, efficiency and hybrid model) developed in Section 6.2 were applied to the ten subsamples extracted in Section 4. The predictive accuracy of these models in three pairs of scenarios
(daytime vs. nighttime, commuting vs. non-commuting, and taxi vs. private-car scenarios) is illustrated in Fig. 4 through box line plots. Table 8 provides the five statistical measures associated with each box line.
The trends in predictive accuracy variations between the safety and efficiency models remain consistent with those observed in the signal sample testing. The safety route choice model performs better in predicting route choices for nighttime trips (particularly private-car trips), but its performance decreases for daytime trips. On the other hand, no significant difference in the trend is observed between work and nonwork trips. Moreover, the safety model outperforms in predicting short-distance trip route choices (especially for private-car trips), while it is less accurate for long-distance trip predictions.
Moreover, the box line plots of the two models demonstrate slight route choice prediction variations across the ten subsamples. Specifically, in the case of the safety model, the highest accuracy variation is observed for commuting taxi trips, with a percentage increase of 17.96 % from the minimum to the maximum value ((69.54–58.95)/58.95 =
Fig. 4. Box line plots of the cross-sample verification.
Table 8 Summary of the statistical measures for cross-sample verification.
| Type | Five number | Safety model | | Efficiency model | | Hybrid model | | | | |-------------------|----------------|----------------|---------------|------------------|---------------|----------------|---------------|--|--| | Private-car trips | | Daytime | Nighttime | Daytime | Nighttime | Daytime | Nighttime | | | | | Max | 74.32 | 77.90 | 82.68 | 24.03 | 84.84 | 87.81 | | | | | Min | 69.64 | 72.10 | 79.34 | 22.08 | 82.24 | 84.84 | | | | | Mean | 72.76 | 75.72 | 81.17 | 23.16 | 83.70 | 86.30 | | | | | Upper quartile | 72.14 | 74.58 | 80.76 | 22.70 | 82.93 | 85.26 | | | | | Median | 72.91 | 76.25 | 81.02 | 23.05 | 83.92 | 86.42 | | | | | Lower quartile | 73.87 | 77.03 | 82.10 | 23.85 | 84.34 | 87.27 | | | | | | Work | Non-work | Work | Non-work | Work | Non-work | | | | | Max | 74.21 | 75.48 | 80.52 | 83.94 | 82.55 | 85.60 | | | | | Min | 68.51 | 70.39 | 77.78 | 80.50 | 78.96 | 83.34 | | | | | Mean | 70.80 | 73.78 | 79.14 | 82.30 | 80.80 | 84.76 | | | | | Upper quartile | 69.10 | 72.66 | 78.12 | 81.84 | 79.79 | 84.17 | | | | | Median | 71.06 | 74.20 | 79.09 | 82.20 | 80.96 | 84.92 | | | | | Lower quartile | 71.85 | 75.01 | 79.99 | 83.04 | 81.50 | 85.53 | | | | | | Short-distance | Long-distance | Short-distance | Long-distance | Short-distance | Long-distance | | | | | Max | 81.29 | 71.71 | 50.50 | 79.23 | 89.64 | 83.14 | | | | | Min | 73.48 | 62.20 | 46.79 | 71.29 | 87.65 | 73.91 | | | | | Mean | 78.00 | 68.08 | 48.52 | 75.40 | 88.51 | 79.21 | | | | | Upper quartile | 76.56 | 65.72 | 47.02 | 73.44 | 87.75 | 77.51 | | | | | Median | 78.23 | 68.76 | 48.81 | 75.71 | 88.45 | 78.99 | | | | | Lower quartile | 79.65 | 70.35 | 49.33 | 77.31 | 89.17 | 81.64 | | | | | | | | | | | | | | | Taxi trips | | Daytime | Nighttime | Daytime | Nighttime | Daytime | Nighttime | | | | | Max | 63.24 | 67.02 | 78.79 | 51.94 | 81.60 | 79.80 | | | | | Min | 60.37 | 62.39 | 72.56 | 46.98 | 76.55 | 77.21 | | | | | Mean | 61.82 | 64.18 | 75.25 | 49.94 | 78.32 | 78.43 | | | | | Upper quartile | 60.43 | 63.03 | 73.80 | 48.59 | 77.01 | 77.68 | | | | | Median | 61.83 | 63.74 | 75.66 | 50.21 | 78.32 | 78.38 | | | | | Lower quartile | 62.97 | 65.40 | 76.16 | 51.48 | 79.19 | 79.17 | | | | | | Work | Nonwork | Work | Nonwork | Work | Nonwork | | | | | Max | 69.54 | 64.65 | 78.26 | 78.45 | 80.77 | 80.65 | | | | | Min | 58.95 | 61.26 | 71.81 | 74.16 | 74.35 | 77.04 | | | | | Mean | 62.68 | 62.76 | 74.26 | 75.99 | 76.50 | 78.44 | | | | | Upper quartile | 59.36 | 61.59 | 73.37 | 74.90 | 75.50 | 77.38 | | | | | Median | 62.19 | 62.59 | 73.60 | 76.23 | 75.87 | 78.45 | | | | | Lower quartile | 64.78 | 64.03 | 75.03 | 76.75 | 77.53 | 79.19 | | | | | | Short-distance | Long-distance | Short-distance | Long-distance | Short-distance | Long-distance | | | | | Max | 73.40 | 56.71 | 61.58 | 66.09 | 89.30 | 69.54 | | | | | Min | 66.07 | 50.22 | 49.65 | 60.88 | 86.00 | 64.33 | | | | | Mean | 70.48 | 53.77 | 56.28 | 63.76 | 87.70 | 67.18 | | | | | Upper quartile | 69.28 | 51.86 | 53.95 | 62.60 | 86.90 | 65.87 | | | | | Median | 70.70 | 53.92 | 57.42 | 63.83 | 87.54 | 67.11 | | | | | Lower quartile | 71.96 | 55.59 | 58.56 | 64.91 | 88.53 | 68.85 | | |
