
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12706-5
10.1016/j.heliyon.2024.e36675
e36675
Research Article
How to maximize the travelers’ shift to rail transit in a Chinese valley city after bus fare adjustment
Fan Mengxing a
Qi Jinping qijinping@mail.lzjtu.cn
abc⁎
Zheng Xiangdong d
Shang Hongtai a
Kan Jiayun e
a Mechatronics T&R Institute, Lanzhou Jiaotong University, Lanzhou 730070, China
b Engineering Technology Center for Information of Logistics & Transport Equipment, Lanzhou 730070, China
c Gansu Industry Technology Center of Logistics &Transport Equipment, Lanzhou 730070, China
d Lanzhou Rail Transit Co., LTD., Lanzhou 730030, China
e School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
⁎ Corresponding author. Lanzhou Jiaotong University, No. 88 , Anning West Road, Anning Zone, Lanzhou, Gansu, 730070, China. qijinping@mail.lzjtu.cn
22 8 2024
15 9 2024
22 8 2024
10 17 e3667530 1 2024
18 8 2024
20 8 2024
© 2024 The Authors. Published by Elsevier Ltd.
2024

https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Existing studies have not analyzed travelers' travel modal shift behavior after bus fare adjustment for special urban topography. In order to fill this gap and explore the strategies that can effectively encourage the shift of valley city travelers to rail transit after the adjustment of bus fare, the price adjustment perception and topographic space perception are introduced to expand the theory of planned behavior (TPB). On this basis, an integrated model combining structural equation model (SEM) and Mixed Logit model (MLM) is established to analyze the factors of travelers’ modal shift behavior of in the valley city after bus fare adjustment, and elastic analysis is carried out. Taking Lanzhou as an example, questionnaire data and traffic data were collected for example analysis. The results show that fare adjustment perception (FAP) and topographic space perception (TSP) have the same significant impact on travel modal shift intention (TMSI) and behavior (TMSB) as subjective norms (SN), shift behavior attitude (SBA) and perceived behavior control (PBC), and the travel characteristics and psychological perception sensitivity of travelers in the valley city are heterogeneous. After the adjustment of bus fares in valley city, the shift to rail transit is the most. When the subjective norms, fare adjustment perception and topographic space perception of travelers in the valley city increase by 50 %. The sharing rate of rail transit is increased by 10.284 %. The effective way to increase the sharing rate of rail transit is to increase the combined factors of subjective norms, topographic space perception and fare adjustment perception. Compared with the Multinomial Logit model and the Logit model combined with structural equation model, the goodness of fit and prediction accuracy of the proposed integrated model are improved.

Highlights

• Fare adjustment perception have significant effects on modal shifting intention and behavior.

• Topographic space perception have significant effects on modal shifting intention and behavior.

• There is heterogeneity in travelers ' perception of fare adjustment and topographic space.

• Enhancing travelers' subjective norms, fare adjustment and topographic space perception can maximize travelers' shift to rail transit.

Keywords

Valley city
Travel modal shift
Planned behavior theory
Structural equation model
Mixed logit model
Psychological perception
==== Body
pmc1 Introduction

Compared to other developed countries, the transportation development in China faces disadvantages such as high population density, limited land availability, a fragile environment, and energy shortages. There are widespread phenomena such as the strong momentum of car development, the lagging development of the rail transit. In addition, valley city refers to the city developed in the valley, which is constrained by its narrow topographic. Road resources are limited, and simply improving the road supply cannot help. In addition to constructing roads, Chinese urban governments have also been implementing bus fare subsidy policies to encourage more people to travel by bus. However, with the change of travel structure and operating costs of bus, the low fare policy of bus has been ineffective in improving the service level and rationalizing the travel structure.

Urban rail transit serves as a crucial mode to alleviate urban traffic issues. It offers the advantages of large capacity, environment friendly and the high speed [1]. The long and narrow shape of the valley city is very suitable for the development of rail transit [2]. Giving priority to the development of rail transit can alleviate traffic problems, which has become a consensus among cities both domestically and internationally. In order to better coordinate and achieve multi-dimensional goals such as increasing the use of rail transit, boosting the operating income of the transportation sector, and enhancing the efficiency of urban transportation systems, some cities in China have recently adjusted bus fares. So, how can we fully utilize the fare adjustment policy to maximize the promotion of passenger flow from other modes to the rail transit in valley city? In general, travelers will estimate the travel utility by combining various influencing factors, and the mode with the greatest utility will be selected [3]. In other words, when the travel utility of rail transit surpasses that of other travel modes, travelers will shift to rail transit.

Understanding the factors that influence traveler modal shift, and analyzing the combined effects of key influencing factors and fare adjustment policy on travel mode shift can provide theoretical support for rationalizing traffic policies, which has significant practical implications. We propose the following question for this paper: What are the key factors influencing travel modal shift behavior in valley city? What policy measures or combination of policy measures will most effectively improve the efficiency of rail transit and encourage travelers to shift to rail transit? These questions will be solved as depicted in Fig. 1.Fig. 1 General research framework.

