Analyzing the Influence of Risk Perception on Commuters’ Travel Mode Choice in Heavy Rainfall: Evidence from Qingdao, China, Using the RGWRR Model

Abstract

Risk perception and travel behavior under extreme weather have attracted increasing scholarly attention due to their implications for sustainable transport. This study investigates how perceived risks influence commuters’ travel mode choices during heavy rainfall in Qingdao, China, using data from a pilot survey and a stated choice experiment. A Range-varying Generalized Weberian Regret–Rejoice Model (RGWRRM) is developed to capture nonlinear perceptual sensitivities and decision-making under uncertainty. Results indicate that safety and reliability risks significantly shape travel behavior, with commuters showing heightened loss aversion and increased willingness to pay for safer and more dependable modes. The RGWRRM outperforms traditional utility- and regret-based models, offering deeper behavioral insights. By elucidating the mechanisms linking risk perception to mode shifts, this study contributes to the design of resilient and sustainable urban transport strategies in the face of climate-induced disruptions.

1. Introduction

In recent years, the long-term reliability and functionality of transportation systems under extreme weather conditions have garnered growing research interest [1,2]. Among these conditions, the increasing frequency of intense precipitation events has heightened commuters’ exposure to potential travel risks, thereby influencing their mode choices and travel behaviors. Understanding commuter behavior during adverse conditions enables transit agencies to assess changes in travel demand effectively [3]. Moreover, examining how commuters subjectively evaluate and perceive risks associated with heavy rainfall has significant implications for transport planning [4]. However, risk perception remains a critical yet often overlooked factor, directly influencing individuals’ decision-making processes. Commuters’ responses to risks, such as safety concerns, reliability risks, economic costs, and environmental factors, are shaped not only by actual conditions but also by their personal interpretation of risks. A thorough understanding of these cognition processes is vital for transport agencies to develop infrastructure, provide better service in response to future climate change, and equip emergency measures for unexpected events.

The effect of adverse weather on travel behavior varies across different modes of transportation. Non-motorized and unsheltered travel modes are typically vulnerable to heavy rainfall, experiencing significant negative consequences. There is evidence suggesting that variations in temperature, rainfall, and strong wind influence the perceived utility associated with their usage [5,6,7]. Specifically, exposure to wind and precipitation appears to affect comfort levels, causing issues such as impaired vision, disrupted personal grooming, and difficulty maintaining balance [8]. Regarding public transit, studies conducted in Spain indicate that metro systems are preferred under adverse weather conditions, performing better than buses and private vehicles [9]. In addition, empirical data from New York City reveal a 22% increase in the use of taxis and ride-hailing services during rainfall [10]. As for private vehicles, Khattak and Depalma conducted a comprehensive behavioral survey in Brussels [11]. The results show that approximately 50% of car owners are sensitive to bad weather, leading to changes in their departure time, and 35% of them would divert to alternative routes.

To the best of our knowledge, significant differences exist in travel behavior between normal and extreme weather conditions, particularly concerning risk perception. Rainfall contributes to a complex interplay between road accidents, congestion, and travel time delays [12]. Precipitation is often accompanied by fog and strong winds, further affecting the traffic environment. Empirical studies provide abundant evidence of the impact of rain, including low visibility, slippery road conditions, and increased braking distances, on the frequency and severity of traffic incidents [13,14]. These adverse conditions not only elevate actual accident risks but also shape individuals’ risk perceptions, influencing their route and mode choices. Beyond safety concerns, risk perception also extends to discomfort associated with unfavorable weather. Direct physical and mechanical comfort is often considered a key factor in reality. In addition, a large body of research highlights a substantial reduction in traffic speed due to precipitation [15,16], primarily attributed to increased congestion intensity. Such disruptions heighten uncertainty and reinforce perceived risks, further impacting travel behavior. While extreme precipitation may sustainably reduce the number of trips for leisure purposes, essential commutes, being a necessity, persist despite elevated perceived risks. For that very reason, given the crucial role of risk perception in shaping travel behavior, it is imperative to investigate the fundamental mechanisms that drive commuters’ decision-making in transportation choices.

There are a handful of studies on problems of commuter travel mode choice modeling using utility-based [17,18,19] and regret-based theories [20,21,22]. The widely used random utility model (RUM) assumes that decision-makers are rational economic agents and attempt to maximize the utility of available alternatives based on their preferences. A variety of variants of RUM, such as the multinomial logit (MNL) model, nested logit (NL) model, mixed logit (ML) model, and generalized extreme value (GEV) models, have been extensively applied in transportation research and discrete choice analysis. An alternative approach, the random regret minimization (RRM) model, is based on the premise that individuals experience loss aversion when they realize that their chosen option is not the most beneficial [23,24,25]. Subsequent advancements, such as the logarithmic RRM model [26], the hybrid RUM-RRM model, the generalized RRM (GRRM) model [27], and the µRRM [28] model, among others, have demonstrated that the negative emotion of regret performs slightly better in terms of goodness-of-fit and predictive capabilities. However, both the conventional RUM and regret-based models have inherent limitations. RUM assumes that individuals are fully rational and it follows a fully compensatory decision-making process. This assumption fails to capture real-world decision behaviors characterized by threshold effects, non-compensatory choices, and cognitive limitations [29]. While regret-based models attempt to address some limitations of RUM by considering the role of regret in decision-making, they remain one-sided, as they fail to incorporate the contrasting emotional state of the satisfaction individuals feel when they recognize they have made an optimal choice [30]. Moreover, RRM is less sensitive to minor attribute differences, as regret is primarily triggered when the chosen alternative is noticeably outperformed by another option [31]. To address these gaps, Rasouli and Timmermans introduced the regret–rejoice model, which integrates both regret and rejoice by evaluating the differences between the best alternative and all other available options [30]. This model has been successfully applied in various domains, including trip purpose analysis [31], parking choice behavior [32], and travel demand forecasting [33], providing deeper insights into how individuals weigh both positive and negative emotions in their decision-making processes.

