Travel Mode Choices for Connecting Urban Rail Transit System During Irregular Time Periods: A Case Study in Beijing

Abstract

The varying operating schedules of urban rail transit (URT) lines, combined with the distance between travelers’ origins and the URT stations, pose challenges for selecting their travel modes during irregular time periods such as early mornings and late evenings (EMLE). The choices during these special time periods may be influenced by personal attributes, travel attributes, environmental attributes, and psychological perceptions. We first conduct a questionnaire survey to explore travelers’ choice behaviors when they commute to or from URT stations, considering various influencing factors. After completing the statistical analysis, we then proceed with a preliminary assessment of the factors impacting travel mode preferences. Subsequently, a hybrid methodology that integrates structural equation modeling (SEM) and a random parameter logit model (RPLM) is introduced to investigate the impacts of factors. Notably, the interaction terms among travel time, cost, and psychological perception are considered as random variables. As a result, the heightened interaction between travel time and safety perception leads to a reduced probability of opting for walking or bike-sharing as transportation modes. Similarly, there is a notable decrease in the probability of selecting a taxi when the interaction terms of travel cost and safety perception increase. The above results identify that travelers prefer to take safer and more convenient travel modes during the EMLE period.

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1. Introduction

With the rapid pace of urbanization, large cities are increasingly confronted with significant traffic management challenges, particularly during morning and evening peak hours when both surface streets and underground urban rail transit (URT) experience substantial congestion. As the China’s capital, the URT system of Beijing plays a crucial role in alleviating urban traffic pressure. However, the travel complexity during peak hours is further compounded by the varying operating schedules of different URT lines and the different distances between travelers’ origins and stations. While travel constraints during standard peak hours are relatively well understood, the travel conditions during early morning (4:30 a.m. to 6:30 a.m.) and late-night (9:00 p.m. to 12:00 a.m.) (EMLE) periods present significant differences. During the EMLE period, although travel demand is not high, the decision-making process is influenced by more complex environmental factors and psychological perceptions. Specifically, the purposes of travel during EMLE differ from those during the daytime. For instance, early-morning travelers are more likely to be heading to airports, railway stations, or workplaces with early shifts. Due to the lower number of travelers, the concerns of safety and comfort play a more critical role in influencing travel mode choices with the inadequate street lighting and the relatively sparse number of travelers. In contrast, late-night travelers may be returning from nightlife activities or working night shifts, and they tend to emphasize safety, environmental conditions, and the presence of travel companions. Moreover, the concerns of the adverse weather conditions, the need to carry luggage, and the presence of companions can significantly alter travelers’ decision-making processes. For example, in extreme weather conditions such as heavy rain, snow, or extreme temperatures, taxis or ride-hailing services could be the best choices rather than walking or bike-sharing. The road congestion and the presence of companions are also directly influenced travelers, as well as the psychological perceptions (safety, comfort, convenience, and perceived behavioral control). During the EMLE period, safety perceptions encompass not only the comfort and convenience of the transportation mode but also the psychological evaluation of potential risks. These psychological factors contribute to the variations in different traveler groups (e.g., male vs. female travelers). Therefore, studying on the choice decision of connection modes in URT during EMLE holds both academic and practical significances.

Given the increasing complexity of urban transportation needs, understanding traveler behavior during different times is crucial for transportation planning and service optimization. In traditional studies on travel mode choice, a focus on peak hours is most studies use logit models to analyze travel decisions, emphasizing personal attributes, but the impact of environmental factors and psychological perceptions is missed [1–3]. To supplement the latent variables, such as the safety perceptions and the combination of random coefficient models, we will examine how these interact with each other in a choice decision during the EMLE period. This study aims to support the optimization of URT connections during special periods such as EMLE, enhancing safety, convenience, and comfort for travelers and ultimately improving traffic service quality. First, the research emphasizing environmental factors (e.g., weather, luggage, and companions) and psychological perceptions (e.g., safety, comfort, and convenience) is expanded in EMLE time. Second, the interaction terms between time, cost, and latent variables, offering a deeper understanding of how these factors jointly influence travel mode choices, are considered.

There are 6 sections in the study. Research backgrounds and motivations are introduced in Section 1. Section 2 provides a comprehensive review of the literature related with the connection mode choices. In Section 3, a questionnaire is designed, and the survey data are listed. The theoretical models are introduced in Section 4. Section 5 is dedicated to empirical research and result analysis. Section 6 contains the concluding remarks and illustrates the limitations.

2. Literature Review

In the field of transportation mode choice research, many studies employ various modeling techniques to analyze travel mode choices, and their influencing factors, such as the multinomial logit (MNL) model, are widely applied. [4]​ used the MNL model to analyze the travel mode characteristics in Fujian Province, finding that travelers prefer to take private cars over public transportation. Etminani-Ghasrodashti et al. [5] used a multilevel integration of the MNL model and the structural equation model (SEM) to study the travel behavior of young travelers in Iran, revealing that despite the availability of public transportation, they still prefer private cars. Chen et al. [6] pointed out that socioeconomic status, transportation accessibility, and health issues are key factors influencing mode choice. Shen et al. [7] investigated the impact of electronic road pricing on mode choice, finding that its impact on travel modes is limited. In addition to economic factors, personal attributes also play a critical role. Liu et al. [8] suggested that age, gender, and marital status are indirect factors affecting commute mode choice. Ahmed and Hyland [9] used the binary logit model to study the use of ride-hailing apps, finding that younger age, higher income households, and frequent travelers are more likely to choose ride-hailing services. Liu et al. [10] analyzed the choice between bike-sharing and public transportation among Beijing users, discovering that walking distance, bike lane conditions, travel time, and peak hours statistically significantly affect user preferences. Although traditional logit models are widely used, there are some limitations, such as the independent and irrelevant alternatives (IIA) assumptions, which fail to fully capture travelers’ heterogeneity and the substitution relationships in each mode. To address these issues, researchers proposed a random parameter logit model (RPLM), which offers better flexibility, particularly when considering travelers’ heterogeneity. The RPLM, first proposed by McFadden and Train [11], handles heterogeneity in traveler choices more effectively, especially in complex scenarios involving multiple alternative choices. In this context, many studies begin using the RPL model to explore the influencing factors of mode choice in greater depth. For example, Risdiyanto et al. [12] used a mixed logit model to analyze the preferences of high school seniors and university students when choosing between buses and private cars, finding that travel time and cost statistically significantly affect mode choice. Yu et al. [13] used a nested logit model to analyze the travel modes of young travelers in Nanjing, discovering that higher education, lower income, a clear travel purpose, and longer travel distances increase the preference for ride-hailing services.