Fig. 1

2 Literature review

Travelers' willingness to travel modal shift will change with their socioeconomic characteristics, travel characteristics, subjective and objective built environment, and traffic policies. It is concluded that personal socioeconomic attributes, such as census register and the number of private cars, have a significant impact on travel choices [[4], [5], [6], [7]]. It is evident that the number of travel companions, distance, departure time, and other travel characteristics will influence the travel mode choice [8]. Scholars also believe that the choice of individual travel mode will change with the change of urban built environment [[10], [11], [12], [9]]. Areas with a higher land use mix degree will reduce the additional short-distance travel, thereby decreasing travelers' reliance on cars [13,14]. Parking availability, including the sufficiency of parking space supply and the acceptability of parking fees significantly impact on travel decision-making [9,10]. Travelers' perception of built environment, such as perception of road grade [15] and congestion [16], has been proven to significantly affect the intention to shift travel modal [17,18]. In terms of object characteristic variables that change with the scheme, it is also believed that reducing the travel cost and the walking distance to the station of rail transit will help encourage travelers to choose rail transit [19,20]. A similar conclusion has been drawn [21]. Fu et al. proved the significant influence of travelers' SN, PBC, and SBA of travel modes on travel decisions [8]. Narrow the gap between the level of public transport and car in terms of travel service level is effective measures for encouraging travelers to choose public transportation [[22], [23], [24]]. When it comes to transportation policy, it is well known that fare adjustments are an important means of allocating transportation resources, which has been examined by a lot of studies [25]. Simply put, from the perspective of travelers, individuals affected by the fare adjustment shift or maintain the travel mode to obtain the optimal travel utility by integrating their own conditions and the travel characteristics and travel perception of each mode [26].

Vary methods are used to study travel modal shift behavior. The discrete choice model is used the most, which based on individual travel data modeling to gets more accurate results. Pan et al. and Vedagiri both plotted the travel mode shift probability curve by developing the Logit model [27,28]. Zhang et al. verified that MLM can reflect the heterogeneity of different travelers more accurately than Nested Logit model [29]. A Nested Logit model was established to analyze the impact of cities sizes, travel characteristics, and traffic policies on travel modal shift [30,31]. However, the discrete choice model is unable to analyze the psychology of travelers. For this reason, the structural equation model is proposed, which quantitatively explores how travelers' psychological perception affect their choice of travel mode [[32], [33], [34]]. In these studies, only the direct impact of latent variables on travel mode choice is considered, the correlation between them ignored which leading to erroneous frameworks and factor duplications for potential categories [35,36]. By combining Logit models with SEM based on TPB, researchers have been able to more accurately characterize unobservable factors. It was determined that travelers' attitudes, preference, and perception positively influenced individual travel modal shift intention and behavior [[37], [38], [39], [40]].

An in-depth understanding of travelers' adherence to expected shifts in travel modes after fare adjustments, influenced by various complex factors, is crucial for urban transportation managers to formulate policies and implement effective improvement measures. The built environmrnt of travelers in valley city differ from those in other type cities, leading to distinct changes in their travel behaviors. Therefore, the study of travel mode shift after bus fare adjustments in valley city cannot merely reference to plain cities, but should comprehensively consider various factors. After conducting a comprehensive review of the relevant literature on travel modal shift, the author is not aware of any research on travel modal shift following bus fare adjustments in special valley city. Therefore, this research developed a SEM based on the extended TPB to analyze the perception factors affecting the TMSI. Then, the MLM covering potential factors and dominant factors is established to analyze TMSB.

3 Research areas, data, and methods

3.1 Research area

Located at the crossroads of northwest China, Lanzhou is the second largest city in the northwest and the only provincial capital in China where the Yellow River runs through the city. With mountains facing each other in the north and south and the Yellow River running through the city from west to east, Lanzhou has become an important transportation hub and tourist attraction due to its historical connection to the Silk Road. Spanning about 30 km from east to west and only about 5 km from north to south at its narrowest point, Lanzhou is a typical valley city.

Compared with plain cities of the same scale, valley cities have a lower degree of land mixed use, larger road slope, and the river in the region is parallel to the main axis of the city [41,42]. In addition, the group characteristics are obvious, and the traffic develop-ment at the edge of urban group is significantly behind that at the center of urban group, and the junction of each group is narrow, which is prone to traffic congestion [43].The road network in valley city exhibits a high non-linear coefficient, marked by its its inherent complexity, the prevalence of fragmented roadways, and the existence of one-way streets [44]. Furthermore, residents are compelled to navigate through the city center to establish communication between the two extremities of the city [45]. In valley cities, the river traverses the urban area in alignment with the primary thoroughfare [46]. Consequently, road users in valley cities are required to undertake more extensive detours to access bridges and cross the river, in contrast to those in typical flat cities. Additionally, peak traffic periods in valley cities tend to be prolonged when compared to similarly sized flat cities [41]. This phenomenon can be largely attributed to the inadequately developed traffic infrastructure on the outskirts of valley cities, the narrow intersections within urban clusters, the unidirectional flow of passengers, the significant interactions between the central area and other urban clusters, and the multitude of detours necessitated by the river and the intricate road network [45].

