Spatially Varying Effect Mechanism of Intermodal Connection on Metro Ridership: Evidence from a Polycentric Megacity with Multilevel Ring Roads

Abstract

Understanding the spatially varying effect mechanism of intermodal connection on metro ridership helps policymakers develop differentiated interventions to promote metro usage, especially for megacities with multiple city sub-centers and ring roads. Using multiple datasets in Shanghai, this study combines Light Gradient Boosting Machine (LightGBM) with Shapley additive explanations (SHAP) to explore these effects with the consideration of the built environment and metro network topology. Results show that the collective impacts of intermodal connection are positive, not only within the main city but also alongside the main commuting corridors, while negative effects occur in the peripheral area. Specifically, bike sharing trips increase metro ridership within the inner ring of the city, while bus services lower metro usage at stations alongside the elevated ring roads. Parking facilities enable metro usage at city sub-centers, and the small pedestrian catchment area increases metro riders alongside the main commuting corridors. Empirical findings help policymakers understand the effect mechanism of intermodal connection for stations in different regions and prioritize customized planning strategies.

1. Introduction

Transit-oriented development (TOD) and metro systems have been globally utilized to counter environmental challenges and achieve sustainable development [1]. Understanding the effect mechanism of station-level metro ridership is critical for decision-makers and urban planners to regulate the scale of metro stations and encourage metro usage [2]. The determinants of metro ridership have been explored by many previous studies, such as pricing, weather conditions, land use, built environment, socioeconomics and metro network topology [3]. Among these factors, intermodal connection, also known as the first/last-mile services, are considered to have significant impacts on metro-integrated travel utility [4]. In this case, fare subsidy, emerging shared mobilities and first/last-mile facilities have been provided in many countries to enhance intermodal connection and metro attractiveness [5].

Previous studies have considered intermodal connection (e.g., bus stop density, parking facilities, bike-sharing stations) as the measure of the built environment to investigate their effects on metro ridership within different contexts. The parametric regression model has been employed by studies in Spain [6], South Korea [7] and China [8]. Machine learning algorithms have been recently utilized to discover multiplex nonlinear effects on metro usage in the United States and China, including gradient boosting decision trees (GBDT) [9,10], eXtreme Gradient Boosting (XGBoost) [11], Light Gradient Boosting Machine (LightGBM) [12] and Random Forest (RF) [13]. Compared to classic parametric models, machine learning approaches can illustrate the exact nonlinear patten and identify the threshold effects on metro usage, which can benefit planning practice [14]. However, most of these empirical studies explored the nonlinear associations between intermodal connectivity and metro ridership from a global perspective, ignoring the spatial heterogeneity in reality.

Understanding the spatial heterogeneity of travel demand can help urban planners develop customized planning strategy and policy for different urban areas [15]. The effect mechanism of intermodal connection on metro ridership may vary from downtown to suburban areas, especially in megacities with large metropolitan areas and typical spatial variations. The difference in population density, income level, commuting distance and transport infrastructure between different areas can lead to heterogeneity in travel behaviors. For example, spatially varying impacts of these determinants have been discovered to exist in several transport-related aspects [15,16,17,18,19,20,21,22]. Misunderstanding of spatial heterogeneity may lead to inaccurate policy implications, and influence the effectiveness of public priority policy and transit-oriented development [13]. However, studies on the spatially varying impacts of intermodal connection on metro ridership are rather limited.

Moreover, spatial heterogeneity is not only related to the geographic location of the metro station, but also to the position of the metro station within the entire metro network [23]. Some existing studies have involved one or two metro network attributes (e.g., transfer/terminal dummy, betweenness centrality, shortest path) in their research [10,18,24]. However, the study of one or two of these attributes cannot comprehensively reflect the network topology and real position of stations within the metro network. For example, a transfer station can be not only a transfer station of two lines, but also a transfer station of four lines. Therefore, it is crucial to uncover the spatially varying effects of intermodal connectivity on metro ridership with the consideration of metro network topology.

To jointly fill the abovementioned gaps, this study investigates the spatially varying effect mechanism of intermodal connection on metro ridership in Shanghai, while controlling for other external determinants (e.g., the built environment) and internal determinants (e.g., network topology). Shanghai was selected as the study area for a number of reasons. First, Shanghai is a megacity with 24.89 million people and a 6340.5 km² area, which has significant public transit and metro demand. Second, Shanghai is a polycentric megacity with a hierarchy spatial system and multilevel ring roads, which may have typical spatial heterogeneity in travel behavior. Third, the Shanghai metro system has the longest operation routes in the world, with more than 500 metro stations, which provides a sufficient data sample for a metro ridership study. LightGBM, a machine learning approach, is employed to explore the nonlinear patterns and importance of various determinants on metro ridership, while SHapley Additive exPlanations (SHAP) are utilized for model interpretation from the spatial perspective, and to estimate the heterogeneity between different stations.

This study has the potential to enrich existing literature and guide policy practice in two aspects. First, it estimates the spatial variation in the associations between intermodal connectivity and metro ridership by considering network topology. Second, it is among the first attempts to explicitly explore the spatial heterogeneity of the effect mechanism, by comparing six typical stations with similar ridership, but different geographic location and metro network position. Empirical findings may help decision-makers develop customized intermodal connectivity optimization strategies in different urban regions.

The remainder of this article is organized as follows: Section 2 presents the literature review on intermodal connectivity and spatial heterogeneity; Section 3 introduces the study area, data sources and model variables; Section 4 describes the methodology; Section 5 presents and discusses the model results; Section 6 concludes important findings and associated policy implications.

2. Literature Review

2.1. Intermodal Connection of Metro Systems

The improvement of intermodal connection is widely believed to enhance the utility of metro systems and facilitate metro usage [25]. Although different emerging mobilities have been developed in recent years, commonly used access modes to metro systems can be categorized into walking, bike, bus and auto [26].

Walking access to a metro station can be influenced by various factors, including walking distance, sidewalk design, and personal demographics [26]. Many studies on metro ridership have involved street density as a built environment factor [10,24], ignoring the influence of non-walking segments for pedestrians. Pedestrian catchment area, which is calculated based on the sidewalk or pedestrian network by removing non-walking segments, has been proposed to evaluate the walking environment of metro station areas, [27] and to explore its effect on metro ridership [12].