The consideration of psychological perceptions and environmental factors becomes an important direction in recent transportation mode choice research. Increasingly, studies recognize that factors such as travelers’ psychological perceptions and the environmental characteristics of travel destinations play a crucial role in travel decision-making. Liu et al. [14] pointed out that planned travelers are less sensitive to weather changes, but adverse weather statistically significantly affects public transportation travel times. Additionally, Sabir [16] find that under adverse weather conditions, some travelers prefer URT. Wu and Liao [17] used OLS regression to analyze the impact of weather on travel behavior, finding that extreme weather conditions statistically significantly affect leisure travel and mode shifts. The introduction of psychological perception factors, particularly understanding travelers’ psychological states, can statistically significantly enhance the explanatory power of transportation mode choice models. For example, Paulsen et al. [18] studied how changes in personal attitudes and values influence travel mode choices, especially highlighting the profound impact of personal emotions and cognition on decision-making processes. Cheng et al. [19] analyzed the travel modes of low-income groups, finding that incorporating latent variables can more accurately reveal their decision-making processes. Wang et al. [20] incorporated latent variables into the study of shared bicycle choices, showing that psychological perception factors play a statistically significant role in mixed logit models. While the research models and influencing factors on mode choice are rich in variety, there are still areas for further optimization. To more clearly illustrate the differences between previous studies and this paper, this paper summarizes and synthesizes the influencing factors and modeling methods of mode choice in core journals in recent years. The details are shown in Table 1.

Table 1

Literature review summary.

Authors	Research methods	Influencing factor (attributes)				Emphasis
		Personal	Travel	Environmental	Psychological
Zou et al. [21]	Bayesian/ABM	√	√	√	×	Travel mode and departure time
Tamim Kashifi et al. [22]	Machine learning	√	√	×	×	Forecast
Etminani-Ghasrodashti et al. [5]	MNL/SEM	×	×	√	√	Youngster
Wang and Song [23]	RP/SP	√	×	×	√	Car sharing
Yang et al. [24]	MNL	×	√	×	√	Built environment
Chen et al. [6]	MNL	√	√	√	×	COVID-19
Wu and Liao [17]	OLS	×	×	√	×	Extreme weather
Shen et al. [7]	Nested logit	√	×	×	×	Ride-hailing
He et al. [25]	Random forest	×	√	×	×	Short distance travel
He et al. [26]	Random forest	×	√	×	×	Travel distance
De Vos et al. [27]	SEM	×	×	×	√	Travel attitude and relocation
Ingvardson et al. [28]	ICLV	×	×	×	√	Psychological need
Ahmed [29]	Binary logit	√	√	√	×	Ride-hailing
Liu et al. [8]	MNL/Binary logit	√	√	×	×	Commuter
Risdiyanto et al. [12]	Hybrid logit	√	√	×	√	Students, private cars, and motorcycles
Chen et al. [30]	RPL	×	√	×	√	Travelers and public transport
This paper	RPL/SEM	√	√	√	√	Period (4–6.30 a.m. and 9–12 p.m.) and heterogeneity

Existing studies fail to consider multidimensional factors such as personal attributes, travel characteristics, environmental conditions, and psychological perceptions. Most researches focus on regular commute periods, overlooking the dynamics during EMLE periods. While some studies have mentioned psychological factors, they often treat them in isolation and neglect interactions with other variables, leading to misinterpretations of real-world scenarios. To address this gap, this study integrates personal, travel, environmental, and psychological factors, analyzing five modes of transportation: on-foot, bike-sharing, public transport, taxi/ride-hailing, and private cars. Using the RPLM, this study explores traveler preferences for accessing and departing from URT and the interactions among influencing factors. Combining the RPLM with the SEM, a mode choice model for URT connections during EMLE is proposed. The innovation lies in focusing on EMLE periods, particularly the combined impact of psychological perceptions and environmental factors. Unlike most studies, this research analyzes the effects of psychological perceptions, travel time, and costs using the RPLM and the SEM, with interaction terms to explore relationships between these factors. While existing research focuses on personal attributes and environmental factors, studies integrating psychological perceptions and environmental factors during EMLE are rare. This paper provides new insights and theoretical support for URT connection mode choice by considering psychological and environmental factors.

3. Research Objects and Questionnaire Design

There is a largest and busiest transportation network in Beijing (China), providing travelers with various convenient modes of urban traveling. The government has promoted the expansion of URT infrastructure to enhance the commuting, offering multiple transportation choices. However, most of travelers need additional transport modes to reach their final destinations from URT stations. Therefore, integrating different modes of transport is crucial to meet diverse travel needs, especially during EMLE periods. The city has also developed bike-sharing systems and improved taxi/ride-hailing connections. Understanding travelers’ mode choice behavior in these scenarios is key. As shown in Figure 1, various factors—personal attributes, travel characteristics, environmental conditions, and psychological perceptions—affect mode choice. Some questions are included: How many factors influence mode choice? What impact do these factors have on decisions? Are there differences in travelers’ decision-making? Which factors directly or indirectly influence choices? Do interactions between cost, time, and psychological perceptions matter? Finally, are travelers more likely to choose faster, safer, and more comfortable transport during EMLE periods?

[figure(s) omitted; refer to PDF]

To address the research questions, we design a questionnaire to explore factors influencing mode choice during EMLE periods, focusing on traveler behavior before and after using URT. The questionnaire integrates revealed preferences (RP) and stated preferences (SP) methods, with latent variables measured. To ensure reliability, we apply Cronbach’s alpha (α), which exceed 0.8 for all latent variables, and the Kaiser–Meyer–Olkin (KMO) test, which also exceed 0.8, confirming the instrument’s reliability and validity (see Appendix A, Table A2). After confirming the reliability of the questionnaire data, we first conduct a preliminary analysis of the statistical results based on the data to gain an overall understanding of the factors influencing mode choice. Next, since latent variables cannot be directly measured, we use the SEM to quantify them for subsequent analysis. Finally, we use directly observable variables (personal attributes, travel attributes, and environmental attributes) along with SEM-quantified latent variables as independent variables in an RPLM for regression analysis. This comprehensive and in-depth analysis explores the factors influencing mode choice, ultimately providing scientific and targeted recommendations for travelers and policymakers.