17.96 %). On the other hand, the accuracy for daytime taxi trips exhibits the least variation, with the maximum value being only 4.75 % higher than the minimum ((63.24–60.37) = 4.75 %). Similarly, when considering the efficiency model, the maximum accuracy variation is observed in short-distance taxi trips, which is 24.02 % ((61.58–49.65)/49.65 = 24 %). In contrast, private-car working trips show the least variation, with only a 3.52 % difference between the maximum and minimum accuracy values ((80.52–77.78)/77.78 = 3.52 %). Thus, this further confirms the findings presented in the previous section.
The findings from both the overall and scenario-specific testing are summarized in Table 9. The two tests provide evidence in support of the
Table 9 Summary of the hypotheses testing results.
| Overall test | Scenario test | Conclusion | |
|---|---|---|---|
| Overall hypothesis (Safety route choice) |
Acceptable | Acceptable | Acceptable |
| Dn-RCD, hypothesis 1 (Daytime/nighttime) |
Acceptable | Acceptable | Acceptable |
| Tp-RCD, hypothesis 2 (Commuting/non-commuting) |
Acceptable | Refuse | Refuse |
| Pn-RCD, hypothesis 3 (Professional/non-professional) |
Acceptable | Acceptable | Acceptable |
| Td-RCD, hypothesis 4 (Short/long distance) |
Refuse | Acceptable | Refuse |
Overall hypothesis and two scenario hypotheses (Dn-RCD and Pn-RCD). Consequently, this study draws the following conclusions: 1) motorists select routes with safety attributes over travel efficient routes; 2) motorists are more prone to select safer routes during nighttime trips than during daytime trips; and 3) private-car motorists traveling for private mobility needs show greater priority to choose safer routes than the taxi motorists traveling for livelihood. However, the tow tests have not supported the hypotheses of Tp-RCD (commuting/non-commuting scenarios) and Td-RCD (short/long distance). As a result, a definitive conclusion regarding these two hypotheses cannot yet be drawn.
8. Conclusions
This study empirically investigates whether motorists select routes with safer attributes or routes that a more travel efficient. A large-scale vehicle trajectory reconstructed by the ALPR (Automatic License Plate Recognition) data (which contains essential information collected by the ALPR system, including "Plate Number", "Time stamp", "Intersection ID", "Lane Number", and "Driving Direction") is used for analysis. The PSC method is proposed to demonstrate the existence of motorists' safety route choices by examining the possible variation of the effects under different scenarios. An overall test is first conducted using a twolayer GRPL model with one safety variable (SI) in level-1 and four bivariate scenario-specific variables (visibility, purpose, occupation and LE) in level-2. This is followed by a scenario-specific test, in which the
predictive accuracy between safety- and efficiency-specified route utility models are compared among paired two scenarios. The results of these two tests are validated by a cross-10-sample validation. The result indicates that: 1) motorists select routes with safety attributes over travel efficient routes; 2) choice of routes varies for daytime and nighttime trips, 3) and associates with whether or not the motorist travels for livelihood needs (e.g., taxi); 4) no solid evidence can illustrate the effects of motorists' travel purpose and trip distance on their choice of routes with more safety attributes; 5) route attributes, including intersection turnings, road width, and median types, present significant associations with motorist's route choice.
This study contributes to the emerging field of route safety research (Huang et al., 2022; Sohrabi and Lord, 2022). Specifically, this study highlights the significance of motorists' safety route choice behaviors, emphasizing the need for research focused on safety-oriented route performance estimation, as well as the development of safety-motivated mobility advertising and guidance system. Additionally, the empirical evidence provided by this study regarding the variability in motorists' choices between safe routes and efficient routes assist researchers and developers better understand that when motorists would prioritize safe routes instead of efficient routes. Furthermore, by identifying route attributes linked to safety route choices, this study advances efforts to model motorists' safety route behaviors.