3.2 Research methods

TPB is frequently utilized to analyze the decision-making processes of commuters regarding their transportation choices in studies related to traffic [47,48]. It explains how individuals behave under specific circumstances. In this study, the TMSI may be influenced by three factors. SBA encompasses an individual's comprehensive assessment of the outcomes related to the shift in travel modes. Additionally, SN pertains to how an individual perceives the potential changes in their behavior due to influence or encouragement from family, friends, and the broader community. PBC, on the other hand, relates to the individual's perception of the challenges or ease associated with making this shift. However, research indicates that beyond these factors, various psychological elements can also impact the TMSI [49]. Consequently, in light of the unique characteristics of valley cities, this study integrates the variables of FAP and TSP to enhance the TPB.

SEM is an essential technique for multivariate analysis, typically implemented using AMOS. Unlike traditional regression analysis, SEM offers the benefit of simultaneously estimating relationships among multiple variables and testing various hypotheses within a single structural model. Additionally, SEM is effective in quantifying the psychological variables. Consequently, it has become a popular choice among researchers investigating travel behavior. SEM comprises two components: the measurement model, which defines potential variables through their corresponding observed variables, and the structural model, which employs exogenous latent variables to explain endogenous latent variables.

In the study of travel behavior, researchers frequently employ discrete choice models, with the Logit model being the most prevalent. However, a limitation of the multinomial Logit model is that its explanatory variables only account for subject attributes that remain constant regardless of the chosen option, which does not accurately reflect real scenarios. In contrast, the explanatory variables of the MLM incorporate both subject and object attributes that fluctuate based on the selected option. The parameters within its utility are random and adhere to specific distribution. To address the potential bias arising from the Independence of Irrelevant Alternatives (IIA), this research utilizes the MLM to examine the travel mode shift behavior.

MLM is a valuable tool for analyzing travel behavior; however, it falls short in fully capturing the effects of travelers' psychological factors on their travel choices [50]. A review of existing literature suggests that incorporating psychological elements could provide a more comprehensive understanding of individual travel mode shift behavior compared to focusing solely on travel factors [51,52]. Consequently, this study centers on Lanzhou City as the focal point, utilizing an extended TPB, we introduce SEM to explore how various psychological factors influence travel mode shift choice. We propose the following hypotheses: H1∼H5, SN, PBC, SBA, FAP, and TSP will significant impact TMSI. MLM analyzes the effects of these psychological factors alongside individual socioeconomic attributes (ISA), travel characteristics attribute (TCA), and objective built environment attributes (OBEA) on TMSB, as illustrated in Fig. 2.Fig. 2 Theoretical model.

Fig. 2

Assuming that the set of options available to traveler n is represented as A and the utility derived from scheme i is denoted as Uin, as represented in Eq. (1). In the MLM, ein consists of two components: one is a random error term that accounts for correlation and variability among choices, while the other is a random term.(1) Uin=Xinβn+ein=Xinμb+(Xinηb+εin)

Where Xin denotes the measurable part of the choice's utility, βn and ein are random influence variables that cannot be directly measured. μb is the mean of βn, ηb is the random error term of βn, and εin is the random error term.

The maximum likelihood estimation is employed to estimate the parameters of MLM. When the parameter is designated as random, the probability of the traveler n selecting scheme i can be represented as Eq. (2).(2) Pin=∫exp(βnXni)∑i∈Aexp(βnXni)f(βn|θ)dβn

Where f(βn|θ) is the probability density function obeying a certain distribution. The parameters of the object characteristic variables are normally distributed.

Elasticity is a dimensionless measure of the sensitivity of one of two related variables to changes in the other. It is usually expressed as a ratio of the rate of change of a variable (the elasticity coefficient). Suppose that when traveler n adopts a certain mode of transportation i, the sharing rate of this mode of transportation is Pin. Assuming two transportation modes i and j, the cross-elasticity of the sharing ratio of the selected mode j to the change of the k attribute of mode i can be determined by Eq. (3) [53].(3) EXjnkPin=XjnkPin·dPindXjnk=−θkXjnkPjn

Where Xjnk is the value of the k attribute of the j mode of traveler n; θk is the parameter of the k attribute.

The combined influence of several factors can be determined by Eq. (4) [54].(4) E=1−(1−E1)×(1−E2)×⋯×(1−Em)

Where, E is the elasticity of the combination factor and Em is the elasticity of factor m.

3.3 Research data

The research centers on travelers in Lanzhou, a representative valley city in China, utilizing a questionnaire survey to gather travel-related data. The questionnaire about travelers' choice of travel mode after bus fare adjustments in valley city consists of two parts. The initial segment is employed to examine the behavioral decision-making process regarding the alteration of travel modes, which encompasses four distinct subsets. In view of the characteristics of valley cities summarized in Section 3.1, we introduced census register factor to explore the impact of residence time in valley city on travel decision. According to the characteristics of valley cities, such as high work-residence separation, large road grade, low land mixed use degree, obvious urban group characteristic and the need to find bridges to cross the river, the factors of work-residence distance, road grade, land mixed use degree of origin, travel grouping characteristic and river crossing demand were taken into account. The ISA set of travelers include gender, age, census register, income and ownership of a private car. The TCA set includes the distance, travel grouping characteristic, number of travel companions, departure time, river crossing demand, travel cost and walking distance of the last travel. The OBEA set includes work-residence distance, road grade and the mixed land use degree of origin of the last travel, the data pertaining to the built environment is sourced from Points of Interest (POI) information obtained via the Gaode map [19].