Shared bikes and private electric bikes have been widely integrated with metro systems because of their convenience and health benefits [28,29,30]. Existing literature has investigated the nonlinear effects of bike sharing on metro ridership with the data of docked bike sharing stations in Washington, D.C [9] and Nanjing [31]. Dockless bike sharing, which is currently prevalent in many cities, has only been investigated in its effect on metro usage by few studies [12].

Bus is another popular feeder mode to access the metro systems, which is usually promoted by fare subsidies with the metro [16]. Previous studies have estimated the nonlinear impacts of bus services on metro usage from several aspects, such as bus stop [9,10,13], bus line [24,31,32], bus accessibility [33] and trips made by bus [34].

The nonlinear impacts of auto facilities on metro ridership are discovered by estimating parking lots [8,12,13,31,35] and park-and-ride facilities [9]. Other auto options, such as taxi and ride-sourcing can also provide on-demand intermodal connection for metro riders [36]. However, few studies have examined the relationship between these feeder modes and metro usage because of the lack of data availability.

2.2. Determinants of Metro Ridership

The determinants of metro ridership can be categorized into exterior determinants (e.g., built environment, socioeconomics) and interior determinants (e.g., metro fare, service level, departure frequency, station attributes, network topology) [3,18].

Although the built environment can be examined from a variety of angles, most scholars investigated them by using ‘‘7Ds’’. The effects of the built environment on travel behavior was first measured by ‘‘3Ds’’, including density (e.g., population density, employment density), diversity (e.g., land use mix entropy, dissimilarity index) and design (e.g., block size, pedestrian provision, site design) [37]. Then, destination accessibility (e.g., distance to CBD, suburb CBD, shopping center) and distance to transit (e.g., number of bus stops, bus line density) were involved as the ‘‘5Ds’’ measurement [38]. After that, demand management (e.g., parking facilities) and demographics (e.g., age, gender, income, education) were considered to compose the ‘‘7Ds’’ measurement [39].

Previous studies have examined impacts of the built environment on metro usage within several contexts [31,40,41,42,43]. However, most of these studies relied on parametric regression models with pre-assumed linear parameters and certain distribution of variables [14], which can lead to questionable empirical conclusions [44]. Recent studies on the associations between the built environment and metro ridership employed machine learning approaches to uncover the nonlinear pattern, which identified different thresholds of the determinants on metro usage in the United States [9] and China [10,12,13,24].

For internal factors, since the metro fare and departure frequency are usually consistent, most studies explored the impacts of interior determinants on station-level metro ridership by estimating station attributes and network topology. Station attributes include transfer station [18,31,32], terminal station [8,9,12], passing lines [35,45], transfer time [24], intercity station [18,31], metro service level [9] and metro accessibility [35].

Metro network topology has also been proven to affect metro ridership, including distance to central station [10], betweenness centrality [8,10], detour and route distance of metro network [24]. However, the combination of these variables cannot reflect the real position of stations in metro network. Under these circumstances, network theory has been widely utilized to comprehensively estimate the structure and topology of metro networks, because the metro network can be presented by multiple nodes and links [46]. Network centrality, including degree centrality, betweenness centrality, closeness centrality and eigenvector centrality, are the most widely used measurement on metro systems [47]. Network centrality has been explored to significantly affect bus ridership in Beijing [48], and metro ridership in Shenzhen [49] and Athens [23].

2.3. Spatial Heterogeneity of Travel Behavior

Understanding the spatial heterogeneity of travel behavior can help urban planners develop customized planning strategies and policies for different urban areas [15]. Spatial variation has been noted to exist in several travel behaviors, including transit commuting mode choice [17], bus usage [50], metro ridership [51], taxi ridership [52], ridesplitting adoption rate [15], urban rail transit ridership [19], intercity commuting trip [22], commuting by car [20], intermodal transit trip [16] and bike sharing parking [21].

The misunderstanding of the spatially varying impacts of intermodal connection on metro ridership may lead to inaccurate policy implications, and influence the effectiveness of TOD and public priority policy [13]. Parametric regression models have been employed to analyze the spatially varying impacts of land use on metro usage [7,31,32], which found that metro usage is associated with land use within different regions, and the coefficients varied across different geographic locations. With the emergence of machine learning approaches, the spatial investigation of nonlinear impacts of accessibility on metro usage have been explored by employing the GBDT model, which identified the threshold effects and spatial heterogeneity [18].

In summary, although some studies investigated nonlinear effects of the determinants on metro ridership, most of them ignored the spatially varying impacts of intermodal connectivity. To fill this research gap, this study employs LightGBM and SHAP to explore the spatially varying impacts of intermodal connectivity on metro ridership, with the consideration of metro network topology in Shanghai, China.

3. Research Design

3.1. Study Area

We conducted the case study in Shanghai, a megacity with 24.89 million people and a 6340.5 km² area [53]. The Shanghai metro system has the longest operation routes in the world, totaling 795.36 km in 2022 [54].

To facilitate the integration of urban and rural areas, Shanghai aims to create differentiated spatial development strategies by forming a hierarchical spatial system with multi-centers and town clusters [55]. The main city of Shanghai refers to the area within the outer ring, which is only a tenth of the area of Shanghai, at about 664 km². The area within the inner ring is about 116 km², while the area between inner ring and middle ring is about 200 km². City sub-centers include nine sub-centers of the main city and five centers of new cities (Figure 1). The Huangpu River is another important geographical boundary in Shanghai, which flows through the main city and joins the Pacific Ocean.

The daily metro ridership of 17 metro lines and 325 stations are analyzed. Geographically, 89 metro stations are located within the inner ring, 75 stations are between the inner and middle ring, 69 stations are between the middle and outer ring, and 92 stations are outside the outer ring. All ring roads were constructed as viaducts or tunnels. Thirty stations have more than 80,000 daily riders, while twenty-two stations have less than 10,000 passengers. Metro line 2, 1 and 9 are the top three lines with highest metro ridership, which together constitute the main transportation corridor from west-east, north-south, southwest-northeast, respectively.

3.2. Data and Variables

Station-level daily metro ridership is used as the dependent variable, with the smartcard data of Shanghai metro users from December 2019. Twenty-three independent variables are utilized in this study, including six intermodal connection variables, four network topology variables and thirteen built environment variables (Table 1).