The purpose of this paper is to explore risk perception factors influencing commuter mode choice during heavy rainfall by applying a regret–rejoice-based modeling approach. Firstly, a pilot survey was conducted to identify key determinants from a range of potential perceived risk factors. Subsequently, a stated choice experiment was designed to systematically analyze the key risk perception factors, including travel time, travel cost, possible delay, and incident probability, on commuter decision-making. The data was collected in Qingdao, a coastal city in China. In addition, there is a growing need to incorporate behavioral insights that go beyond conventional frameworks. We integrate the development of Weber’s law into the regret–rejoice model to improve the gap of the insensitivity of small attribute differences and propose the Range-varying Generalized Weberian Regret–Rejoice Model (RGWRRM). Finally, the estimation of the RUM, RRM, traditional regret–rejoice model, and RGWRRM provides a comparative assessment of how risk perception influences commuter mode choice, offering deeper insights into the behavioral mechanisms underlying travel decision-making.

The remainder of the study is structured as follows. Section 2 describes the survey design and data collection process. Section 3 presents the RGWRRM’s formulation. In the next section, the estimation results and the comparative analysis of various models are shown and discussed. Finally, we conclude the paper and outline the future work in Section 5.

2. Data Description

Extreme weather conditions, particularly thunderstorms and torrential downpours, have increasingly impacted urban transportation systems by causing widespread waterlogging and significant commuting disruptions. Given these challenges, this study aims to explore variations in risk perception affecting commuters’ mode choice decisions during heavy rainfall. To achieve this, we designed a willingness-to-pay questionnaire tailored to different demographic groups in Qingdao, providing an empirical foundation for understanding commuter behavior in extreme weather conditions.

The questionnaire was designed to include both revealed preference (RP) and stated preference (SP) components to obtain a comprehensive understanding of commuter mode choice under extreme weather conditions. The RP section gathered respondents’ socio-demographic information and their typical travel behavior, while the SP section focused on travel decisions under hypothetical scenarios involving heavy rainfall. In the SP experiment, five travel modes were provided as alternatives: non-motorized vehicles (such as bicycles and electric bikes), buses, metro, taxis or ride-hailing services, and private cars. These options were selected based on their prevalence in the local context and their varying levels of accessibility, comfort, cost, and sensitivity to weather conditions. Non-motorized vehicles, although widely used for short urban trips, are particularly vulnerable to adverse weather. Buses are an affordable option but may experience delays during heavy rain. Metro services, being largely weather-independent, offer relatively high reliability. Taxis and ride-hailing services provide flexibility and comfort at a higher cost, while private cars offer the greatest autonomy but are also subject to traffic congestion and high operational expenses. Walking was excluded from the alternatives, as the commuting distances assumed in the SP design were beyond what is typically considered feasible on foot during heavy rain.

Given the limited understanding of factors influencing individuals’ risk perception during heavy rainfall, a pilot survey was conducted from 2 June to 18 June 2023 as a preliminary step before administering the SP survey. The primary objective was to identify key determinants of risk perception affecting commute mode decisions in the context of extreme weather conditions. The feedback from the pilot survey could help streamline the questionnaire by eliminating redundant or overly complex questions to enhance clarity and manageability.

In the pilot survey, risk perception was categorized into five dimensions: safety risks, reliability risks, economic risks, environmental conditions, and perceived travel experience. Each dimension was represented by specific indicators. Safety risks refer to the increased likelihood of traffic accidents due to slippery road conditions, reduced visibility, and driver errors, all of which are exacerbated during heavy rainfall. Reliability risks pertain to travel time uncertainty and traffic delays caused by unforeseen disruptions, impacting commuters’ travel plans. Here, travel time factors include walking time, waiting time, and in-vehicle travel time. Economic risks stem from increased travel costs associated with choosing safer and more reliable but more expensive transport options to avoid delay. Environmental risks encompass roadway conditions, such as flooding and slippery surfaces, as well as weather-related factors like temperature fluctuations and reduced visibility. These factors collectively diminish both the safety and comfort of commuting. Finally, perceived travel experience, including both travel comfort and crowding of travel modes, was also identified as a significant risk factor in this pilot survey. These factors directly influence commuters’ physical well-being and psychological state, particularly during extreme weather events. Discomfort and high levels of crowding can exacerbate stress and anxiety, leading to changes in travel behavior and mode choices. A Likert-scale questionnaire was developed to assess these risk factors, and 121 valid responses were collected. Based on the response scores, the four most influential factors were identified as travel time, possible delays, incident probability, and travel cost. These variables ranked highest in the aggregated concern levels and were therefore selected as attributes for the SP experiment. Each of the four attributes was assigned four levels. Figure 1 presents a heatmap summarizing respondents’ concern levels across all evaluated factors.