The subset of travel decisions encompasses the following options: rail transit, car (including taxi, online car, and private car), slow-moving traffic options (such as walking, cycling, and mopeds), and bus. The subsequent section of the questionnaire evaluates SN, PBC, SBA, FAP, TSP, and TMSI, utilizing a 5-point Likert scale. Given the considerable differences in traffic dynamics and contextual factors, the investigation of travel mode choice behavior in valley cities cannot be entirely based on the scales employed for general flat cities of comparable size. Consequently, building upon the established scales of the TPB [47,48], additional dimensions specific to valley cities, namely TSP and FAP, have been incorporated [55]. The observed variables associated with the latent constructs are detailed in Table 1.Table 1 Variable description.

Table 1Latent variable	Variable symbol	Observed indicator variable	
Subjective Norms	SN1	Relatives and colleagues supported me to shift to other travel modes after bus fare adjustment.	
SN2	The social policy supports me to shift to other travel modes after bus fare adjustment.	
SN3	The shift of people around me to other travel modes will also influence my decision.	
Shift Behavior Attitude	SBA1	Shift to other modes of travel is more secure.	
SBA2	The convenience of shifting to other modes of travel is higher.	
SBA3	It is more economical to shift to other travel modes.	
SBA4	The comfort of shifting to other modes of travel is higher.	
SBA5	Shift to other modes of travel has higher accessibility.	
Perceived Behavior Control	PBC1	The shift of travel mode depends entirely on myself.	
PBC2	I can afford to shift travel mode.	
PBC3	It is easy for me to shift travel mode.	
Fare Adjustment Perception	FAP1	I think the bus fare adjustment will have a greater impact on my travel.	
FAP2	I think the bus fare adjustment will have a greater impact on bus travel.	
FAP3	I think that after the bus fare adjustment, some people will shift their travel mode.	
Topographic Space Perception	TSP1	The detour of travel mode after shift is relatively fewer.	
TSP2	The travel mode after shift is more convenient to travel between urban groups.	
TSP3	The travel mode after shift is less affected by the rivers in the region.	
TSP4	The travel mode after shift is less affected by the road grade.	
TSP5	The travel mode after shift is less affected by the congestion of the wasp waist.	
Travel Modal Shift Intention	TMSI1	After the bus fare adjustment, I am willing to shift the mode of travel.	
TMSI2	After considering the topographic conditions, I am willing to shift the mode of travel.	
TMSI3	I 've been planning to shift to other travel modes frequently in the future.	

According to existing studies [56], 220 samples are sufficient for 22 items of latent variables. According to Green [57], for discrete selection analysis, the minimum sample size is determined by the formula “50+8M″, where “M" represents the number of factors. The largest factor covered in the study was 20 in the questionnaire. Therefore, a minimum sample size of 210 is required.

A total of 350 questionnaires were distributed. Following the guidelines set by DeSimone et al. [58], any invalid questionnaires that contained missing data or extreme continuous values were excluded. This process yielded 316 valid questionnaires, resulting in an effective response rate of 90.28 %, which satisfied the sample size criteria [57]. The characteristics of the sample across various travel modes, after fare adjustments, are illustrated in Fig. 3(a–d).Fig. 3 Characteristics of travelers with different travel modes. (a) Characteristics of travelers who use bus. (b) Characteristics of travelers who use rail transit. (c) Characteristics of travelers who use car. (d) Characteristics of travelers who use slow-moving traffic.

Fig. 3

Only the reliability and validity test of the scale data in the questionnaire can ensure the effectiveness of the subsequent modeling. Reliability is used to evaluate whether there is a high intrinsic consistency between items. As shown in Table 2, Cronbach's alpha test value of the questionnaire data was greater than 0.7, Kaiser-Meyer-Olkin (KMO) test value was greater than 0.9 [59], and Bartlett's sphericity test value was less than 0.05. This indicates that the data meet the requirements of multivariate normality and sampling adequacy [36]. SPSS 26 software was used to calculate the composite reliability (CR) to evaluate the internal consistency of each project. As shown in Table 2, CR is greater than the minimum value of 0.7, which meets the requirement. Validity is used to measure the reliability of an item. AMOS 28 software was used to calculate average variance extraction (AVE), and the AVE values in Table 2 were all greater than 40 % [59]. The total variance explanation rate represents the factor information contained in the original data, and generally more than 40 % is considered to have good explanatory power. In conclusion, the scale shown in Table 1 has good reliability and validity [60].Table 2 Reliability and Validity checks.

Table 2Latent class	Cronbach's Alpha	KMO	AVE	CR	Total variance explained cumulative %	
Criteria	>0.700	>0.900	>0.400	>0.700	>40.00 %	
Subjective Norms	0.867	0.943	0.694	0.871	77.77 %	
Shift Behavior Attitude	0.898	0.648	0.902	
Perceived Behavior Control	0.820	0.635	0.838	
Fare Adjustment Perception	0.763	0.539	0.776	
Topographic Space Perception	0.935	0.759	0.940	

4 Travel modal shift intention and behavior

4.1 Travel modal shift intention

The SEM of the four modal-shift, namely, rail transit, car, slow traffic and bus, has been established as shown in Fig. 4.Fig. 4 Structural equation model.