Intermodal connection is evaluated by four typical access modes, that is auto, bike, bus and pedestrian [26]. Auto connection is estimated by number of registered parking facilities to represent the convenience of driving to metro stations. Other auto access modes, such as taxi and ridesharing are not considered in this study, due to inaccessible data. Bike connection is analyzed by number of metro-integrated dockless bike sharing trips, if either the origin or destination of the trip is close to metro station entrances (<100 m). Previous studies usually used a 50 m buffer from the metro station to estimate the metro-integrated bike sharing trips [29,56]. Considering there are many no parking areas for shared bikes near the metro station in Shanghai, we identified the dockless bike sharing trips as metro-integrated if their lock or unlock locations are within a 100 m buffer of the metro station entrances. Bus connection is estimated by three variables, from the perspective of bus stop, bus route and distance to the nearest stop. Pedestrian connection is evaluated by pedestrian catchment areas, which are measured by detaching unreachable parts for pedestrians from the street network.

Table 1. Variable description, statistics and data sources.

Variable Name	Variable Definition	Mean	St. Dev.	Min	Max	Data Source
Dependent Variable
Metro ridership	Number of daily passengers on weekday (count)	40,898	35,084	1334	245,870	Metro smartcard data Dec 2019
Independent Variable
Intermodal Connection
Bike sharing	Number of metro-integrated dockless bike sharing trips (count)	2131.35	1571.97	0	8253	Bike sharing trajectory data 2018
Parking facility	Number of registered parking lots (count)	2.960	3.433	0	23	Registered parking data 2019
Bus stop	Number of bus stops (count)	6.612	3.579	1	26	Point-of-interest (POI) data 2019
Bus route	Number of bus routes (count)	17.465	11.208	0	63	POI data 2019
Nearest bus stop	Distance to the nearest bus stop (km)	0.124	0.076	0.008	0.425	POI data 2019
Pedestrian shed	Proportion of 500 m pedestrian catchment area (scale)	0.551	0.188	0.045	0.878	OpenStreetMap (OSM) data 2019
Network Topology
Betweenness centrality 1	The measure of shortest paths that passing the station (scale)	0.044	0.042	0	0.268	Shanghai Metro Map 2019
Closeness centrality 2	The measure of distance or time to other stations (scale)	0.071	0.018	0.034	0.105	Shanghai Metro Map 2019
Degree centrality 3	The measure of number of linked stations (scale)	0.007	0.003	0.003	0.022	Shanghai Metro Map 2019
Eigenvector centrality 4	The measure of neighbor stations and their centralities (scale)	0.021	0.052	0.000	0.368	Shanghai Metro Map 2019
Built Environment
Population density	Population density within 500 m buffer (1000 persons/km2)	18.573	16.169	0.169	110.007	WorldPop population data 2019
Residential density	Residential density within 500 m buffer (1000 persons/km2)	11.238	14.567	0.00	82.616	Mobile signaling data 2021
Employment density	Employment density within 500 m buffer (1000 persons/km2)	14.643	38.734	0.00	37.709	Mobile signaling data 2021
Land use mix 5	The entropy index estimating land use diversity (scale)	0.710	0.117	0.152	0.858	Land use data 2019
Emp-pop balance 6	The index measuring the balance between employment and residential population (scale)	0.301	0.287	0.001	0.992	Mobile signaling data 2021
Street density	Total street length divided 500 m buffer area (km/km2)	5.619	1.977	1.249	14.086	OSM data 2019
Intersection	Number of intersections within 500 m buffer (count)	9.606	6.373	0	43	OSM data 2019
Built-up area	Ratio of rooftop area within 500 m buffer (scale)	0.184	0.065	0.004	0.433	Vectorized rooftop area data 2020 [57]
Dis. to city center	Distance to the People’s Square (km)	12.302	9.069	0	56.530	OSM data 2019
Dis. to city sub-center	Distance to the nearest city sub-center (km)	6.556	5.293	0	38.090	OSM data 2019
Dis. to ring road	Distance to the nearest elevated ring road (km)	1.203	1.019	0.042	6.623	OSM data 2019
House price	Average transaction price for pre-owned house (103 Chinese Yuan/m2)	57.149	20.695	16.045	133.414	Self-crawled data from Lianjia
Entrance	Number of entrances/exits of the metro station (count)	4.037	2.375	1	19	POI data 2019

Notes: ¹ Betweenness centrality of node k can be calculated as ${\mathrm{B}\mathrm{C}}_{\mathrm{k}}={\sum }_{\mathrm{m}\ne \mathrm{n}\ne \mathrm{k}}{\displaystyle \frac{{\mathsf{\delta }}_{\mathrm{m}\mathrm{n}}\left(\mathrm{k}\right)}{{\mathsf{\delta }}_{\mathrm{m}\mathrm{n}}}}$, where ${\mathsf{\delta }}_{\mathrm{m}\mathrm{n}}\left(\mathrm{k}\right)$ refers shortest paths between node m and n which passes though k. ² Closeness centrality of node k can be calculated as ${\mathrm{C}\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{\mathrm{n}-1}{{\sum }_{\mathrm{m}\ne \mathrm{k}}{\mathrm{d}}_{\mathrm{m}\mathrm{k}}}}$, where ${\mathrm{d}}_{\mathrm{m}\mathrm{k}}$ is distance between node k to node m, while n is total number of nodes. ³ Degree centrality of node k can be calculated as ${\mathrm{D}\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{d}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}}}{\mathrm{n}-1}}$, where ${\mathrm{N}}_{\mathrm{d}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}}$ is number of nodes linked with node k, while n is total number of nodes. ⁴ Eigenvector centrality of node k can be calculated as ${\mathrm{E}\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{1}{\mathsf{\lambda }}}\sum _{\mathrm{j}=1}^{\mathrm{n}} {\mathrm{A}}_{\mathrm{k}\mathrm{j}}{\mathrm{E}\mathrm{C}}_{\mathrm{j}}$, where $\mathsf{\lambda }$ is eigenvalue, ${\mathrm{A}}_{\mathrm{k}\mathrm{j}}$ is adjacency matrix, ${\mathrm{E}\mathrm{C}}_{\mathrm{j}}$ is eigenvector centrality of node j. ⁵ Land use mix can be calculated as an entropy index: ${\displaystyle \frac{-\sum _{\mathrm{i}=1}^{\mathrm{m}} \left({\mathrm{q}}_{\mathrm{i}}\right)\mathrm{l}\mathrm{n}\left({\mathrm{q}}_{\mathrm{i}}\right)}{\mathrm{l}\mathrm{n}\left(\mathrm{m}\right)}}$, where m is the total land categories and ${\mathrm{q}}_{\mathrm{i}}$ denotes the ratio of each type $\mathrm{i}$. ⁶ Emp-pop balance is calculated as ${\displaystyle \frac{1-\left(\right|\mathrm{E}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{o}\mathrm{y}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}-\mathrm{m}\ast \mathrm{P}\mathrm{o}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left|\right)}{(\mathrm{E}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{o}\mathrm{y}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}+\mathrm{m}\ast \mathrm{P}\mathrm{o}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})}}$, where m is the ratio of employment population to residential population.