In the SP survey, trip distance was also a crucial consideration that influences the trade-offs commuters make when choosing their travel modes. Each respondent was presented with three typical scenarios: Scenario I for trips less than 6 km, Scenario II for trips between 6 km and 12 km, and Scenario III for trips longer than 12 km. This categorization of commuting distances is based on previous research on travel behavior in Qingdao [34], which reflects common patterns of short-, medium-, and long-distance commutes in the local context. A full factorial design (4⁴) was initially considered to capture all possible combinations, but given the low likelihood of strong interactions between attributes, we simplified it using an orthogonal fractional factorial design [35]. In our study, every scenario initially included 16 choice sets. However, based on pilot survey feedback, respondents found 16 sets per scenario to be excessively burdensome, potentially leading to reduced engagement and response quality. Following the sampling strategy proposed in [32], the final questionnaire randomly assigned four subsets per scenario, resulting in a total of 12 choice sets, ensuring a more manageable and reliable survey process.

The online survey was conducted from 1 July to 15 August 2023. Figure 2 provides an example scenario from the actual survey.

Table 1. Socio-demographic characteristics of the respondents.

Characteristics	Description	Percentage
Gender	Male	50.68%
	Female	49.32%
Age	18 or below	4.05%
	19–30	36.49%
	31–55	42.57%
	56 or above	16.89%
Education	Below Middle School	22.30%
	High school/Technical	24.32%
	Bachelor’s Degree	46.62%
	Postgraduate or above	6.76%
Occupation	Student	26.35%
	Corporate employee	28.38%
	Civil servant	8.11%
	Self-employed	24.32%
	Retired	2.7%
	Others	10.14%
Income (CNY/mo)	≤3000	16.49%
	3001–6000	43.73%
	6001–9000	31.00%
	9000 or above	8.78%
Car ownership	Yes	39.86%
	No	60.14%

Note: CNY is the unit of Chinese currency; 1 CNY = USD 0.145 = EUR 0.127 in August 2023.

presents the descriptive statistics of socio-demographic information for the 333 respondents, constituting the effective sample. The gender distribution was nearly balanced, with 50.68% of respondents identifying as male and 49.32% as female. The age distribution showed that the majority of respondents were between 30 and 55 years old (42.57%), while 36.49% were aged 19–30, and 16.89% were 56 or above. Regarding education, the largest proportion of respondents held a bachelor’s degree (46.62%), followed by those with high school or technical education (24.32%) and those with an education level below middle school (22.30%). A smaller percentage of respondents (6.76%) had postgraduate or higher education qualifications. In terms of occupation, corporate employees formed the largest group at 28.38%, followed by students at 26.35% and self-employed individuals at 24.32%. Civil servants accounted for 8.11% of the sample, while retirees and others represented 2.70% and 10.14%, respectively. Middle-income respondents (43.73%) and upper-middle-income respondents (31.00%) constituted the majority of the sample, while 16.49% fell into the low-income category. High-income respondents (8.78%) formed a smaller proportion, indicating a skew towards middle-income groups. In terms of car ownership, 39.86% of respondents reported owning a car, while 60.14% did not.

The demographic distribution suggests a representative sample of urban commuters in Qingdao, with a balanced gender ratio and a predominance of middle-aged, middle-income individuals. These insights provide a robust foundation for analyzing how risk perception influences travel mode choices under extreme weather conditions.

3. Model Specifications

Traditional discrete choice models, such as the RUM, assume that decision-makers seek to maximize utility in a fully compensatory manner. However, this framework struggles to explain behaviors under uncertainty, particularly in the presence of heightened perceived risks [34,36,37,38]. RRM was introduced as an alternative approach to address these limitations by incorporating loss aversion into decision-making. A number of studies have argued that the fully compensatory nature of the RUM framework results in poor predictive performance, especially under conditions of uncertainty characterized by heightened perceived risks. Regret-based models can generally be categorized into two main types: the original specification [25] and the logarithmic formulation [26]. Some further studies have developed the fundamental proposition based on the regret theory [28,39,40,41] and expanded their range of application scenarios [38,42,43,44].

However, it is a point for discussion whether individuals become aware of rejoice when they make a choice. Rasouli and Timmermans [30] have discussed this issue and evidenced that regret arises from recognizing a suboptimal choice, while rejoice represents the contrasting emotional response to realizing that one has made an optimal decision. In practice, individuals often exhibit limited sensitivity to the trade-off between regret and rejoice emotions when making decisions. However, traditional regret-based models account only for regret, which is insufficient to accurately capture choice behavior. In addition, both the constant term [26] and the regret weight parameter [39] in the logarithmic approximation specification serve as mechanisms to define the contributions of regret and rejoice. Therefore, Rasouli and Timmermans [30] proposed a more flexible approach that incorporates both regret and rejoice. They developed a regret–rejoice model that evaluates attribute differences between the best alternative and all other available choices. When the chosen alternative i is compared to a non-chosen alternative j, the regret-rejoice model can be expressed as

$$RG{J}_{nk}^{i\leftrightarrow j}=R{J}_{nk}^{i\leftrightarrow j}-R{G}_{nk}^{i\leftrightarrow j}$$