The questionnaire design is divided into three sections: The first section collects personal attributes and travel information. The second section involves hypothetical travel scenarios under different travel costs and environmental conditions. This section aims to capture travelers’ mode choice behavior and reflect their future travel intentions. It adopts the SP survey method, where candidate hypothetical scenarios are generated through orthogonal design. Each scenario includes five travel modes: walking, bike-sharing, public transportation, taxis/ride-hailing, and private cars. Different modes correspond to varying speeds, and the transfer time is calculated based on each traveler’s transfer distance. Travel time and costs differ for each mode. Based on the orthogonal design, eight scenarios are generated, and travelers are asked to select their preferred travel mode in each hypothetical scenario. The third section investigates travelers’ psychological perception latent variables using a five-point Likert scale, with scores ranging from 1 (strongly disagree) to 5 (strongly agree). All indicators and their values are listed in Table 2, and the eight scenarios are detailed in Table 3.

Table 2

Personal, travel attributes, and psychological perception latent variables.

Variant		Meaning
Personal attributes	Genders	0: females 1: males
	Ages	1: 18–25 years2: 26–30 years3: 31–40 years4: 41–50 years5: 51–60 years6: 60 or more
	Education	1: High school and below2: Specialized training school3: Graduate students and above
	Private car ownership	0 and 1 means no private car and private car, respectively
Travel attributes	Time/Cost	The time and cost vary depending on the mode of travel.
	Distance	1: Below 1 km
		2: 1-2 km
		3: 2–4 km
		4: Above 4 km
	Frequency of urban rail travel	1: Close to daily2: 3–5 times per week3: Monthly 3–5 times4: 5–7 times per month5: Less than 3 times per month
Psychological perception latent variables	Safety	S1: I’m very concerned about the safety of my personal life.S2: I’m very concerned about the safety of my personal property.S3: The safety accident report greatly affects my choice.S4: The safety management of travel modes is very important to me.S5: Whether personal information is leaked greatly affects my choice.
	Comfort	C1: Smooth operation is important to me.C2: It’s important to me to have easy access to large luggage.C3: I preferred the better coverage of the splices.
	Punctuality	P1: I tend to travel with flexible routes.P2: I prefer traveling with fewer delays.P3: I prefer a punctual and reliable travel mode.P4: I prefer to travel with less waiting time
	Perceived behavior	B1: I like the mode with a lot of freedom.B2: I prefer travel that is easy to maneuver.B3: The way I travel usually depends on my habits.

Table 3

Stated preference (SP) survey.

Situations	Luggage	Weather	Companions	Congestion	Period
S. 1	√		√	√
S. 2	√	√	√
S. 3
S. 4		√	√	√
S. 5	√		√		√
S. 6	√	√			√
S. 7			√		√
S. 8		√			√

4. Modeling Framework

The RPLM can identify relevant factors and quantify their impact. This section introduces an RPLM to explore the influence mechanism of various factors on travel mode choices. The model incorporates personal attributes, travel characteristics, environmental factors, and latent variables as independent variables.

4.1. RPLM

According to the random utility theory, the utility $U_{ij}$ obtained by the traveler $i$ after choosing the mode $j$ can be categorized by observable utility $V_{ij}$ and unobservable utility ${\epsilon }_{ij}$, as shown in equation (1).$$\begin{array}{}\text{(1)}& U_{ij}=V_{ij}+{\epsilon }_{ij}=\beta X_{ij}+{\epsilon }_{ij},\end{array}$$where $X_{ij}$ is an attribute characterizing the traveler i’s choice on travel mode $j$. β is the attribute coefficient in the observable utility function corresponding to the characteristic variable. In the traditional MNL model, β is a fixed parameter for each identified choice option j, and the random utility is independently and identically distributed. However, the consideration of attitudinal perceptions could not be directly observed. The RPL model used in this study assumes that the parameters β of the explanatory variables are randomly distributed across travelers, while the random error term ${\epsilon }_{ij}$ follows a fixed distribution. Additionally, explaining the effect of traveler preferences on travel mode choice is also difficult. In contrast, the RPLM assumes that the traveler preferences may be inconsistent. That is, ${\beta }_{ij}$ and ${\epsilon }_{ij}$ are varying for different travelers. To effectively capture the impacts of various types of travelers’ characteristics on their choice behavior, we introduce a set of random parameters to account for the heterogeneity in travelers’ preferences. Then, the observable utility $V_{ij}$ can be further expressed as equation (2):$$\begin{array}{}\text{(2)}& V_{ij}={\alpha }_j+{\beta }_{ij}^{\text{CP}}{C}_{ij}{P}_i+{\beta }_{ij}^{\text{TP}}{T}_{ij}{P}_i+{\beta }_{ij}^{\text{CTP}}{C}_{ij}{T}_{ij}{P}_i,\end{array}$$where ${\alpha }_j$ is a constant. It represents the unexplained and long-standing (nonrandom) part of the independent variable. ${\beta }_{ij}^{\text{CP}},{\beta }_{ij}^{\text{TP}},\text{\hspace{0.17em}and\hspace{0.17em}}{\beta }_{ij}^{\text{CTP}}$ are the coefficients of each utility variable. $C_{ij}$ is the travel cost. ${\mathrm{T}}_{ij}$ is the travel time, and ${\mathrm{P}}_{\mathrm{i}}$ is the latent variables. Adding the personal attributes, travel attributes, environmental attributes, and LVs, the travel utility can be formulated as equation (3):$$\begin{array}{}\text{(3)}& V_{ij}={\beta }_{ij}{X}_{ij}={\alpha }_j+{\displaystyle \sum }_r{a}_{ir}^{\text{CP}}{x}_{irj}+{\displaystyle \sum }_s{b}_{is}^{\text{CP}}{y}_{isj}{C}_{ij}{P}_i+{\displaystyle \sum }_r{a}_{ir}^{\text{TP}}{x}_{irj}+{\displaystyle \sum }_s{b}_{is}^{\text{TP}}{y}_{isj}{T}_{ij}{P}_i+{\displaystyle \sum }_r{a}_{ir}^{\text{CTP}}{x}_{irj}+{\displaystyle \sum }_s{b}_{is}^{\text{CTP}}{y}_{isj}{C}_{ij}{T}_{ij}{P}_i,\end{array}$$where $r$ is the number of directly observable traveler personal attributes and travel attributes. $s$ is the number of directly observable environmental attribute variables. $x_{irj}$ is the traveler’s personal attribute variable and travel attribute variable. $a_{ir}^{\text{CP}},a_{ir}^{\text{TP}},a_{ir}^{\text{CTP}}$ are the coefficients of the directly observable personal attribute variables and travel attribute variables. $y_{isj}$ is the directly observable travel environment characteristic attribute variable. The coefficients $b_{is}^{\text{CP}}$, $b_{is}^{\text{TP}}$, and $b_{is}^{\text{CTP}}$ are the coefficients of the directly observable environmental attribute variables. According to the utility maximization theory, the probability that a traveler $i$ chooses an option $j$ in the choice set $s$ can be expressed simplistically as equation (4):$$\begin{array}{}\text{(4)}& \text{Prob}{y}_{is}=j=\frac{\exp {\alpha }_j+{\sum }_r{a}_{ir}^{\text{CP}}{x}_{irj}+{\sum }_s{b}_{is}^{\text{CP}}{y}_{isj}{C}_{ij}{P}_i+{\sum }_r{a}_{ir}^{\text{TP}}{x}_{irj}+{\sum }_s{b}_{is}^{\text{TP}}{y}_{isj}{T}_{ij}{P}_i+{\sum }_r{a}_{ir}^{\text{CTP}}{x}_{irj}+{\sum }_s{b}_{is}^{\text{CTP}}{y}_{isj}{C}_{ij}{T}_{ij}{P}_i}{{\sum }_{k=1}^s\exp {\alpha }_q+{\sum }_r{a}_{ir}^{\text{CP}}{x}_{irq}+{\sum }_s{b}_{is}^{\text{CP}}{y}_{isq}{C}_{iq}{P}_i+{\sum }_r{a}_{ir}^{\text{TP}}{x}_{irq}+{\sum }_s{b}_{is}^{\text{TP}}{y}_{isq}{T}_{iq}{P}_i+{\sum }_r{a}_{ir}^{\text{CTP}}{x}_{irq}+{\sum }_s{b}_{is}^{\text{CTP}}{y}_{isq}{C}_{iq}{T}_{iq}{P}_i}.\end{array}$$