Table 1. Variable description, statistics and data sources.

Variable Name	Variable Definition	Mean	St. Dev.	Min	Max	Data Source
Dependent Variable
Metro ridership	Number of daily passengers on weekday (count)	40,898	35,084	1334	245,870	Metro smartcard data Dec 2019
Independent Variable
Intermodal Connection
Bike sharing	Number of metro-integrated dockless bike sharing trips (count)	2131.35	1571.97	0	8253	Bike sharing trajectory data 2018
Parking facility	Number of registered parking lots (count)	2.960	3.433	0	23	Registered parking data 2019
Bus stop	Number of bus stops (count)	6.612	3.579	1	26	Point-of-interest (POI) data 2019
Bus route	Number of bus routes (count)	17.465	11.208	0	63	POI data 2019
Nearest bus stop	Distance to the nearest bus stop (km)	0.124	0.076	0.008	0.425	POI data 2019
Pedestrian shed	Proportion of 500 m pedestrian catchment area (scale)	0.551	0.188	0.045	0.878	OpenStreetMap (OSM) data 2019
Network Topology
Betweenness centrality 1	The measure of shortest paths that passing the station (scale)	0.044	0.042	0	0.268	Shanghai Metro Map 2019
Closeness centrality 2	The measure of distance or time to other stations (scale)	0.071	0.018	0.034	0.105	Shanghai Metro Map 2019
Degree centrality 3	The measure of number of linked stations (scale)	0.007	0.003	0.003	0.022	Shanghai Metro Map 2019
Eigenvector centrality 4	The measure of neighbor stations and their centralities (scale)	0.021	0.052	0.000	0.368	Shanghai Metro Map 2019
Built Environment
Population density	Population density within 500 m buffer (1000 persons/km2)	18.573	16.169	0.169	110.007	WorldPop population data 2019
Residential density	Residential density within 500 m buffer (1000 persons/km2)	11.238	14.567	0.00	82.616	Mobile signaling data 2021
Employment density	Employment density within 500 m buffer (1000 persons/km2)	14.643	38.734	0.00	37.709	Mobile signaling data 2021
Land use mix 5	The entropy index estimating land use diversity (scale)	0.710	0.117	0.152	0.858	Land use data 2019
Emp-pop balance 6	The index measuring the balance between employment and residential population (scale)	0.301	0.287	0.001	0.992	Mobile signaling data 2021
Street density	Total street length divided 500 m buffer area (km/km2)	5.619	1.977	1.249	14.086	OSM data 2019
Intersection	Number of intersections within 500 m buffer (count)	9.606	6.373	0	43	OSM data 2019
Built-up area	Ratio of rooftop area within 500 m buffer (scale)	0.184	0.065	0.004	0.433	Vectorized rooftop area data 2020 [57]
Dis. to city center	Distance to the People’s Square (km)	12.302	9.069	0	56.530	OSM data 2019
Dis. to city sub-center	Distance to the nearest city sub-center (km)	6.556	5.293	0	38.090	OSM data 2019
Dis. to ring road	Distance to the nearest elevated ring road (km)	1.203	1.019	0.042	6.623	OSM data 2019
House price	Average transaction price for pre-owned house (103 Chinese Yuan/m2)	57.149	20.695	16.045	133.414	Self-crawled data from Lianjia
Entrance	Number of entrances/exits of the metro station (count)	4.037	2.375	1	19	POI data 2019

Notes: ¹ Betweenness centrality of node k can be calculated as ${\mathrm{B}\mathrm{C}}_{\mathrm{k}}={\sum }_{\mathrm{m}\ne \mathrm{n}\ne \mathrm{k}}{\displaystyle \frac{{\mathsf{\delta }}_{\mathrm{m}\mathrm{n}}\left(\mathrm{k}\right)}{{\mathsf{\delta }}_{\mathrm{m}\mathrm{n}}}}$, where ${\mathsf{\delta }}_{\mathrm{m}\mathrm{n}}\left(\mathrm{k}\right)$ refers shortest paths between node m and n which passes though k. ² Closeness centrality of node k can be calculated as ${\mathrm{C}\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{\mathrm{n}-1}{{\sum }_{\mathrm{m}\ne \mathrm{k}}{\mathrm{d}}_{\mathrm{m}\mathrm{k}}}}$, where ${\mathrm{d}}_{\mathrm{m}\mathrm{k}}$ is distance between node k to node m, while n is total number of nodes. ³ Degree centrality of node k can be calculated as ${\mathrm{D}\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{N}}_{\mathrm{d}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}}}{\mathrm{n}-1}}$, where ${\mathrm{N}}_{\mathrm{d}\mathrm{e}\mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}}$ is number of nodes linked with node k, while n is total number of nodes. ⁴ Eigenvector centrality of node k can be calculated as ${\mathrm{E}\mathrm{C}}_{\mathrm{k}}={\displaystyle \frac{1}{\mathsf{\lambda }}}\sum _{\mathrm{j}=1}^{\mathrm{n}} {\mathrm{A}}_{\mathrm{k}\mathrm{j}}{\mathrm{E}\mathrm{C}}_{\mathrm{j}}$, where $\mathsf{\lambda }$ is eigenvalue, ${\mathrm{A}}_{\mathrm{k}\mathrm{j}}$ is adjacency matrix, ${\mathrm{E}\mathrm{C}}_{\mathrm{j}}$ is eigenvector centrality of node j. ⁵ Land use mix can be calculated as an entropy index: ${\displaystyle \frac{-\sum _{\mathrm{i}=1}^{\mathrm{m}} \left({\mathrm{q}}_{\mathrm{i}}\right)\mathrm{l}\mathrm{n}\left({\mathrm{q}}_{\mathrm{i}}\right)}{\mathrm{l}\mathrm{n}\left(\mathrm{m}\right)}}$, where m is the total land categories and ${\mathrm{q}}_{\mathrm{i}}$ denotes the ratio of each type $\mathrm{i}$. ⁶ Emp-pop balance is calculated as ${\displaystyle \frac{1-\left(\right|\mathrm{E}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{o}\mathrm{y}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}-\mathrm{m}\ast \mathrm{P}\mathrm{o}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\left|\right)}{(\mathrm{E}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{o}\mathrm{y}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}+\mathrm{m}\ast \mathrm{P}\mathrm{o}\mathrm{p}\mathrm{u}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n})}}$, where m is the ratio of employment population to residential population.