Fig. 4

We employed AMOS 26.0 to estimate the initial parameters for the SEM. To evaluate the model's fitness, we utilized several indices, including the chi-square degrees of freedom (CMIN/DF), approximate root mean square error (RMSEA), goodness of fit index (GFI), comparative fit index (CFI), normed fit index (NFI), Tucker-Lewis index (TLI), and incremental fit index (IFI). The results indicated a high degree of fit, satisfying the standard requirements and making it suitable for further analysis [36], as detailed in Table 3.Table 3 Model fit index.

Table 3Indicators	Criteria	Indicators	
Rail transit	Car	Slow-moving traffic	Bus	
CMIN/DF	1∼5	1.675	1.722	1.764	1.564	
GFI	>0.8	0.923	0.921	0.921	0.934	
CFI	>0.8	0.975	0.980	0.970	0.971	
NFI	>0.8	0.941	0.953	0.935	0.939	
TLI	>0.8	0.963	0.974	0.962	0.965	
IFI	>0.8	0.975	0.980	0.971	0.974	
RMSEA	<0.08	0.048	0.048	0.049	0.046	
RSMR	<0.05	0.024	0.021	0.025	0.023	

The path coefficients have been normalized, as detailed in Table 4 [61]. It is clear that each latent variable significantly influences the shift in travel modes, confirming the validity of all proposed hypotheses: H1∼ H5. The standardized path coefficients indicate the strength of the direct relationships between the variables. For travelers who shift to rail transit, TSP (0.254), FAP (0.250), SBA (0.199), PBC (0.164), and SN (0.121) show a decreasing trend in their intention to shift. This suggests that adjusting bus fares diminishes the cost advantage of buses compared to rail transit. Additionally, rail transit effectively mitigates traffic challenges such as detours, road grades, and congestion in narrow areas caused by one-way streets or river crossings, which are often encountered by road traffic. Similar findings have been reported in other studies [20]. The influence of SBA (0.272), FAP (0.267), TSP (0.217), PBC (0.215), and SN (0.167) on travelers' intention to shift to car has also shown a gradual decline. This indicates that the shift from bus to car is largely driven by an increased focus on service quality, especially when the perceived difference in travel costs following fare adjustments is minimal. This observation is consistent with previous research findings [23] The impact of SN (0.363), FAP (0.224), PBC (0.175), SBA (0.162), and TSP (0.142) on travelers' inclination to shift to slow-moving traffic exhibited a declining pattern. While slow-moving traffic may not excel in service level and travel reliability, it is recognized as the healthiest, most environmentally friendly, and most cost-effective travel option. Community support and social policies play a crucial role in encouraging travelers to consider slow-moving traffic alternatives [62]. Furthermore, SN (0.287), PBC (0.245), TSP (0.200), SBA (0.195), and FAP (0.117) had a decreasing impact on travelers' intention to shift to bus. Buses benefit not only from supportive social policies but also from being a well-established mode of public transport in urban areas, offering economic and convenience advantages. Choosing to travel by bus presents minimal barriers for travelers, a point further supported by Chen's study [62].Table 4 Hypothesis testing results.

Table 4Hypothesis	Model path	Rail transit	Car	Slow-moving traffic	Bus	
path	adaptation	p	path	adaptation	p	path	adaptation	p	path	adaptation	p	
H1	TMSI←SN	0.121	0.122	***	0.167	0.147	***	0.363	0.341	***	0.287	0.275	***	
H2	TMSI←TBA	0.199	0.201	***	0.272	0.239	***	0.162	0.152	***	0.195	0.187	***	
H3	TMSI←PBC	0.164	0.166	***	0.215	0.189	***	0.175	0.164	***	0.245	0.235	***	
H4	TMSI←FAP	0.250	0.253	***	0.267	0.235	***	0.224	0.210	***	0.117	0.112	***	
H5	TMSI←TSP	0.254	0.257	***	0.217	0.191	***	0.142	0.133	***	0.200	0.192	***	
Note: *** indicates a significant level of 0.001.

4.2 Travel modal shift behavior

We employed Stata 16 software for parameter estimation and to assess the significance level of our model. It is important to note that we assume the parameters of the object characteristic attribute variables are all random and normally distributed. Given that the maximum likelihood model with random coefficients is non-closed and cannot be solved directly, we opted for the imitation method for our analysis [63]. Specifically, we utilized the Monte Carlo simulation method, selecting Halton sampling to extract 500 samples. The results of our analysis are summarized in Table 5. As illustrated, the scheme variables exhibit a normal distribution, highlighting the varying sensitivity of different travelers to changes in these variables [59].Table 5 Estimation results for parameters.