When the fixed parameters are replaced by random parameters that follow a certain distribution, the probability of choosing scenario j can be estimated. It should be the probability expectation after the random parameter traverses all possible values. That is, the probability function of the RPLM described above can be viewed as an integral of the MNL probability function over the distribution function $f{\beta }_{ij}\mathrm{\Omega }$ of the random parameter ${\beta }_{ij}$, where Ω denotes the parameter of the density function, as shown in equation (5).$$\begin{array}{}\text{(5)}& P_{ij}={\int }_{{\beta }_{ij}}P{\beta }_{ij},x_{ij}f{\beta }_{ij}\mathrm{\Omega }d{\beta }_{ij}={\int }_{{\beta }_{ij}}\frac{\exp {\beta }_{ij}{X}_{ij}+{\epsilon }_{ij}}{{\sum }_{k=1}^s\exp {\beta }_{ij}{X}_{ij}+{\epsilon }_{ij}}f{\beta }_{ij}\mathrm{\Omega }d{\beta }_{ij}.\end{array}$$

4.2. SEM-Logit Model

The study adopts a two-step SEM-Logit model for empirical analysis, as depicted in Figure 2. The procedure is as follows: (1) The SEM is constructed and estimated to quantify the latent variables and obtain their fitted values. This study focuses on four latent variables: perceived safety, perceived comfort, perceived punctuality, and perceived behavioral control. The measurement indicators and their corresponding values for each latent variable are provided in Table 2. (2) The fitted values of the latent variables derived from the SEM model are treated as observable variables, and alongside, other manifest variables (personal, travel, and environmental attributes) are included as independent variables in the RPLM. The dependent variable in this model is urban rail transit mode choice, which encompasses five alternatives: walking, bike-sharing, public transit, taxi/ride-hailing, and private car. This two-step modeling approach not only ensures accurate measurement of latent variables but also enhances the model’s explanatory power by integrating the quantified latent variables with manifest variables in a cohesive and comprehensive manner.

[figure(s) omitted; refer to PDF]

5. Results

To investigate the factors influencing travel mode choice during the EMLE period, we design a questionnaire and preliminarily establish a SEM-logit theoretical model for analysis. This section begins with a statistical analysis of the eight scenarios included in the questionnaire’s SP survey, followed by the presentation of SEM results and an evaluation of the questionnaire’s reliability. Finally, a detailed analysis of travel mode choices during the EMLE period is conducted based on the SEM-logit results, revealing underlying factors influencing decision-making and performing elasticity coefficient analysis.

Figure 3 illustrates the mode share rates of five travel modes across the eight scenarios in the questionnaire survey. Scenarios 1–8 feature different environmental attributes, with various colors representing distinct travel modes, and the proportion of each color indicating the frequency of mode selection. Among them, S1–S4 represent the early morning period, and S5–S8 represent the late-night period. Detailed environmental descriptions can be found in Table 2. It can be observed that public transport accounts for a significant and relatively even share across all eight scenarios, with the highest proportions observed in scenarios 1 and 5. Walking exhibits a consistently low share across all scenarios, with the lowest proportion in scenario 6. Additionally, the shares of bike-sharing, taxi/ride-hailing, and private car vary significantly across the eight scenarios. Specifically, the share of bike-sharing reaches its peak in scenarios 3 and 7, both nearing 50%, while the lowest shares are seen in scenarios 2 and 6, each below 5%. Taxi/ride-hailing has the highest share in scenario 6 and the lowest in scenario 3. Private car usage peaks in scenario 6 and is lowest in scenario 3. Overall, during the EMLE period, public transport emerges as the most preferred travel mode across the eight scenarios, followed by private cars and taxi/ride-hailing. Bike-sharing shows the greatest variability, being highly favored in specific scenarios while scarcely considered in others. Walking, on the other hand, is the least preferred mode of travel during this period.