This study explores spatial heterogeneity from the perspective of not only geographic location but also metro network topology. Network topology is measured by four network centralities, including betweenness centrality, closeness centrality, degree centrality and eigenvector centrality. The 19 metro lines and 325 metro stations are represented by 325 nodes and 376 edges in the network analysis (Figure 2).

In Figure 2, stations (nodes) are placed in four loops based on their degree of centrality (higher centrality in the inner circle). Meanwhile, node color and size are associated with the betweenness centrality (higher centrality in red, followed by orange, yellow and green) and closeness centrality (higher centrality as larger nodes), respectively.

Betweenness centrality is related to the number of shortest paths that involve the station, representing station importance in the metro network. Closeness centrality is related to distance or time to all the other stations, which can be used to evaluate the geometric position of the station in the network. Degree centrality is related to the number of linked stations, which can be used to distinguish terminal station and transfer station, with different passing lines. Eigenvector centrality is related to the number of linked nodes and their centrality, which can be used to estimate the importance of a region. The calculation formula of each centrality variable is introduced in the notes of Table 1, while the spatial distribution of the Shanghai metro system and station network centralities are shown in Figure 3.

Meanwhile, widely used “7Ds” models for the built environment are measured within a 500 m buffer of each metro station in this study. Population density is calculated from WorldPop data (https://www.worldpop.org/ (accessed on 15 July 2024)), while residential and employment density are calculated based on mobile signaling data. More specifically, the residential and employment population of each mobile signal base station are provided by the mobile service operator based on the location of users during working hours and overnight. Then, the residential and employment density of each metro station is calculated by dividing the residential and employment population at the nearest signal base station by signal coverage area. Land use mix, as well as the balance of employment to population are utilized to measure diversity. Road density, number of intersections, and built-up area are used to estimate the street design. Distance to city center, sub-center and nearest ring road are calculated to measure accessibility. Average housing prices and metro station entrances are also considered in the study.

Intermodal connection and built environment variables are measured in QGIS 3.34.1 (Figure 4), while network topology variables are calculated by modeling the Shanghai metro system in a network analysis Python package, NetworkX (https://networkx.org/ (accessed on 15 July 2024)). The descriptive and statistical information of variables are summarized in Table 1.

4. Methodology

This study combines the LightGBM algorithm with SHAP to explore the spatially varying effect mechanism of intermodal connection on metro ridership. LightGBM is a highly efficient GBDT implementation, which has been widely employed to investigate associations between land use and travel behavior [14]. LightGBM is suitable for this study because it can handle multicollinearity when the data dimensionality is high. Compared to traditional GBDT, LightGBM was proposed with two novel techniques, Gradient-based One-Side Sampling (GOSS) and Exclusive Feature Bundling (EFB) [58]. GBDT splits the tree based on the information gain, which is often measured by splitting variance:

$$V_{j\mid T}(p)={\displaystyle \frac{1}{n_T}}\left({\displaystyle \frac{{\left(\sum _{\left\{x_i\in T:x_{ij}\le p\right\}} g_i\right)}^2}{n_{l\mid T}^j\left(p\right)}}+{\displaystyle \frac{{\left(\sum _{\left\{x_i\in T:x_{ij}>p\right\}} g_i\right)}^2}{n_{r\mid T}^j\left(p\right)}}\right)$$

(1)

where $V_{j\mid T}\left(p\right)$ is the variance gain of splitting feature $j$ at point $p$ for training dataset $T$ on the node, $x_i$ is the data instance, $g_i$ is the negative gradients of the loss function, $n_T=\sum I\left[x_i\in T\right]$, $n_{l\mid T}^j\left(p\right)=\sum I\left[x_i\in T:x_{ij}\le p\right]$, $n_{r\mid T}^j\left(p\right)=\sum I\left[x_i\in T:x_{ij}>p\right]$.

With GOSS, LightGBM chooses a sample subset A by keeping the top a% instance with highest gradient, and randomly selects subset B from the remaining data. The estimated variance gain is calculated as follows:

$${\tilde{V}}_j\left(p\right)={\displaystyle \frac{1}{n}}\left({\displaystyle \frac{{\left({\sum }_{x_i\in A_l}{g}_i+\frac{1-a}{b}{\sum }_{x_i\in B_l}{g}_i\right)}^2}{n_l^j\left(p\right)}}+{\displaystyle \frac{{\left({\sum }_{x_i\in A_r}{g}_i+\frac{1-a}{b}{\sum }_{x_i\in B_r}{g}_i\right)}^2}{n_r^j\left(p\right)}}\right)$$

(2)

where ${\tilde{V}}_j\left(p\right)$ is the estimated variance gain of the subset $A\cup B$, $A_l=\left\{x_i\in A:x_{ij}\le p\right\}$, $A_r=\left\{x_i\in A:x_{ij}>p\right\}$, $B_l=\left\{x_i\in B:x_{ij}\le p\right\}$, $B_r=\left\{x_i\in B\right.:x_{ij}>p\}$. Compared with GBDT, LightGBM uses an estimated ${\tilde{V}}_j\left(p\right)$ of a subset rather than the accurate $V_j\left(p\right)$ of all samples to split the tree. By combining GOSS with EFB, an effective method to bundle mutually exclusive features for feature reduction, LightGBM can significantly reduce the computation cost and retain accuracy [58].