Table 5Variable (Reference category: Rail transit)	Car	Slow-moving traffic	Bus	
Coefficient	p	Coefficient	p	Coefficient	p	
Subject characteristic variable	Individual socioeconomic variables	
Gender	−1.640**	0.005	−0.215	0.743	−0.255	0.547	
Age	0.666**	0.044	−0.919**	0.031	1.245***	0.000	
Census register	−0.134	0.815	1.802**	0.006	0.666	0.104	
Income	2.292***	0.000	−1.654**	0.004	−0.373	0.342	
Private car	1.606*	0.010	0.261	0.679	−0.340	0.417	
Built environment variable	
Work-residence distance	−0.205	0.528	−1.024**	0.013	−0.202	0.415	
Road grade	1.335**	0.027	−1.257*	0.042	−0.333	0.396	
Mixed land use degree of origin	0.293	0.344	0.873**	0.003	−0.125	0.566	
Travel characteristic variable	
Number of travel companions	1.494**	0.004	−0.551	0.339	−0.252	0.503	
Travel grouping characteristic	2.288**	0.002	−0.621*	0.328	−0.707*	0.089	
Travel distance	0.594	0.162	−1.664***	0.000	−0.957**	0.029	
Departure time	−1.618**	0.007	0.266	0.712	−0.389	0.106	
_cons	1.513	0.691	25.048***	0.000	6.334**	0.015	
Object characteristic variable	Travel characteristic variable	
River crossing demand	−1.202 (0.856)**	0.042	
Travel cost	−1.741 (0.918)***	0.001	
Walk distance	−1.022 (0.812)***	0.001	
Latent psychological perception variables	
Subjective Norms	1.650 (0.978)***	0.001	
Shift Behavior Attitude	1.710 (0.758)**	0.002	
Perceived Behavior Control	1.531 (1.058)**	0.005	
Fare Adjustment Perception	1.374 (1.240)**	0.011	
Topographic Space Perception	1.482 (0.612)**	0.005	
Note:***significant at 0.001, **significant at 0.05 and * significant at 0.1.

4.3 In-sample fit and predictions

To assess the validity and efficiency of the SEM-MLM, we developed traditional Multinomial Logit (MNL) and SEM-MNL models for comparison. The fit indices for all three models are displayed in Table 6. Notably, each model demonstrates a strong ability to explain the data. However, the SEM-MLM consistently surpasses the other two models across all performance metrics [64].Table 6 Model fitting indices.

Table 6Model	-2LL(β)	-2LL (0)	Pseudo R2	AIC	BIC	Model prediction accuracy	
MNL	363.288	842.77	0.569	453.288	622.297	75.00 %	
SEM-MNL	222.771	842.77	0.736	342.771	568.116	87.34 %	
SEM-MLM	185.777	842.77	0.780	305.777	531.121	91.46 %	

The model's specific prediction performance is primarily derived from the confusion matrix statistics of the three models [65]. It can be observed that the SEM-MLM outperforms the other two model in predicting each travel scheme selection (Fig. 5(a–c)).Fig. 5 Confusion matrix of models. (a) Confusion matrix of MNL. (b) Confusion matrix of SEM-MNL. (c) Confusion matrix of SEM-ML.

Fig. 5

4.4 Elastic analysis

The cross-elasticity of the sharing rate of the other three travel modes to the travel cost of the bus, fare adjustment perception, and topographic space perception is calculated, as shown in Table 7. Without considering the influence of other factors, when the bus fare rises by one yuan, the ridership of buses, rail transit, cars, and slow-moving traffic changes by −13.312 %, 7.611 %, 2.721 %, and 2.981 % respectively. Based on this, the elasticity of the sharing rate for each travel mode to the FAP and TSP was calculated, as illustrated in Fig. 6(a and b).Table 7 Elasticity of travel mode sharing rate.

Table 7Travel mode	Rail transit	Car	Slow-moving traffic	
Travel cost of bus	0.357	0.110	0.190	
Fare adjustment perception	0.167	0.101	0.079	
Topographic space perception	0.444	0.109	−0.948	

Fig. 6 Elasticity of travel mode sharing rate to influencing factors after bus fare adjustment. (a)The elasticity of travel mode to bus fare adjustment perception. (b) The elasticity of travel mode to topographic space perception.

Fig. 6

For travelers with fixed travel needs, such as commuting, transportation costs have become a significant part of their expenses. Adjustment in bus fare can impact the distribution of passenger flow of different modes of transportation in the city. It is evident that as travelers' FAP increases, the proportion of bus decreases, while the proportions of rail transit, car, and slow-moving traffic increase to varying degrees. Among these modes, the proportion of rail transit is most sensitive to the FAP. The proportion of rail transit changes in the same direction as the changes in travelers' FAP and TSP, and the sensitivity of rail transit ridership to TSP is higher than FAP. The adjustment of bus fares primarily encourages passenger flow to rail transit which is more conducive to the development of the valley city and enhances the transportation efficiency.

When the traveler's FAP and TSP is increased by 50 % each, the proportion of rail transit will change by 2.425 % and 6.429 % respectively. The proportion of slow-moving changes in the opposite direction of travelers' TSP. As travelers' TSP increases, it becomes difficult for them to choose slow-moving traffic. Both bus and car are forms of road traffic, and the changes trend of their respective proportion exhibit similar to slow-moving traffic. When travelers' TSP increases by 50 %, the proportion of slow-moving traffic, bus, and car changes by −8.840 %, 0.942 %, and 1.470 %, respectively.