[figure(s) omitted; refer to PDF]

During late-night travel, the proportion of travelers choosing private cars is significantly higher than in the early morning, mainly due to heightened safety awareness. Female travelers often rely on family or friends for pick-ups at URT stations, and walking is less preferred due to its slower pace and perceived lack of safety. Key environmental factors, such as traffic conditions, weather, luggage, and companions, strongly influence mode choice. Late-night travelers prioritize safety and comfort, increasing private car usage while reducing walking. Further analysis will examine how personal attributes, travel characteristics, and psychological perceptions shape mode choices during the EMLE period.

5.1. SEM Models

The preceding section primarily analyzed the environmental factors influencing the travel mode choice. However, in addition to environmental attributes, personal attributes, travel characteristics, and psychological perceptions also play a significant role in travel mode choices. To understand and quantify the relationships among these factors, we employ a combined approach of the SEM and RPLM models. This approach aids in identifying the influential factors and evaluating their impact, thereby providing a more comprehensive analytical framework.

The SEM is conducted as a validated factor analysis to evaluate the reliability and validity of the measurement instrument (see Appendix B for the theoretical model of the SEM). This analysis also confirms the structural relationships among the underlying constructs. Specifically, we utilize the Stata 17 software to calibrate the model for the four latent variables, each requiring a different number of observed variables: five observations for conventional security perceptions and three or four observations for the remaining three latent variables. The initial calibration path diagram for the model is illustrated in Figure 4. ε is the error term. The values representing the covariance coefficients between each pair of potential variables are depicted. Below the latent variables, the factor loading values are presented, all of which exceed 0.6. Based on the outcomes of the reliability and validity assessments, the questionnaire results are subjected to latent variable modeling. The corresponding model fitting indicators are presented in Table 4. The results demonstrate a strong model fit, as indicated by all metrics meeting or exceeding the reference values.

[figure(s) omitted; refer to PDF]

Table 4

The table of indicator fitting values.

Indicators	$X^2$	df	$p$	Chi-square degree-of-freedom ratio	GFI	RMSE	SRMS	CFI	NFI	NNFI
Standards	—	—	> 0.05	< 3	> 0.9	< 0.10	< 0.05	> 0.9	> 0.9	> 0.9
Values	221.981	84	0.185	2.643	0.915	0.068	0.041	0.977	0.964	0.971

5.2. SEM-Logit Models

In this study, we address identifiability issues in the mixed logit model by designing a reasonable structure and limiting random parameters [31]. Stepwise variable elimination and significance tests ensure robustness and identifiability of key parameters such as travel time, cost, and latent variables [32, 33]. Interaction terms with insignificant standard deviations are excluded to enhance validity. The pseudo-$r^2$ (0.3347) confirms strong model fit, supporting parameter stability. The following sections provide detailed coefficient analysis.

5.2.1. Attribute Coefficient Analysis

In performing random coefficient estimation, this study establishes walking as the baseline travel mode. Three random parameters are assumed to follow a normal distribution: travel time × latent variables (TP), travel cost × latent variables (CP), and travel time × travel cost × latent variables (CTP). The regression results are derived through an iterative process of eliminating variables that demonstrate no statistically significant impact on the random parameters, as outlined in Table 5. The model’s McFadden pseudo-$R^2$ exceeds 0.3, indicating a strong fit for the constructed model. The $p$ values of mean for the two variables, ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$, ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ and ${\mathrm{C}}_{\text{ij}}{\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$, are less than 0.05, indicating that the corresponding factors statistically significantly influence the behavior of the travel mode choice. Both ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ and ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ coefficients are negative, suggesting a negative effect of the interaction term on the mode choice. The mean coefficient of ${\mathrm{C}}_{\text{ij}}{\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ is positive, implying that this term has a positive effect on the choice decision. Moreover, the mean and standard deviation of ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ and ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ are statistically significant, which indicates that these two terms are random parameters. As a result, travelers exhibit varying preferences regarding “time, cost, and perceived safety,” which subsequently impact their choice of the transportation mode. But the standard deviation of the interaction term ${\mathrm{C}}_{\text{ij}}{\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ is not statistically significant, so it is not a random coefficient. In addition, we remove ${\mathrm{P}}_{\mathrm{i}}$ and its related coefficients, resulting in poor fitting and unsatisfied significance of other coefficients. Overall, the inclusion of latent variables enhances the model’s fit and increases the significance of the coefficients. Therefore, we will explore the factors affecting travelers’ mode choice in relation to ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ and ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$.

Table 5

Regression coefficients for random parametric logit models.

Parameters		Coefficient	Standard deviation	Z value	$p$ value	95% confidence interval
Random parameter	${\beta }_{\text{TP}}$	−1.5612∗∗	0.6338	−2.46	0.0138	−2.8033	−0.3191
	${\sigma }_{\text{TP}}$	1.6628∗∗∗	0.2102	7.91	≤ 0.001	1.2508	2.0747
	${\beta }_{\text{CP}}$	−0.0300∗∗∗	0.0066	−4.55	≤ 0.001	−0.0428	−0.0171
	${\sigma }_{\text{CP}}$	0.0056∗∗∗	0.0011	5.17	≤ 0.001	0.00343	0.0076
	TP: gender	−0.5095∗∗∗	0.1768	2.88	0.0039	0.1631	0.8559
	TP: age	−0.1862∗∗∗	0.0600	−3.10	0.0019	−0.3037	−0.0687
	TP: education	−0.2474∗∗	0.0981	−2.52	0.0117	−0.4396	−0.0551
	TP: private car	0.9507∗∗∗	0.1811	5.25	≤ 0.001	0.5958	1.3055
	TP: frequency	−0.2510∗∗∗	0.0712	−3.53	0.0004	−0.3907	−0.1115
	TP: distance	−0.8296∗∗∗	0.1471	−5.64	≤ 0.001	−1.1179	−0.5414
	TP: weather	−1.3982∗∗∗	0.2188	−6.39	≤ 0.001	−1.8271	−0.9693
	TP: luggage	−1.2823∗∗∗	0.2061	−6.22	≤ 0.001	−1.6863	−0.8784
	TP: day	−0.4396∗∗	0.1900	−2.31	0.0207	−0.8120	−0.0672
	CP: gender	0.0126∗∗∗	0.0024	5.19	≤ 0.001	0.0078	0.0173
	CP: education	0.0012∗	0.0007	1.66	0.0960	−0.0002	0.0026
	CP: frequency	−0.0016∗∗∗	0.0005	−3.02	0.0026	−0.0027	−0.0006
	CP: distance	−0.0146∗∗∗	0.0021	−6.88	≤ 0.001	−0.0187	−0.0104
	CP: weather	0.0029∗∗	0.0012	2.42	0.0155	0.0005	0.0052
	CP: luggage	0.0022∗	0.0012	1.90	0.0571	−0.0001	0.0045
Fixed parameter	Way 1	10.644∗∗∗	1.20439	8.84	≤ 0.001	8.2831	13.0042
	Way 2	4.0059∗∗∗	0.43632	9.18	≤ 0.001	3.15075	4.86111
	Way 3	3.3317∗∗∗	0.26283	12.68	≤ 0.001	2.81654	3.84681
	Way 4	3.1717∗∗∗	0.56341	5.63	≤ 0.001	2.06745	4.27596
	${\beta }_{\text{CTP}}$	0.8579∗∗∗	0.13452	6.38	≤ 0.001	0.59421	1.12153
Overall parameter	$\text{McFadden}’\mathrm{s}{R}^2$	0.335