SHAP was proposed as a game theoretic approach for machine learning model interpretation [59]. Shapley value is calculated and utilized as the feature attribution [60]:

$${\varphi }_q(f,x)=\sum _{e^{\prime }\subseteq x^{\prime }} {\displaystyle \frac{\left|e^{\prime }\right|!\left(Q-\left|e^{\prime }\right|-1\right)!}{Q!}}\left[f_x\left(e^{\prime }\right)-f_x\left(e^{\prime }/Q\right)\right]$$

(3)

where ${\varphi }_q(f,x)$ is the Shapley value of feature $q$ in model $f\left(x\right)$, $Q$ denotes number of features, $\left|e^{\prime }\right|$ refers number of nonzero elements, while $e^{\prime }\subseteq x^{\prime }$ includes each $e^{\prime }$ which is a subset of $x^{\prime }$.

In this study, five-fold cross-validation was conducted in Python 3.11 to moderate the overfitting [61]. Grid search was employed to optimize the hyper-parameters, while number of boosted trees, boosting learning rate, maximum tree leaves and maximum tree depth was set as 8832, 0.001, 10 and 6, respectively. By minimizing root mean square error (RMSE), the Pseudo R-Squared of the final model is 0.91.

5. Results and Discussion

5.1. Global Effects of Determinants on Metro Ridership

Table 2. Importance and rankings of independent variables.

Variable and Category	Rankings	Relative Importance
Intermodal connection (Sum: 32.06%)
Bike sharing	3	6.69%
Parking facility	4	6.59%
Bus stop	8	4.97%
Bus route	7	4.85%
Nearest bus stop	16	3.42%
Pedestrian shed	6	5.54%
Network topology (Sum: 18.17%)
Betweenness centrality	1	9.30%
Closeness centrality	12	4.14%
Degree centrality	23	1.47%
Eigenvector centrality	17	3.27%
Built environment (Sum: 49.77%)
Population density	21	2.62%
Residential density	22	1.52%
Employment density	5	6.44%
Land use mix	2	6.73%
Emp-pop balance	20	2.63%
Street density	13	3.90%
Intersection	14	3.56%
Built-up area	19	2.78%
Dis. to city center	15	3.49%
Dis. to city sub-center	9	4.51%
Dis. to ring road	11	4.24%
House price	18	3.09%
Entrance	10	4.27%

shows the relative feature importance of each variable in predicting metro ridership, which sums up to 100%. The collective contribution of six intermodal connection variables on metro ridership is 32.06%, while it is 18.17% for four network topology variables and 49.77% for thirteen built environment variables.

Among six intermodal connection variables, five of them rank in the top eight in terms of relative importance, including bike sharing (6.69%), parking facility (6.59%), pedestrian shed (5.54%), bus route (4.97%), and bus stop (4.85%). These factors show more than average (100%/23 = 4.34%) impacts on metro ridership, supporting the significant role of intermodal connection noted by existing studies in different contexts [9,13,24,31]. Distance to the nearest bus stop only contributes 3.42% in predicting metro ridership, which is unexpected in such a megacity with rapid population aging and a large number of older individuals.

In terms of network topology, the relative importance of betweenness centrality (9.30%) ranks first among all independent variables, while the other three centrality variables contribute 8.87% in total in relation to metro ridership. The important role of betweenness centrality indicates that station position in a metro network can significantly affect metro usage, which supports previous literature in Seoul [62], Shanghai [8] and Shenzhen [10].

In the built environment, land use mix ranks second among all variables, with a relative importance of 6.73%. The critical role of diversified land use on metro usage has also been explored in previous studies [12,24,31,33,35]. Other variables, including employment density (6.44%), distance from sub-CBD (4.51%) and station entrances (4.27%), also show nontrivial contribution to metro ridership.

5.2. Individual Effects of Determinants on Metro Ridership

Although we have estimated the global effects of the independent variables on metro ridership by generating relative feature importance, the effects of these variables for different metro stations are still vague. To investigate the individual effects of determinants on metro ridership, SHAP summary and heatmap plots are also depicted to investigate the effects of variables on metro usage by each station (Figure 5).

In the SHAP summary plot, SHAP values are presented by the x-axis, while feature value is shown by dot color. In the SHAP heatmap plot, SHAP values are presented in color, while the predicted ridership of each station is shown above the heatmap as $f\left(x\right)$ by centering with the average. Features in the summary plot are sorted by the average absolute value of SHAP value, while features in the heatmap plot are sorted by the maximum absolute SHAP value, which is labeled in the black bar plot on the right.

With regards to intermodal connection, it is noted that the feature values of bike sharing, parking facility, bus stop and bus route are positively related with their SHAP values, while pedestrian shed and nearest bus stop show negative associations (from SHAP summary plot). Therefore, more metro-integrated bike sharing trips, parking facilities and bus lines are associated with higher metro ridership (left part of the SHAP heatmap plot), which is consistent with previous studies [31,41,62,63,64]. However, the SHAP values of pedestrian shed, bus stop and nearest bus stop do not show a clear relationship with metro ridership, because of the small absolute value of their SHAP values (in light color). Betweenness centrality and closeness centrality also show substantial positive impacts on the model output, emphasizing the critical role of station centrality in affecting metro usage, as demonstrated in existing literature [8,10].

5.3. Spatially Varying Effects of Intermodal Connection on Metro Ridership

Previous studies have investigated the marginal effects of determinants on metro ridership by depicting partial dependence plots or accumulated local effect plots [14]. However, the visualization of these plots is from the global perspective, which cannot uncover the effect mechanism of the determinants for stations within different regions. To explore the spatially varying impacts of intermodal connection on metro usage, the local SHAP value is visualized with the geographic location of each metro station. Since the magnitude of the SHAP value is different for each variable, a customized threshold of SHAP value is chosen for each variable to better show spatial heterogeneity.