Further research could include a broad questionnaire survey. The psychological survey method could supplement the behavior-based PSC method. Integrating analyses of motorists' actual route choice with investigations into their psychological considerations regarding route safety could provide a more comprehensive understanding of their safety route choice behaviors. Additionally, the questionnaires could cover more travel scenarios involving the trade-off between safety routes and efficiency routes among motorists. This could help to uncover additional factors that might influences motorists' safety route choices. Furthermore, future research could benefit from using trip data collected from various cities to validate the findings of the current study. A dataset spanning multiple regions may provide a more comprehensive understanding of how trip purpose and distance impact motorists' safety route choices, which is not fully clarified in this study.
CRediT authorship contribution statement
Wei Hao: Writing – original draft, Software, Methodology, Investigation, Funding acquisition, Conceptualization. Fang Liu: Writing – original draft, Validation, Software, Methodology, Conceptualization. Chunyang Han: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. Amjad Pervez: Writing – review & editing, Visualization, Software, Methodology, Investigation. Kai Wang: Writing – original draft, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. Jie Chen: Validation, Supervision, Project administration, Formal analysis, Data curation. Jinjun Tang: Supervision, Conceptualization.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The study is supported by: 1) National Key R&D Program of China (No. 2022YFC3803703); 2) The Ministry of Education Humanities and Social Science Research (Youth) Project (No. 24YJC630065); 3) Yunnan Fundamental Research Projects (Youth) (No. 202401AU070217); 4) Guangxi University Key Laboratory of Intelligent Logistics Technology; 5) The China Postdoctoral Science Foundation (No. 2021M701898 and No. 2022T150357); 6) Key R&D Program of Hunan Province (No. 2023GK2014).
Appendix I
According to the TOPSIS method, the safety indicator for a route can be calculated by the following six steps: Step 1: Develop initial matrix S based on selected route safety attributes.
$$S = \begin{bmatrix} s{11} & s{12} & \cdots & s{1g} \ s{21} & s{22} & \cdots & s{2g} \ \vdots & \vdots & \ddots & \vdots \ s{i1} & s{i2} & \cdots & s_{ig} \end{bmatrix} #$$
$$(18)$$
where sig is the selected safety attribute g for route i.
Step 2: Calculate the normalized matrix R.
$$R = \begin{bmatrix} r{11} & r{12} & \cdots & r{1g} \ r{21} & r{22} & \cdots & r{2g} \ \vdots & \vdots & \ddots & \vdots \ r{11} & r{12} & \cdots & r_{lg} \end{bmatrix} #$$
$$(19)$$
$$r{ig} = \frac{s{ig}}{\sqrt{\sum{l=1}^{I} s{ig}^2}}, g \in G#$$ (20)
where rig is normalization of sig, I is the total number of alternative routes between all the OD pairs, G is the set of route safety attributes. Step 3: Calculate the weighted normalized matrix V.
$$V = \begin{bmatrix} v{11} & v{12} & \cdots & v{1g} \ v{21} & v{22} & \cdots & v{2g} \ \vdots & \vdots & \ddots & \vdots \ v{i1} & v{i2} & \cdots & v_{ig} \end{bmatrix} #$$ (21)
$$v_{ig} = wg r{ig}, g \in G# \tag{22}$$
where vig is the weighted normalized value of sig .
Step 4: Calculate the ideal and negative-ideal solution.
$$A^{+} = \left{ v{1}^{+}, \cdots, v{g}^{+} \right} = \left{ \left( \max{i \in C} v{ig} | \mathbf{g} \in G^{-} \right), \left( \min{i \in C} v{ig} | \mathbf{g} \in G^{-} \right) \right} #$$
$$(23)$$
$$A^{-} = \left{ \mathbf{v}{1}^{-}, \cdots, \mathbf{v}{g}^{-} \right} = \left{ \left( \min{i \in C} \mathbf{v}{ig} | \mathbf{g} \in \mathbf{G}^{i} \right), \left( \max{i \in C} \mathbf{v}{ig} | \mathbf{g} \in \mathbf{G}^{i} \right) \right} #$$
$$(24)$$
where A+ is the ideal solution, and A− is the negative-ideal solution; *G*ʹ is the set of variables that have negative correlations with risk rating, and *G*˝ contains the variables that are positively associated with risk rating, C is the set of all the alternative routes.
Step 5: Calculate the Euclidean distance of each alternative from the ideal solution.
$$Di^+ = \sqrt{\sum{g=1}^{N^G} (\nu_{ig} - \nu_g^+)^2} #$$ (25)
where D+ *i*is the distance of alternative route i from the ideal solution, *NG*is the number of route safety attributes.
Similarly, the Euclidean distance from the negative ideal solution is given as
$$D{i}^{-} = \sqrt{\sum{m=1}^{M} (v{ig} - v{g}^{-})^{2}} #$$ (26)
where D− *i*is the distance of alternative route i from the negative ideal solution.
Step 6: Calculate the relative distance to the ideal solution, which is the safety indicator of route i. The equation is expressed as:
$$SI_i = \frac{D_i^-}{D_i^+ + D_i^-} #$$ (27)
Data availability
The data that has been used is confidential.
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