(1)

where $RG{J}_{nk}^{i\leftrightarrow j}$ denotes the regret–rejoice experienced by individual n with respect to attribute k. This function consists of two components: regret $R{G}_{nk}^{i\leftrightarrow j}$ and rejoice $R{J}_{nk}^{i\leftrightarrow j}$. Regret $R{G}_{nk}^{i\leftrightarrow j}$ of individual n associated with attribute k in the context of the chosen alternative i and the non-chosen alternative j is formulated following the original RRM, which can be expressed as [31]

$$R{G}_{nk}^{i\leftrightarrow j}={\displaystyle \sum _k\max \left[0,{\beta }_k^{RG}\left(x_{jnk}-x_{ink}\right)\right]}$$

(2)

where ${\beta }_k^{RG}$ denotes the parameter for regret, and $x_{jnk}-x_{ink}$ represents the difference in attribute values when alternative j outperforms alternative i with respect to attribute k. In addition, the amount of rejoice $R{J}_{nk}^{i\leftrightarrow j}$ with regard to attribute k between alternatives i and j is defined as follows:

$$R{J}_{nk}^{i\leftrightarrow j}={\displaystyle \sum _k\min \left[0,{\beta }_k^{RJ}\left(x_{jnk}-x_{ink}\right)\right]}$$

(3)

where parameter ${\beta }_k^{RJ}$ denotes the perceived weight from observed choices for attribute k. Therefore, the regret–rejoice model in Formula (1) could be rewritten as

$$\begin{array}{ll}RG{J}_{nk}^{i\leftrightarrow j}& =R{J}_{nk}^{i\leftrightarrow j}-R{G}_{nk}^{i\leftrightarrow j}\\ & ={\displaystyle \sum _k\left\{\min \left[0,{\beta }_k^{RJ}\left(x_{jnk}-x_{ink}\right)\right]-\max \left[0,{\beta }_k^{RG}\left(x_{jnk}-x_{ink}\right)\right]\right\}}\end{array}$$

(4)

Nevertheless, this model is limited to capturing absolute differences in attributes and does not account for how individuals perceive changes in attribute intensity [45]. Thus, Jang [33] introduced psycho-physical mapping into the regret–rejoice model based on Weber’s law. Weber’s law, originally developed in psychology, describes the relationship between stimulus intensity and perceptual differences. It suggests that as the intensity of the initial stimulus increases, significantly greater strength is required in subsequent stimuli to achieve the same perceived difference [46]. When Weber’s law is applied to the regret–rejoice model, $x_{jnk}-x_{ink}$ should be replaced by $(x_{jnk}-x_{ink})/x_{ink}$, that is

$$\begin{array}{ll}RG{J}_{nk}^{i\leftrightarrow j}& =R{J}_{nk}^{i\leftrightarrow j}-R{G}_{nk}^{i\leftrightarrow j}\\ & ={\displaystyle \sum _k\left\{\min \left[0,{\beta }_k^{RJ}\left(\frac{x_{jnk}-x_{ink}}{x_{ink}}\right)\right]-\max \left[0,{\beta }_k^{RG}\left(\frac{x_{jnk}-x_{ink}}{x_{ink}}\right)\right]\right\}}\end{array}$$

(5)

This new regret–rejoice model is not only determined by the attribute differences between the chosen and non-chosen alternatives but is also influenced by the magnitude of the attribute itself. However, the generalized Weber’s law is not applicable to the perception of high-intensity stimuli. Therefore, the power parameter ${\theta }_k\in \left[0,1\right]$ is introduced in the denominator to moderate the Weber model specification, that is

$$\begin{array}{ll}RG{J}_{nk}^{i\leftrightarrow j}& =R{J}_{nk}^{i\leftrightarrow j}-R{G}_{nk}^{i\leftrightarrow j}\\ & ={\displaystyle \sum _k\left\{\min \left[0,{\beta }_k^{RJ}\left(\frac{x_{jnk}-x_{ink}}{{(x_{ink})}^{{\theta }_k}}\right)\right]-\max \left[0,{\beta }_k^{RG}\left(\frac{x_{jnk}-x_{ink}}{{(x_{ink})}^{{\theta }_k}}\right)\right]\right\}}\end{array}$$

(6)

where the power parameter ${\theta }_{ink}$ at attribute level k is estimated from the observed choices related to the relationships between the parameters ${\gamma }_k$ and ${\delta }_k$. As shown in Figure 3, the psycho-physical mapping function is expected to exhibit a unimodal function. Traditional Weber’s law performs well in the middle range of attribute intensity. However, the generalized Weber’s law results in greater perceived attribute differences. The power parameter ${\theta }_{ink}$ could be expressed as [33]

$${\theta }_{ink}=\exp \left(-\left({\gamma }_k{x}_{ink}-{\delta }_k\right)\right)$$

(7)

where the parameter ${\gamma }_k$ is termed the scale parameter, which captures the arbitrary scale of the attribute. The parameter ${\delta }_k$ is referred to as the shift parameter, reflecting the level of the attribute. This can involve increasing or decreasing the perceived difference between levels of an attribute, thereby shifting the output in response to the attribute’s variation.