Figure 6 illustrates the impacts of bike sharing trips on metro ridership for different regions. The SHAP value of bikes seems to be negatively related to the distance from the city center. Most stations with high positive SHAP values are located within the inner ring, while others are located within the middle or outer rings as radial lines from the city center. Relatively narrow streets and high intersection density may cause severe traffic congestion within main city areas, which lower the travel utility of private vehicles and feeder buses. Other factors can also increase the bike sharing usage within the main city, such as high population and employment density [65], diversified land use [66] and improved bike lanes [67]. Meanwhile, the large number of metro-integrated bike sharing trips points to sufficient parking facilities for shared bikes and even private bikes, which may facilitate metro usage by expanding the catchment area of metro stations.

Negative SHAP values occur in suburban areas, which are far away from city center and even sub-centers. Although launching bike sharing services in this peripheral area is an effective method to attract bike sharing users [68], the provision and usage rate of shared bikes in these areas may not be as high as in the main city. Moreover, relatively low street density and light traffic may increase the attractiveness of other access modes such as ride-sourcing, taxi and bus. Encouragement towards metro usage seems to be more effective in these areas by increasing trip generation and attraction with higher land use density and diversity, rather than improving the metro ridership by providing more shared bicycles.

Figure 7 visualizes the effects of parking facilities on metro ridership for different stations. The complicated impacts of parking facilities on metro usage have been investigated in different contexts with controversial findings [9,12,31]. High positive SHAP values occur at stations within the inner ring, and most of them close to the city center or city sub-centers. Due to land scarcity and high-density development, separate public parking lots rarely exist within the inner ring area. Most parking facilities are the allocated garages provided with residential buildings, commercial buildings and shopping centers. Therefore, more parking facilities within the inner ring are associated with more residents, employees and customers, which can result in higher levels of metro trip generation. Working, industrial and commercial accessibility have also been found to increase the metro usage by other studies [8,18,69]. Many stations between the inner and middle rings show negative SHAP values, suggesting a negative effect of parking facilities on metro ridership in this region. It is also noted that most of these stations are located close to the ring roads. Since the street density of the inner-middle area is much smaller than the inner ring area, the easy access to viaducts and existence of more parking facilities may increase the proportion of driving trips, which leads to a decrease in metro usage.

In terms of bus services, the SHAP values of bus stop, bus line and nearest bus stop are summed up to examine the spatial heterogeneity in Figure 8. Station-level bus services have been found to have positive nonlinear [13,24] and threshold effects [9,10,12] on metro ridership from the global perspective. In this study, most positive SHAP value stations are either located within the inner ring or near to a city sub-center, and some terminal stations also have large positive SHAP values. The existence of bus lanes within the inner ring or sub-center area can significantly reduce the travel time of feeder buses during peak hour, and thus increase the travel utility of bus-metro integration. To have enough spaces for metro vehicle parking, reversing and maintenance, terminal stations are usually constructed with metro depots and thus located in suburbs outside the outer ring. According to the vehicle restriction policy in Shanghai, vehicles without certain vehicle license plates are not allowed to drive into the outer ring area during peak hour on weekdays. Under these circumstances, bus-metro integration becomes a cheap and convenient commuting mode for people who live in the suburbs but work in the main city. Since working and education trips are the leading contributors towards metro usage [8,69], a high level of feeder bus services near terminal stations can encourage metro usage by extending the catchment area and attracting more commuting trips. Most stations with high negative SHAP values of bus services are located alongside the ring roads, which are elevated, like the viaducts. Since the streets near ring road entrances are usually congested, and buses are not allowed to drive on the viaducts in Shanghai, the efficacy of feeder buses may not compare to biking and walking in these regions.

The magnitude of pedestrian SHAP values is smaller than other intermodal connections, which is associated with less impacts on metro ridership (Figure 9). Stations with high positive SHAP values of pedestrian catchment area are either located at the city periphery or alongside the main corridors (line 1, 2 and 9) from periphery to main city, and negative SHAP values occur within the inner ring. As shown in the SHAP summary plot, pedestrian catchment area is negatively associated with the SHAP value. Peripheral areas usually have broader streets, leading to inconvenience for crossing pedestrians, which can be moderated by overbridges or underground street crossings [13]. The small block size and good connectivity of sidewalks within the inner ring can result in a large pedestrian catchment area, while the short distance between metro stations within the inner ring makes it less effective in attracting more metro usage. Meanwhile, the excessive spread of walking segments can reduce space for auto vehicles and bicycles, which may lower the number of metro riders coming by other access modes. Pedestrian services, such as narrow sidewalks and pedestrian-unfriendly environments may weaken the efficacy of walking access [26,70].

Figure 10 visualizes the impact of all intermodal connection variables on metro ridership for different stations. Overall, there are large positive SHAP values located within the main city, especially the west side of the Huangpu River, while high negative SHAP values occur in the suburbs. The intermodal connection also shows high positive SHAP values at stations alongside the main commuting corridors (metro line 1, 2 and 9), which are the radial lines from the central activity zone to southern or southwest suburbs. Previous studies suggested that residential areas are much more scattered than working areas in megacities [31,71]. In Shanghai, many people who work in the main city choose to live in the peripheral area to avoid expensive rent and housing prices. Although the proportion of non-home-based trips have become remarkable in megacities [72], providing sufficient intermodal connection facilities for them may encourage commuter metro usage within these regions.

5.4. Comparison of the Effect Mechanism between Different Stations

This study further explores the differences of the effect mechanism between metro stations in different regions. To get comparable results, six metro stations with similar ridership but different geographic locations are selected to compare the effect mechanism of determinants on metro ridership (Figure 11).

SHAP waterfall plots and decision plots are derived to illustrate the effect of each variable for each station. SHAP waterfall plots are utilized to show explanations for predicted metro ridership of each station (Figure 12). Waterfall plots move from the expected ridership (at bottom) to the predicted ridership (at top) by displaying feature value (at left) and associated positive (red) or negative (blue) impact of each feature on the predicted ridership (at each row). For example, in Figure 12a, the bus line, parking and bike sharing near Dashijie Station increase the predicted metro ridership by 12,460, 10,284 and 6019, respectively, while pedestrian catchment area lowers the ridership by 10,642. The fourteen least influential variables have been aggregated into one row to control the figure size.

The SHAP decision plot also summarizes how selected metro stations get their predicted ridership in the model (Figure 13). The x-axis shows the model output, while the y-axis lists all variables (intermodal connection variables are stuck on top). Selected stations are displayed as lines with different colors, while six lines intersect the color bar at their associated predicted ridership. The contribution of each feature shows on each row, and all lines converge at the bottom, which is the average ridership from model output.