According to the results of cross-elasticity analysis, when considering the traveler's FAP and TSP, rail transit and car will be more dominant. However, if we want to address the urban traffic problem, we should try to emphasize the advantages of rail transit rather than car. Therefore, building upon this foundation, we take into account the negative impact of travelers' SN on car since the research results of Mou et al. [64] have provided a key insight: lack of support from social policies and one's immediate circle significantly impedes car travel options.

To examine the combined influence of travelers' SN, FAP, and TSP on travel mode shift behavior after bus fare adjustment, we analyzed the combined elasticity of each travel mode's sharing rate on travelers' SN, FAP, and TSP, as depicted in Fig. 7. As travelers' SN, FAP, and TSP continue to improve, the proportion of rail transit increases significantly. Conversely, the proportion of car and slow-moving traffic decreases steadily, while the proportion of bus initially increases and then decreases. It is roughly consistent with our expected compliance of travel modal shift. Mainly, it can be influenced from these three aspects to achieve the goal of guiding travelers to shift to rail transit.Fig. 7 The combined elasticity of SN, FAP, and TSP.

Fig. 7

5 Discussion

The findings of our research present several noteworthy conclusions as outlined below. The principal demographic categories of rail transit users include women, middle-aged and young adults, individuals with local census register, those with middle to low income, car-free people, those who have a long work-residence distance or travel between urban groups which resulting a large travel distance, those with low mixed land use at their departure location or those who with a large road grade in the travel section, individuals with fewer travel companions, those who need to cross rivers, and those who travel during peak hours. In comparison to their male counterparts, women exhibit a greater reluctance to utilize car travel, which may be attributed to heightened concerns regarding travel safety [66]. Additionally, older travelers demonstrate a preference for car and bus travel. Drawing upon the findings of Talbot et al. [67], we seek to elucidate the potential rationale behind this trend, suggesting that it may be linked to the complexities associated with rail transit experiences. One disadvantage of slow-moving traffic is that it places high physical demands on travelers which is not suitable for middle-aged and elderly travelers. Local travelers prefer rail transit, cars and bus. This may be attributed to the tendency of local tourists to possess private vehicles [4] and their familiarity with the topography of the valley city. Additionally, the study's findings suggest that travelers with higher incomes are more inclined to utilize cars, whereas those with lower incomes tend to prefer bus transportation [68]. This preference is further supported by the analysis indicating that the expenses associated with car travel are significantly higher compared to those of bus travel. Private car ownership will influence travelers' willingness to choose car.

It is almost certain that travel cost and walk distance have negative effects on each travel mode, as demonstrated by Iraganaboina et al. [69]. To add, our research indicates that the demand for river crossings exerts a considerable negative impact on the mode choice behavior among individuals. Additionally, there exists heterogeneity among travelers regarding their perception to factors such as river crossing demand and walking distances. For traveling with a large number of travel companions, bus and rail transit are less dominant in terms of ticketing mode [65]. Our conclusion challenges stereotypes by demonstrating that it is possible to travel the same distance in a car at a lower cost than by bus when the number of travel companions is large enough. Research conducted by Luan et al. indicates that during periods of peak hours, individuals are less likely to choose car and bus [70]. The benefits of rail transit, particularly its immunity to traffic congestion in valley city, and the advantages of slow-moving traffic, such as having independent lane flexibility, were not taken into account by them. however, we acknowledged these. Rail transit and car are more prominent in valley city where the average travel distance is greater [70]. As travel distance increases, the appeal of rail transit to passenger flow is more obvious because of its high cost performance compared with car. The mechanism by which travel grouping characteristic and work-residence distance influences travel behavior is similar, the valley city has a high degree of work-residence separation and a long travel distance between groups, which is very beneficial to the development of rail transit with long-distance travel. As we have previously guessed, our study found that when the road grade is large, slow-moving traffic will be effectively suppressed. In addition, we found that higher land mixed use will promote the use of slow-moving traffic, which is also in alignment with the research conducted by Eldeeb et al. [71]. In fact, when the land use mix degree of origin is low, travelers are compelled to create additional travel requirements to satisfy diverse lifestyle needs.

SN exert a considerable influence on the travel choices. Due to the high carbon emissions and high cost, car travel receives less support from relatives, friends, and society, which is consistent with Mou et al. [64]. Environmentally friendly and economical modes such as rail transit and slow-moving traffic are more acceptable to people. Rail transit is clearly a means to achieve multiple objectives such as economy, speed, environmental protection and not being disturbed by the topographic of valley city simultaneously, especially after the adjustment of bus fares. Therefore, travelers have the most positive SBA to rail transit. In addition, the behavior of shift to rail transit does not impose any burdens on travelers regarding physical strength and economy. Considering the long-distance travel and road grade, travelers perceived difficulty in shifting to slow-moving traffic in valley city. It is important to note that this study presents two novel indicators, namely FAP and TSP, which are developed based on the TPB. Result shows that, on the one hand, a stronger FAP leads travelers to reconsider the “cost-effective" travel mode when faced with a smaller travel cost gap. This promotes former bus travelers to shift to other modes. On the other hand, with the improved understanding of the topographic in valley city by travelers, it is clear that rail transit is not required to navigate detours when faced with one-way street or the river, in contrast to other modes of road transportation. Furthermore, rail transit is not influenced by road gradients in the same manner as slower-moving traffic.