When the power parameter $\theta$ approaches 1, it indicates the decision-maker is more likely to perceive the relative difference in the attribute [45]. Conversely, when the power parameter $\theta$ approaches 0, the decision-maker tends to focus on the absolute difference. Finally, the regret–rejoice model in Equation (1) gives

$$\begin{array}{ll}RG{J}_{nk}^{i\leftrightarrow j}& =R{J}_{nk}^{i\leftrightarrow j}-R{G}_{nk}^{i\leftrightarrow j}\\ & ={\displaystyle \sum _k\left\{\min \left[0,{\beta }_k^{RJ}\left(\frac{x_{jnk}-x_{ink}}{{(x_{ink})}^{{\theta }_k}}\right)\right]-\max \left[0,{\beta }_k^{RG}\left(\frac{x_{jnk}-x_{ink}}{{(x_{ink})}^{{\theta }_k}}\right)\right]\right\}}\\ & ={\displaystyle \sum _k\left\{\min \left[0,{\beta }_k^{RJ}\left(\frac{x_{jnk}-x_{ink}}{{(x_{ink})}^{\exp \left(-\left({\gamma }_k{x}_{ink}-{\delta }_k\right)\right)}}\right)\right]-\max \left[0,{\beta }_k^{RG}\left(\frac{x_{jnk}-x_{ink}}{{(x_{ink})}^{\exp \left(-\left({\gamma }_k{x}_{ink}-{\delta }_k\right)\right)}}\right)\right]\right\}}\end{array}$$

(8)

4. Results

4.1. Estimation Results

The estimation results of the RUM, RRM, RGJ, and RGWRGJ models for three different distance scenarios are shown in

Table 2. Estimation results of the RUM, RRM, RGJ, and RGWRGJ models for Scenario I (distance < 6 km).

Variables	RUM	RRM	RGJ	RGWRGJ
Travel time (t value)	−0.401 (−6.33)	−0.226 (−8.43)	−0.203 (−4.47)	−0.182 (−4.82)
Travel cost (t value)	0.120 (4.08)	0.003 (−2.26)	0.008 (6.25)	0.041 (4.81)
Possible delays (t value)	−0.128 (−2.97)	−0.069 (−2.79)	−0.141 (−3.26)	−0.118 (−4.01)
Incident probability (t value)	−0.414 (−2.04)	−0.289 (−1.99)	−0.236 (−2.57)	−0.271 (−6.65)
Gamma_travel time (t value)				0.246 (5.21)
Delta_travel time (t value)				3.510 (2.55)
Gamma_travel cost (t value)				0.196 (2.30)
Delta_travel cost (t value)				0.959 (3.95)
Gamma_possible delays (t value)				0.267 (3.05)
Delta_possible delays (t value)				2.752 (5.95)
Model fit
Rho-squared	0.312	0.317	0.328	0.382
BIC	4261.326	4233.533	4208.469	4224.098
Final log-likelihood	−2116.274	−2102.378	−2075.457	−2083.271

,

Table 3. Estimation results of the RUM, RRM, RGJ, RGWRGJ models for Scenario II (distance 6–12 km).

Variables	RUM	RRM	RGJ	RGWRGJ
Travel time (t value)	−0.394 (−10.10)	−0.193 (−11.7)	−2.550 (−2.95)	−0.994 (−3.14)
Travel cost (t value)	0.164 (9.72)	0.013 (2.10)	0.026 (9.57)	0.233 (7.96)
Possible delays (t value)	−0.161 (−3.98)	−0.125 (−8.26)	−3.121 (−9.54)	−1.161 (−8.37)
Incident probability (t value)	−0.923 (−2.46)	−0.571 (−3.82)	−1.48 (−3.63)	−2.952 (−3.01)
Gamma_travel time (t value)				0.145 (4.27)
Delta_travel time (t value)				4.227 (3.82)
Gamma_possible delays (t value)				0.138 (5.11)
Delta_possible delays (t value)				1.664 (2.25)
Model fit
Rho-squared	0.342	0.346	0.388	0.389
BIC	4125.886	4110.424	3951.359	3946.827
Final log-likelihood	−2048.554	−2040.732	−1946.902	−1944.636

and

Table 4. Estimation results of the RUM, RRM, RGJ, RGWRGJ models for Scenario III (distance > 12 km).

Variables	RUM	RRM	RGJ/RGWRGJ
Travel time (t value)	−0.378 (−14.7)	−0.160 (−14.6)	−2.840 (−3.03)
Travel cost (t value)	0.157 (11.7)	0.006 (1.99)	0.323 (9.33)
Possible delays (t value)	0.090 (3.88)	−0.023 (−2.67)	−1.670 (−5.9)
Incident probability (t value)	−0.185 (2.485)	−0.394 (−2.51)	−0.807 (−1.96)
Model fit
Rho-squared	0.354	0.352	0.391
BIC	4073.149	4083.054	3935.806
Final log-likelihood	−2022.186	−2027.138	−1939.135

. All estimated attributes are statistically significant at the 95% confidence level and their signs are consistent across models. In the RGWRGJ model, power coefficients are not included when they fail to reach statistical significance at the 95% threshold. Meanwhile, when the RGWRGJ model exhibits poor fit, the power coefficients are not applied. In such cases, as seen in Table 4, the RGWRGJ model reverts to the RGJ framework, where perception variations are still considered, but the additional parameterization for attribute scaling is omitted.

The respondents face significant risk pressure from safety concerns and time reliability factors, exhibiting a strong loss aversion psychology for incident probability, travel time, and possible delay during extreme weather conditions. This is consistent across all three commuting distance scenarios, as reflected in the negative signs of these parameters in Scenario II and Scenario III. However, there are significant variations in the intensity of these effects depending on the commuting distance. Heavy rainfall introduces heightened risks and uncertainties, amplifying the psychological impact of safety concerns and time reliability on travel behavior. The relative importance of these attributes shifts as commuting distance increases, suggesting that individuals weigh risks differently over short, medium, and long trips.