Table 3. Spatially varying effects of intermodal connection on metro ridership for six stations.

ID	Station	Location	Region	District	Direction	Ridership	Predicted Ridership	Bike	Bus	Parking	Pedestrian	Intermodal Connection
1	Dashijie	CBD	Within inner ring	Huangpu	Central	57,507	54,663	+ +	+ + +	+ + +	– – –	+ + +
2	Jiangwan Stadium	Sub-CBD	Between middle-outer ring	Yangpu	North	56,540	64,690	+ + +	+ + +	+ + +	–	+ + +
3	Songjiang Uni Town	New city	Outside outer ring	Songjiang	Southwest	57,311	53,478	–	+ +	/	+	+ +
4	Lancun Road	Main city	Within inner ring	Pudong	East	56,980	57,047	+ + +	+ + +	/	/	+ + +
5	Daduhe Road	Main city	Between inner-middle ring	Putuo	West	57,034	50,185	+ + +	/	/	/	+ + +
6	Luheng Road	Suburb	Outside outer ring	Minhang	South	53,880	44,590	– –	+	/	+	+

Notes: + + + and – – – : |SHAP value| > 10,000; + + and – – : 5000 < |SHAP value| < 10,000; + and – : 2500 < |SHAP value| < 5000; /: |SHAP value| < 2500.

summarizes the effects of intermodal connection on predicted metro ridership, and spatially varying effects of intermodal connection can be noticed from the results. The bike sharing shows positive effects on metro ridership for four stations within the outer ring, and negative effects for two stations outside the outer ring. In terms of the bus service, all selected stations show positive impacts on ridership in general, but significant positive impacts only occur for stations located within the inner ring or near the city sub-center. Parking facilities at two stations, which are located at the city center or city sub-center, have notable positive effects on metro ridership, while parking facilities at the other four stations only have trivial effects. The effects of pedestrian catchment area seem to have obvious spatial variation. Two stations outside the outer ring show negative effects, while two stations at the city center or sub-center have positive impacts, and the other two stations only have negligible effects.

As shown in the decision plot (Figure 13), the total effects of intermodal connection are more significant than the built environment and network centrality for all six stations. Specifically, the total effects of intermodal connection at Songjiang Uni Town (#3) and Luheng Road (#5) are relatively small, which is shown from the horizontal dash line to the color bar. These two stations are located at the city periphery, which is also outside the outer ring. The intermodal connection of the other four stations in the main city are significant, increasing the predicted metro ridership by about 15,000 to 25,000.

6. Conclusions

This study combined LightGBM with SHAP to explore the spatially varying effect mechanism of intermodal connection on metro ridership in Shanghai, with the considerations of built environment and network topology. The contributions of this study are from three aspects, and empirical results can inform policymakers’ intermodal connection interventions in planning practice.

First, this study explicitly investigates feature importance and impacts of intermodal connection on metro usage from the global perspective. Six intermodal connection variables collectively account for 32.06% of the predictive power, emphasizing the critical role of intermodal connection in affecting metro usage. It is suggested that high values of bike sharing, parking facility, bus stop and bus route are positively related with their SHAP values, while pedestrian catchment area and nearest bus stop show negative associations. These findings help policymakers understand the general relationship between first/last-mile services and metro usage, while ignoring spatial heterogeneity.

Second, the study analyzes the local effects of intermodal connection variables at different stations to explore the spatial heterogeneity by visualizing their SHAP values. Overall, the impacts of intermodal connection on metro ridership are positive within the main city, and negative in the peripheral area. Positive effects also occur at stations alongside the main corridor between the city center and residential suburbs. Specifically, the impacts of bike sharing trips on metro usage are associated with distance from the city center, showing positive effects within the inner ring and negative effects in the suburbs. Bus services can increase metro usage for stations within the inner ring, stations at the city sub-center and terminal stations. However, bus services have negative impacts at stations alongside the ring road because of the inconvenience of bus operation in these areas. Parking facilities can increase the metro usage within the inner ring or stations near the city sub-center. However, parking facilities between the inner and middle ring may lower the ridership by increasing auto-based trips. Pedestrian catchment area shows complicated associations with metro ridership, which may increase metro usage by increasing walkability in the suburbs, while decreasing the amount of metro riders using other access modes in high density areas. Policymakers and urban planners should consider differentiated intermodal connection interventions for stations in different regions to promote metro usage.

Third, six stations are selected to investigate the spatially varying effect mechanism of intermodal connection on metro ridership, which have similar daily ridership but are in different regions, with different geographic locations, directions and districts. Overall, the positive effects of intermodal connection on metro ridership are significant for four stations within the main city, but relatively small for two stations in the city periphery. Specifically, bike sharing shows positive effects for four stations within the outer ring, and negative effects for two stations outside the outer ring. Bus services show positive impacts for all selected stations, and the effects are significant only for stations within the inner ring or near the city sub-center. Parking facilities have significant positive impacts at stations near the city center or sub-center, but trivial effects at other stations. The spatially varying effects of pedestrian catchment area are also obvious, in that two stations at the city center or sub-center show positive impacts, two stations outside the outer ring show negative effects, and other two stations have negligible effects. The comparison between these stations helps policymakers understand the effect mechanism of spatial heterogeneity of intermodal connection on metro ridership in Shanghai, which may also guide optimization strategies of first/last-mile services in other megacities.

This study also has some limitations, which could be further investigated in several aspects. First, although six commonly used intermodal connection variables are considered in the research design, the impacts of other intermodal connection such as private bike/e-bike, taxi and ride-sourcing need further exploration, if data is available. With a higher number of independent variables, it would also be interesting for further studies to employ principal component analysis to reduce the dimensionality of the data. Meanwhile, the spatially varying effect mechanism of intermodal connection on metro ridership has been assessed in this study with cross-sectional data, while temporal or spatiotemporal effects can be investigated with longitudinal and panel data. Moreover, the demarcation of transportation analysis zones (TAZs) can significantly impact research outcomes, so further studies with different TAZs are welcomed. Finally, because of the unique hierarchical polycentric urban-rural structure, multilevel ring roads and extensive metro network in Shanghai, the validity and generalizability of these empirical findings are encouraged to be further explored in different contexts.