^∗∗∗, ^∗∗, ^∗1%, 5%, and 10% significance levels, respectively.

For ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$, the factors of the age, education, travel frequency, travel distance, weather conditions, carry-on baggage, and travel time parameters are all negative. This indicates that the older the traveler, the higher the education, the lower the frequency of travel, the higher the travel distance and the greater the effect of ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ on the traveler’s travel utility. Travelers with lower travel frequencies may have more specific needs, rendering them more time-sensitive. Similarly, travelers covering longer distances tend to be more sensitive to both time and latent variables. At the same time, the mean value of the coefficients of ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ decreases when the travelers are female, the weather condition is bad, carrying baggage, and travels late at night. When environmental conditions deteriorate, such as during rain or snow, travelers tend to prioritize travel time. Additionally, the impact of latent variables on decision-making becomes more pronounced under such circumstances. This heightened influence is attributed to the adverse effects of poor travel conditions on the traveler’s comfort, convenience, and physical and mental well-being. The coefficient term of the private car is positive, and the mean value of ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ increases, which indicates that the travelers with private cars are less sensitive to time and less affected by latent variables.

For ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$, the coefficients corresponding to travel frequency and travel distance are negative. That is, the lower the travel frequency and the longer the travel distance, the smaller the mean values of the coefficients of ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$, which indicates that the lower the travel frequency and the longer the travel distance of the traveler, the greater the effects of ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ on travel utility. This suggests that the longer the travel distance, the more sensitive the traveler is to cost and latent variables. The higher the level of education, the larger the mean values of ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$, which indicates that the higher the traveler’s education level, the lower the impacts of travel cost and latent variables on the travel utility. Meanwhile, the mean values of ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ are increasing when the traveler is female, the weather condition is bad, and the luggage is carried; when the environmental conditions become worse, the effects of cost on the traveler’s travel utility become smaller. As a result, it is worth mentioning that the effects of ${\mathrm{C}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ are smaller than the effect of ${\mathrm{T}}_{\text{ij}}{\mathrm{P}}_{\mathrm{i}}$ on a travel decision. It may be the fact that when traveling during this period, travelers are more influenced by the travel time and the effect of the travel cost is relatively small.

5.2.2. Elasticity Coefficient

To delve deeper into the random parameters, this subsection incorporates elasticity coefficients into the estimation process to compute the stochastic terms in Nlogit5. The specific formulas are outlined in Appendix C, with the corresponding calculation outcomes presented in Table 6.

Table 6

Elasticity coefficient.

Parameters/modes	On-foot (%)	Bike-sharing (%)	Public transport (%)	Taxi/ride-hailing (%)	Private car (%)
${\mathrm{C}}_{ij}{P}_i$ (+1%)	+2.14	+0.22	+0.42	−2.53	+0.90
${\mathrm{T}}_{ij}{P}_i$ (+1%)	−5.50	−2.05	−0.04	+0.50	+1.02

From Table 6, for every 1% increase in ${\mathrm{C}}_{ij}{P}_i$, the probabilities of walking, bike-sharing, public transport, and private car increase by 2.14%, 0.22%, 0.42%, and 0.90%, respectively. Conversely, the probability of taking a taxi/ride-hailing service decrease by 2.53%. As travel costs and latent factors increase, travelers prefer walking or bike-sharing for their low cost and safety perception. Public transport remains somewhat appealing, but private cars are favored due to cost-effectiveness, safety, and comfort. Taxis and ride-hailing are less likely chosen due to higher costs and fewer advantages. When ${\mathrm{T}}_{ij}{P}_i$ is increasing, the choice probabilities for taxi/ride-hailing services and private cars increase by 0.50% and 1.02%, respectively. Conversely, the choice probabilities for walking, bike-sharing, and public transport decrease by 5.50%, 2.05%, and 0.04%, respectively. As the importance of travel time and safety perception increases, the likelihood of choosing walking or bike-sharing decreases significantly. This suggests that travelers prioritize safety and time efficiency. Public transport is also less preferred, while taxis, ride-hailing, and private cars see a significant increase in selection, likely due to their advantages in safety and time flexibility. Overall, travelers prefer modes that offer greater safety, comfort, and time flexibility, while simpler options are less favored due to concerns over safety or time constraints. Factors such as weather, luggage, late-night travel, and lack of private cars influence these choices, highlighting the complex trade-offs travelers make between time, cost, and safety.

6. Conclusions and Limitations

In this study, we developed and implemented a SEM-logit integration model using data collected from the city of Beijing. Given the diversity among travelers, we utilized an RPLM to study the factors influencing the choice of “off-peak hours” URT connections, with a focus on the EMLE period. Considering the considerations, this study incorporated interaction terms for travel time, cost, and latent variables as random parameters to examine their impact on choice decisions.