As for the short commute distance (Scenario I) in Table 2, safety concerns play a dominant role in travel mode choice, as the proximity of the destination makes accidents seem more avoidable. According to prospect theory, individuals exhibit greater loss aversion when they perceive risks as preventable, which intensifies their sensitivity to incident probability. The perceived risk is further heightened by environmental factors such as skidding hazards for motorcycles and bicycles, reduced visibility on wet roads, and direct exposure to adverse weather for pedestrians and cyclists. These challenges reinforce commuters’ risk-averse behavior, making safety the most critical factor in their mode selection. While travel time and possible delays also influence decisions, they play a secondary role in short trips. The inherently shorter travel duration minimizes the impact of delays, making them less disruptive compared to longer commutes. Additionally, commuters perceive short-trip delays as more manageable, reducing their weight in the decision-making process. As a result, while reliability remains relevant, immediate safety risks outweigh time-related concerns in shaping commuting behavior under heavy rainfall.

For medium-distance commutes (Scenario II) in Table 3, the incident probability remains the top concern, but possible delay becomes more significant than travel time. As commuting distance increases, uncertain delays are more disruptive than minor variations in travel speed. Commuters begin prioritizing delay reliability, since the psychological cost of uncertainty becomes more pronounced over long trips. Furthermore, different transportation modes have various characteristics impacted by rainfall-induced delay. Buses and taxis/ride-hailing services are particularly vulnerable to delays in heavy rainfall due to traffic congestion and reduced speeds on wet roads. Private cars face similar risks, especially on congested routes. Although metro systems offer a relatively safe and delay-free alternative, commuters may still perceive delays due to increased passenger demand and potential disruptions caused by rain-related operational issues. These factors collectively reinforce the perception that delays introduce greater uncertainty than variations in travel time, prompting commuters to adjust their decision-making accordingly.

For long-distance commutes (Scenario III) in Table 4, travel time becomes the most critical factor, followed by possible delay, and finally incident probability. In heavy rainfall, safety concerns take a backseat to time management due to a shift in how commuters evaluate risk over longer trips. While incidents remain a concern, the prolonged duration of long-distance travel leads commuters to focus more on the cumulative impact of travel time and possible delays on their overall schedule. Moreover, commuters may perceive incidents as less likely over longer routes, particularly when using metro systems or regulated highways, which are generally considered safer. The psychological process of risk normalization leads commuters to downplay incident probability in longer trips [47]. In such scenarios, travelers prioritize efficiency, as delays in long-distance travel tend to accumulate, further worsening the discomfort of adverse weather conditions.

The positive parameter for travel cost is positive, which means the respondents have a greater willingness to accept higher travel costs to reduce the potential risk factors when choosing commuting modes. This finding contrasts with prior studies emphasizing that lower travel costs increase the likelihood of a mode being chosen, as affordability typically plays a major role in commuting decisions [48,49]. Even during the COVID-19 pandemic, studies observed that travel cost retained its expected negative sign, indicating that affordability remained a critical factor influencing commuting behavior [34,35]. However, the current result suggests that a shift of monetary cost in priorities is driven by a heightened perception of safety and convenience during adverse weather conditions. This behavior is consistent with risk aversion theory, which posits that individuals tend to prioritize risk reduction over cost savings when faced with uncertainty [23]. From a behavioral economics perspective, commuters’ willingness to pay more reflects the perceived value of reduced uncertainty, reinforcing the importance of safety and reliability. Furthermore, travelers perceive travel time, delays, and incident probabilities differently based on their individual experiences and risk tolerance. These variations necessitate converting such factors into monetary terms to quantify their willingness to pay for safer and more reliable commuting options [50]. These findings are consistent with previous research indicating that, in uncertain environments, travelers place greater emphasis on reliability and comfort, often adjusting their willingness to pay in response to perceived risks [4,10].

McFadden’s likelihood ratio index (pseudo-Rho-squared), the Bayesian Information Criterion (BIC), and final log-likelihood are crucial indices to evaluate the goodness of fit for these models. The Rho-squared index ranges from 0 to 1, with a value closer to 1 indicating a better fit. A lower BIC suggests a more optimal model by balancing goodness of fit with model complexity [51]. The final log-likelihood represents the probability of the observed data given the model’s estimated parameters at convergence, where a higher value indicates better model performance.

Comparing the Rho-squared values, the RGWRGJ model consistently achieves the highest value across all three scenarios, indicating the best fit among the models evaluated. Scenarios I and II show that the RRM model slightly outperforms the RUM, suggesting that the semi-compromise effect of the regret-based model is more applicable in emotionally driven risk-averse environments [52]. These findings are in line with the results reported in previous studies [21,53]. Nevertheless, in Scenario III, the performance of the Rho-squared and BIC values of the RUM is superior to that of the RRM model. Sometimes, decision-makers exhibit rational behaviors, which enhances the explanatory power of the RUM [54]. Furthermore, the final log-likelihood values show a similar trend to that observed with the Rho-squared values and BIC results.