On the contrary, in long-distance travel between valley city, the accessibility of rail transit is higher. Therefore, as travelers' TSP increases, the likelihood of shifting to rail transit also increases. When SN, FAP, and TSP are significantly improved, rail transit gains a distinct advantage. It is worth noting that excessive increase in the FAP may lead to a decrease in the bus sharing rate, which may make it lower than the car. This outcome is also detrimental to addressing urban traffic issues. Therefore, changes in travelers' FAP should be carefully managed to an appropriate extent. There is heterogeneity in the psychological perception of different travelers.

6 Conclusions, suggestion, and limitations

The study contributes in the following three aspects. First, we examine the travelers’ mode shift behavior after bus fare adjustment in valley city, a topic that has not been discussed before.

Building on prior studies, we broaden the range of influencing factors by considering the unique characteristics of valley city and incorporate the concepts of FAP and TSP to enhance TPB. Second, we develop the SEM-MLM to identify the primary demographic characteristics influencing rail transit usage in valley city after bus fare adjustment. This model elucidates the significant factors that affect travelers' TMSI. In comparison to the other two models, the SEM component of the SEM-MLM provides a more precise quantification of potential psychological perceptions, while the MLM aspect accounts for the heterogeneity in sensitivity among different travelers regarding the influencing factors, thereby enhancing the model. Finally, through the elastic analysis of the key influencing factors, we find an effective way to promote the travelers' shift of valley city to rail transit——Improve the travelers’ SN, FAP and TSP of valley city.

Lanzhou City's bus operation has been experiencing long-term losses, making it difficult to sustain. This fare adjustment has facilitated the shift of bus passenger shift to rail transit, bolstered the sustainable development capacity of bus operations, enhanced the transportation efficiency of Lanzhou City, met the public's demand for safe and rapid travel, and established a public transportation model that is widely accepted, conducive to enterprise development, and financially viable. We encourage the travelers shift from road traffic to rail transit and propose the following suggestions. From the perspective of travelers' personal factors and travel characteristics, safety, travel efficiency, and cost performance are key competitive factors. Efficiency can be enhanced by scheduling rail transit fast and slow line at different times. Streamlining ride procedures for middle-aged and elderly people to take rail transit. The introduction of preferential policies for the travel modal shift can further increase the economy of rail transit after the adjustment of bus fare, and the formulation of group tickets also works. What's more, the helpful security personnel provide passengers with a sense of security against aggression and harassment, especially for women. It is essential for rail transit operation department to minimize the disparity in convenience, comfort and accessibility compared to cars, while upholding the advantages of safety and high cost performance. For instance, keep the subway clean and comfortable and the temperature is suitable, provide comfortable and sufficient seats in waiting areas, and add elevators at stations with high passenger traffic.

Enhance the connectivity of rail transit stations by implementations. It is essential to expedite the development of mixed-use land to achieve a more balanced work-residence distance, relatively improve the ratio of medium and long-distance travel dominated by rail transit mode. Reasonable planning of rail transit stations in the valley city group crowded place to shorten walking distance, as well as reduce the pressure in the bee waist area. As for psychological factors, government initiatives designed to promote low-carbon travel can strengthen travelers’ subjective norms influencing their shift to rail transit. The relevant department should employ diverse strategies to widely publicize the advantages of rail transit in valley cities relative to road traffic methods, especially for non-local populations. In addition, we recommend that the transportation sector regularly conduct surveys to gather subjective psychological perception data from travelers. This data can then be used to support the development and enhancement of transportation policies.

This study presents several limitations. Prior research has rarely examined the travel mode shift behavior of individuals in valley cities following adjustments in bus fares, particularly from the perspective of topographic space perception. Consequently, the observational variables lack a mature scale for reference. Although the indicators proposed in this paper can better explain the data from this questionnaire, follow-up studies are still needed to prove the scale's applicability to other environmental data. Secondly, this paper utilizes a MLM to demonstrate the existence of heterogeneity in the travelers' perceptions in valley cities. However, the factors that contribute to perceptual heterogeneity are uncertain and require further research. In the future, the comprehensive influence of various factors on shift behavior will be analyzed by considering moderating effects.

Ethics statement

This study was reviewed and approved by the ethics committee of the Lanzhou Jiaotong University with the approval number: 2023112701, dated November 27, 2023.

All participants were informed that consent to participate in the study and publish their data would be assumed on completion and submission of the study questionnaire.

Data availability

Data will be made available on request.

CRediT authorship contribution statement

Mengxing Fan: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Conceptualization. Jinping Qi: Writing – review & editing, Project administration, Funding acquisition, Conceptualization. Xiangdong Zheng: Investigation, Data curation. Hongtai Shang: Writing – review & editing, Investigation, Formal analysis, Data curation, Conceptualization. Jiayun Kan: Writing – review & editing, Visualization, Validation, Software, Methodology.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A Supplementary data

The following is the Supplementary data to this article.Multimedia component 1

Multimedia component 1

Appendix A Supplementary data to this article can be found online at https://doi.org/10.1016/j.heliyon.2024.e36675.
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