The results showed that the influences of ${\mathrm{C}}_{ij}{P}_i$ and ${\mathrm{T}}_{ij}{P}_i$ on travelers’ choice preference were not fixed but heterogeneous among different travelers. In both EMLE scenarios, public transport emerged as the predominant mode of travel, with a choice frequency exceeding 40% across all scenarios. Walking was consistently the least favored mode of travel, accounting for less than 12% across all travel scenarios. In inclement weather or when burdened with luggage, travelers tended to opt for taxi/ride-hailing services, private cars, and other more comfortable means of transportation. When weather conditions were favorable or travelers had small bags, bike-sharing emerged as a more popular option. Conversely, the preference for private cars was more pronounced during late-night travel compared to early morning journeys. The results showed that the interaction terms ${\mathrm{T}}_{ij}{P}_i$ and ${\mathrm{C}}_{ij}{P}_i$ were heterogeneous among different travelers and had a negative effect on the choice of the travel mode. For every 1% increase of interaction ${\mathrm{C}}_{ij}{P}_i$, the probability of walking, bike-sharing, public transportation, and private car increase by 2.14%, 0.22%, 0.42%, and 0.90%, respectively. Conversely, the likelihood of selecting a taxi or ride-hailing service decreased by 2.53%. When the interaction item ${\mathrm{T}}_{ij}{P}_i$ increased by 1%, the probability of travelers choosing walking decreased by 5.50%, the probability of sharing bicycles decreased by 2.05%, and the probability of choosing public transportation decreased by 0.04%. On the other hand, the likelihood of travelers opting for a taxi or ride-hailing service increased by 0.50%, while the probability of selecting a private car rose by 1.02%. Travelers engage in trade-offs among factors such as time, cost, and latent variables depending on their current circumstances.

This study recommends prioritizing safe and convenient transport during the EMLE period. Travelers should consider taxis, ride-hailing, or private cars in adverse conditions and bike-sharing for low-cost flexibility at night. Policymakers should enhance night public transport safety, increase service frequency, and promote shared mobility to meet diverse travel needs. Despite the extensive research conducted in this paper, there were several notable limitations. Firstly, the study exclusively focused on large cities such as Beijing, raising questions about its applicability to small or medium-sized cities. Secondly, the restricted mobility of travelers during this unique period posed challenges in conducting origin-destination (OD) surveys using traditional RP methods, leading to small sample sizes. Considering the rapid advancement in autonomous driving technology, it becomes imperative to investigate whether these modes will persist as convenient and safe means of transportation in the future.

Funding

The authors gratefully acknowledge the supports by the National Natural Science Foundation of China, under grant nos. 72371006, U2469201 and 72301037 and the Fundamental Research Funds for the Central Universities (2023RC35).

Acknowledgments

The authors gratefully acknowledge the supports by the National Natural Science Foundation of China, under grant nos. 72371006, U2469201 and 72301037 and the Fundamental Research Funds for the Central Universities (2023RC35).

Appendix

Appendix A: Questionnaire

A questionnaire is constructed into three parts:

Part 1: The RP survey is used to explore the personal attributes and travel characteristics of travelers who take rail transit. The personal attributes of travelers include gender, age, education, occupation, monthly household income, car ownership, possession of physical or electronic IC cards for public transportation, and cohabitants. Table A1 presents the values and interpretations of personal attributes, travel attributes, and the observed variables associated with the four latent variables (see Appendix A). Part 2: The SP survey is used to involve a hypothetical scenario to investigate the mode choice behaviors of travelers under various scenarios. This paper designs 8 travel scenarios for the focusing time periods such as luggage, weather conditions, companions, and traffic congestion. The restrictions for the 8 scenarios are shown in Table A2 (see Appendix A). “√” refers to large baggage, bad weather, unaccompanied, traffic congestion, and late night. The remainder without a “√” will be treated as the opposite condition. These 8 scenarios correspond to 5 alternate travel options. For example, walking, bike-sharing, public transport, taxis/ride-hailing, and private cars. There are also different time costs associated with congested and uncongested conditions due to the different speeds at which transportation modes operate. Part 3: The scoring scale of generalized safety perception is considered to measure the travelers’ psychological feelings. The response options are set as “1–5” signifying “completely disagree”, “mostly disagree”, “neither agree nor disagree”, “mostly agree”, and “completely agree”, respectively.

I. Basic Personal Information

1. Your gender (A. Male, B. Female)

2. Your age group (A. 18–25, B. 26–30 ,C. 31–40, D. 41–50, E. 51–60, F. 60 or more)

3. Your occupation (A. Corporate, B. Institutional, C. Traveler, D. Student, E. Other)

4. And other basic information, not listed for space reasons.

II. Travel Characteristics

1. How often do you take the URT. (A. Nearly every day, B. 3–5 times a week, C. 3–5 times a month, D. 5–7 times a month, E. Less than 3 times a month)?

2. Your most recent transportation mode of choice for travel at that time of day? (A. Walking, B. Bike-sharing, C. Public transportation, D. Taxi/ride-hailing, E. Private car)

3. Distance of your residence from a subway station (A. within 1 km. B. 1–2 km. C. 2–4 km. D. more than 4 km)

III. Travel Scenario Options

  The questionnaire used in this study contained eight different travel scenarios divided into two groups. During the survey, respondents were randomly selected from one of the two sets of questionnaires to reduce the burden on the respondents. It is important to note that the speeds in the questionnaire represent typical speeds for each mode of transportation, with different speeds specified for congested and noncongested scenarios. As an example, the questionnaire includes one congested situation and another noncongested situation.

  Scenario 1: In this scenario, envision arrives at a URT station between 4:00 a.m. and 6:30 a.m. The roads are experiencing moderate congestion, and the weather conditions are favorable. Furthermore, you are carrying large luggage, and no travel companions accompany you. Considering these factors, which mode of transportation would you be most likely to choose to reach the URT station?

A. Walking (speed 4.5 km/h, cost 0)

B. Bicycle sharing (15 km/h, cost 1.5)

C. Public transportation (25 km/h, 2)

D. Taxi/internet car (speed 30 km/h, starting price 13)

E. Private car transfer (speed 30 km/h, fuel cost 1 yuan/km)

  Scenario 2: Imagine arriving at a subway station between 4:00 a.m. and 6:30 a.m. The roads are free of congestion, but the weather is inclement. In this situation, you are carrying luggage and have no travel companions. Given these circumstances, which mode of transportation would you be most likely to choose to reach the URT station?

A. Walking (4.5 km/h, cost 0)

B. Bicycle sharing (18 km/h, cost 1.5)

C. Public transportation (35 km/h, 2)

D. Taxi/internet car (50 km/h, starting price 13)

E. Private car transfer (speed 50 km/h, fuel cost 1 yuan/km)

IV. Generalized Security Perception Scale

  Following the indicator variable provided below, kindly select your identity score for that variable by indicating the score within parentheses.

V. Questionnaire Test.

Table A1

Generalized security perception scale.