The estimation results for the RUM, RRM, RGJ, and RGWRGJ models across different scenarios reveal that the RGWRGJ model consistently outperforms the others in terms of model fit, explanatory power, and the ability to capture nonlinear relationships between variables. One of the key advantages of the RGWRGJ model is its ability to account for nonlinear relationships through the introduction of power parameters. This parameter offers a more flexible representation of perception variance by assigning a unique coefficient value for each attribute level. In the case of Scenario I, the RGWRGJ model allows the power coefficient of travel time to vary dynamically based on its value, unlike the fixed perception in the RGJ model. The estimated values for the parameters are $\delta =3.510$ and $\gamma =0.246$, respectively. This indicates that as travel time increases, the value of the power coefficient initially increases until it reaches a maximum at ${\displaystyle \frac{\delta }{\gamma }}={\displaystyle \frac{3.510}{0.246}}\approx 14$ min, after which it starts to decrease. $x_{ink}={\displaystyle \frac{{\delta }_k}{{\gamma }_k}}$ is called as the Weber point. In Scenario II, the Weber point of travel time occurs at ${\displaystyle \frac{\delta }{\gamma }}={\displaystyle \frac{4.227}{0.145}}\approx 29$ min. In Scenario III, the estimation of $\delta$ and $\gamma$ does not reach statistical significance at the 95% confidence level. Thus, ${\theta }_{ink}=1$, and the RGWRGJ model converts to the RGJ model. The results further indicate that the RGJ model outperforms the RUM and RRM models based on Rho-squared values, BIC, and final log-likelihood metrics.

4.2. Elasticity Analysis

Choice elasticities were calculated using a finite difference approach based on the estimated parameters from each model. These elasticities reflect the percentage change in the probability of choosing a specific travel mode in response to a 1% change in a particular attribute. The results allow for a comparative assessment of behavioral sensitivity across models with different underlying assumptions about decision-making and perception.

Table 5. Elasticities of the RUM, RRM, RGJ, RGWRGJ models for Scenario I.

RUM	Alt. 1	Alt. 2	Alt. 3	Alt. 4	Alt. 5
Attribute	Non-motorized vehicles	Buses	Metro	Taxis/ride-hailing services	Private cars
Travel time	−0.492	−0.661	−0.443	−0.374	−0.673
Possible delays	−0.105	−0.053	−0.102	−0.092	−0.162
Travel costs	0.000	0.010	0.019	0.206	0.040
Incident probability	−0.102	−0.034	−0.033	−0.030	−0.035
RRM
Travel time	−0.272	−0.364	−0.248	−0.230	−0.370
Possible delays	−0.056	−0.028	−0.055	−0.054	−0.086
Travel costs	0.000	0.000	−0.001	−0.006	−0.001
Incident probability	−0.070	−0.023	−0.023	−0.023	−0.024
RGJ
Travel time	−0.211	−0.325	−0.210	−0.201	−0.362
Possible delays	−0.048	−0.021	−0.049	−0.049	−0.078
Travel costs	0.000	0.000	−0.001	−0.005	−0.001
Incident probability	−0.059	−0.017	−0.017	−0.017	−0.017
RGWRGJ
Travel time	−0.192	−0.261	−0.179	−0.196	−0.300
Possible delays	−0.039	−0.017	−0.035	−0.036	−0.067
Travel costs	0.000	0.000	−0.000	−0.002	−0.001
Incident probability	−0.047	−0.012	−0.012	−0.013	−0.013

,

Table 6. Elasticities of the RUM, RRM, RGJ, RGWRGJ models for Scenario II.

RUM	Alt. 1	Alt. 2	Alt. 3	Alt. 4	Alt. 5
Attribute	Non-motorized vehicles	Buses	Metro	Taxis/ride-hailing services	Private cars
Travel time	−1.072	−1.347	−1.148	−0.632	−1.144
Possible delays	−0.137	−0.069	−0.134	−0.105	−0.370
Travel costs	0.001	0.014	0.041	0.390	0.119
Incident probability	−0.236	−0.079	−0.077	−0.055	−0.079
RRM
Travel time	−0.624	−0.798	−0.492	−0.489	−0.652
Possible delays	−0.019	−0.019	−0.018	−0.021	−0.076
Travel costs	0.000	0.000	0.002	0.025	0.006
Incident probability	−0.096	−0.033	−0.030	−0.030	−0.032
RGJ
Travel time	−0.433	−0.589	−0.298	−0.277	−0.215
Possible delays	−0.075	−0.019	−0.018	−0.018	−0.019
Travel costs	0.000	0.000	0.000	0.014	0.001
Incident probability	−0.073	−0.014	−0.011	−0.012	−0.014
RGWRGJ
Travel time	−0.319	−0.418	−0.175	−0.166	−0.141
Possible delays	−0.061	−0.007	−0.007	−0.007	−0.008
Travel costs	0.000	0.000	0.000	0.012	0.001
Incident probability	−0.058	−0.009	−0.008	−0.009	−0.009

and

Table 7. Elasticities of the RUM, RRM, RGJ, RGWRGJ models for Scenario III.

RUM	Alt. 1	Alt. 2	Alt. 3	Alt. 4	Alt. 5
Attribute	Non-motorized vehicles	Buses	Metro	Taxis/ride-hailing services	Private cars
Travel time	−1.578	−2.059	−1.226	−0.877	−1.519
Possible delays	0.079	0.082	0.073	0.063	0.291
Travel costs	0.002	0.014	0.051	0.503	0.165
Incident probability	−0.049	−0.017	−0.015	−0.011	−0.015
RRM
Travel time	−0.624	−0.798	−0.492	−0.489	−0.652
Possible delays	−0.019	−0.019	−0.018	−0.021	−0.076
Travel costs	0.000	0.000	0.002	0.025	0.006
Incident probability	−0.096	−0.033	−0.030	−0.030	−0.032
RGJ/RGWRGJ
Travel time	−0.533	−0.681	−0.387	−0.365	−0.501
Possible delays	−0.009	−0.009	−0.009	−0.012	−0.059
Travel costs	0.000	0.000	0.001	0.018	0.004
Incident probability	−0.081	−0.024	−0.021	−0.021	−0.023

present the direct elasticity estimates of travel mode choices with respect to four key attributes (travel time, possible delays, travel costs, and incident probability), based on four different modeling approaches. Across all these models, the elasticities of the RUM show the greatest sensitivity to change of attribute, especially for time- and risk-related attributes. This is attributed to the linear and fully compensatory nature of the RUM, which assumes that individuals respond proportionally to any marginal change in attribute levels. In contrast, the RGWRGJ model consistently produces the smallest elasticities across all attributes and scenarios, indicating a more attenuated behavioral response. This result reflects the influence of perceptual thresholds and nonlinear attribute processing embedded in the RGWRGJ formulation, which reduces sensitivity to small or excessive changes that may fall outside the commuter’s perceptual range. The RRM and RGJ models lie between these two extremes, capturing moderate sensitivity adjustments through regret-based or range-sensitive mechanisms.

As commuting distance increases from Scenario I to III, a shift in the relative importance of attributes is observed. On shorter trips, travelers are more responsive to risk-related attributes, such as incident probability and possible delays. However, as distance increases, travel time becomes the dominant determinant of mode choice. This trend is captured by all models, though the rate of change is more gradual in RGWRGJ, suggesting its advantage in reflecting bounded rationality. Additionally, the elasticities associated with travel costs are consistently low in all models and scenarios. In some cases, particularly under RGWRGJ, cost elasticities are close to zero or slightly positive, suggesting that during adverse weather conditions, individuals may accept higher costs if associated with safer or more reliable modes, such as taxis or ride-hailing services.

5. Conclusions

Understanding how and why travel mode choices shift under extreme weather conditions is essential for designing resilient and adaptive transportation systems. This study investigates the influence of risk perception on commuters’ travel mode choices under heavy rainfall. To explore commuter risk perception factors, we conducted a pilot survey, as well as RP and SP surveys, based on data collected in Qingdao, China. The pilot survey aimed to identify key determinants from various risk categories, including safety risks, reliability risks, economic risks, weather-related environmental factors, and perceived travel experience. The four most influential factors identified were travel time, possible delays, incident probability, and travel cost. A stated choice experiment was subsequently designed, incorporating these four attributes and categorizing commutes into short-, medium-, and long-distance scenarios to analyze how travel mode choices vary with distance and perceived risk factors. In this study, we use the RGWRGJ model, a regret–rejoice model integrating psycho-physical mapping based on the range-varying generalized Weberian law. This model accounts for the nonlinear perception of attribute differences and provides a more flexible representation of decision-making under uncertainty.

Bearing in mind the objective of our paper and the restrictions of this case study, the conclusions are evident. Results show that commuters exhibit loss-averse behavior during heavy rainfall, with incident probability, travel time, and possible delays being the most influential factors across different commuting distances. In both short- and medium-distance scenarios, incident probability emerges as the dominant factor, as safety risks significantly affect travel mode choices. Travel time ranks second in short-distance commutes, while in medium-distance trips, concerns about delays become more prominent due to increased uncertainty in traffic conditions. For long-distance commutes, travel time overtakes other factors as the primary determinant, indicating that minimizing time burdens becomes the central priority. Interestingly, the travel cost variable exhibits a slightly positive coefficient, suggesting that commuters are willing to incur higher expenses in exchange for safer and more reliable options under heavy rainfall. In this study, the RGWRGJ model consistently outperforms the RUM, RRM, and RGJ models across all three commuting scenarios, as evidenced by its higher Rho-squared values and lower BIC scores, demonstrating superior explanatory power. The power coefficients in the RGWRGJ model dynamically adjust based on attribute intensity, effectively capturing variations in risk perception.

Our findings provide valuable insights for transportation planners and policymakers. Given that perceived travel time and possible delays significantly impact mode choice, improving the reliability of bus and metro services could enhance their attractiveness during extreme weather conditions. This can be achieved by increasing service frequency, which reduces waiting times, alleviates crowding, and encourages commuters to opt for public transportation. In addition, as safety concerns strongly impact travel decisions, implementing real-time risk alerts, improving road drainage, and enhancing street lighting could help mitigate perceived risks. For taxi and ride-hailing services, dynamic pricing mechanisms could be effective in managing demand surges during extreme weather events, ensuring that service availability remains balanced with fluctuating demand. In addition, collaboration between ride-hailing platforms and local authorities could also facilitate the development of optimized routing strategies, directing drivers along safer and more efficient routes during adverse weather conditions.

Lastly, this study is based on empirical data collected in Qingdao, which may constrain the generalizability of the findings to other urban settings. While Qingdao shares many characteristics with other large Chinese cities—such as multimodal transport systems and exposure to climate-induced risks—differences in land use, commuting culture, and urban planning may lead to variations in travel behavior and risk perception. In future work, we plan to extend the current framework to other cities with different geographical and socioeconomic profiles, in order to examine whether the behavioral patterns observed here are consistent and to explore potential context-dependent differences in travel mode choices under extreme weather conditions.