Strongly disagree. (1)	Disagree (2)	General (3)	Agree with (4)	Could not agree more (5)
1. At that time, I am very concerned about the safety of my life and health.
2. At that time of day, I’m very concerned about the safety of my personal property.
3. The coverage of security incidents at that time of the year is very much influencing my choices.
4. At that time of day, the safety management of the travel is important to me.
5. Whether or not my personal information is compromised has a big impact on my choices.

Table A2

Reliability analysis.

Latent variable	Indicator variable symbols	Factor load values	Cronbach’s α	Factor analysis
General security perception	A1	0.890	0.943	Cronbach’s α (0.949); KMO measure (0.955); Bartlett’s test significance value (0).
	A2	0.880
	A3	0.880
	A4	0.861
	A5	0.867
Comfort perception	C1	0.876	0.824
	C2	0.861
	C3	0.867
Perceived punctuality and convenience	P1	0.894	0.897
	P2	0.877
	P3	0.908
	P4	0.890
Sensory-behavioral control	B1	0.893	0.804
	B2	0.847
	B3	0.842

Appendix B: Structural Equation Modeling (SEM)

The load factors ${\mathrm{\Lambda }}_{\lambda n}$ of the latent variables can be obtained by constructing the measurement model of travelers. The measurement model is as the following equation (B.1):$$\begin{array}{}\text{(B.1)}& Y={\mathrm{\Lambda }}_{\lambda }\eta +\epsilon ,\end{array}$$where Y is a vector of the observed variable or the indicators of the latent variables; ${\mathrm{\Lambda }}_{\lambda }$ is the matrix of the load factor for Y on $\eta$; $\eta$ is the latent variables, reflecting travelers’ mode choices for last-mile travel, including conventional safety, comfort, convenience, and perceptual behavior control; and $\epsilon$ is the error vector of the observed variable y. $n$ represents the position of the observed variable. For example, ${\lambda }_{11}$ represents the first observation of the first latent variable. ${\lambda }_{1n}$ is the nth observation of the first latent variable, and ${\lambda }_{n1}$ is the first observation of the nth latent variable. By converting the coefficient relationship between the latent variables and the observed variables, the fitness values of the latent variables based on the survey data of observed variables, together with travelers’ personal attributes, travel attributes, and environment attributes, are added into the utility function of different travel mode choices as influencing factors. The specific steps are as follows: For the measurement model of the SEM, taking a latent variable as an example, if it is expressed in a vector form, equation (B.2) can be converted to equation (B.3).$$\begin{array}{}\text{(B.2)}& \begin{array}{c}{\lambda }_{11}\\ {\lambda }_{12}\\ \cdots \\ {\lambda }_{1n}\end{array}=\begin{array}{c}{\mathrm{\Lambda }}_{\lambda 1}\\ {\mathrm{\Lambda }}_{\lambda 2}\\ \cdots \\ {\mathrm{\Lambda }}_{\lambda n}\end{array}{\eta }_1.\end{array}$$

The path coefficients ${\mathrm{\Lambda }}_{\lambda 1},{\mathrm{\Lambda }}_{\lambda 2},\dots ,{\mathrm{\Lambda }}_{\lambda n}$ of the latent variable ${\eta }_1$ are standardized and regarded as the weights of the observed variables, and the assigned weights are represented as ${\alpha }_{\lambda 1},{\alpha }_{\lambda 2},\dots ,{\alpha }_{\lambda n}$. This can be seen in equation (B.2):$$\begin{array}{}\text{(B.3)}& \begin{array}{c}{\alpha }_{\lambda 1}=\frac{{\mathrm{\Lambda }}_{\lambda 1}}{{\mathrm{\Lambda }}_{\lambda 1}+{\mathrm{\Lambda }}_{\lambda 2}+\cdots +{\mathrm{\Lambda }}_{\lambda n}}\\ {\alpha }_{\lambda 2}=\frac{{\mathrm{\Lambda }}_{\lambda 2}}{{\mathrm{\Lambda }}_{\lambda 1}+{\mathrm{\Lambda }}_{\lambda 2}+\cdots +{\mathrm{\Lambda }}_{\lambda n}}\\ \cdots \\ {\alpha }_{\lambda n}=\frac{{\mathrm{\Lambda }}_{\lambda n}}{{\mathrm{\Lambda }}_{\lambda 1}+{\mathrm{\Lambda }}_{\lambda 2}+\cdots +{\mathrm{\Lambda }}_{\lambda n}}\end{array}.\end{array}$$

The fitness value of the latent variables such as safety and comfort in the latent variables will be obtained after bringing the value of the observed variables as equation (B.4).$$\begin{array}{}\text{(B.4)}& {\eta }_1={\alpha }_{\lambda 1}{\lambda }_{11}+{\alpha }_{\lambda 2}{\lambda }_{12}+\cdots {\alpha }_{\lambda n}{\lambda }_{1n}.\end{array}$$

Similarly, the fitness values of all the latent variables can be calculated in the same way.

Appendix C: Other Equations

1. The coefficients of elasticity.

  Since the RPLM is nonlinear, the estimated coefficients could not capture the influencing degrees of each factor on the travel mode choice. Therefore, the elasticity coefficients shown by equation (5) are introduced:$$\begin{array}{}\text{(C.1)}& E_{X_{ij}}^{P_{i}j}=\frac{1}{N}{\displaystyle \sum }_{i=1}^N\frac{P_{i}j{X}_{ij}=1-P_{i}j{X}_{ij}=0}{P_{i}j{X}_{ij}=0},\end{array}$$

  where $E_{X_{ij}}^{P_{i}j}$ is the elasticity coefficient of the influence factor $X_{ij}$ on the travel mode choice $j$. It is used to measure the change in the probability of the travel mode choice when the influencing factor (attributes) $X_{ij}$ changes from 0 to 1.

2. Frequency of choices

  To analyze the influence of latent variables, investigated objects are divided into two groups: caring and ignoring latent variables based on the score levels. $W_{cj}$ is the ratio of the choosing frequency. c represents the type of the traveler. A is the total number of travelers who care about latent variables, and B is the traveler number who do not care about latent variables. The frequency of a certain type of travelers choosing a certain mode could be formulated as follows:$$\begin{array}{}\text{(C.2)}& W_{cj}=\frac{F_j}{{{\displaystyle \sum }}_{i=1}^{A/B}{{\displaystyle \sum }}_{j=1}^5{F}_j}\times 100\%.\end{array}$$

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