1.1.1 Classification of urban rail rapid transit stations.

Selecting appropriate station classification indicators is key to the classification of rail transit stations. Existing research can be divided into single-indicator and multi-indicator classification approaches. The single-indicator classification includes:

1. (1). Classification of station characteristic indicators: Wu Jiaorong (2007) categorized subway stations into distinct functional types based on their varying transfer facilities [9].
2. (2). Land use index classification: In the United States, the Center for Transit-Oriented Development (2010) classified stations into 15 types by considering factors such as the number of jobs around the stations, the annual total mileage of households in the traffic area, and whether the surrounding areas were residential, employment-focused, or mixed-use [10].
3. (3). Passenger flow index classification: Meekyung (2018) grouped 233 subway stations in Seoul into eight categories using data on subway card swipes, passenger flow at different times, and fluctuations in passenger flow curves [11]. Similarly, Li et al. classified stations into six categories based on passenger traffic characteristics such as the number of peaks and troughs and the skewness in flow fluctuations [12].

In recent years, more researchers have combined multiple indicators to classify stations. For instance, Higgins. et alused data from 372 rail transit stations in Toronto, Canada, to extract land use and passenger flow characteristics, classifying them into ten categories [13]. Kim et al. combined passenger flow and land use data to classify Seoul’s stations [14]. Similarly, Pang Lei et al. classified Tianjin’s rail transit stations into three categories—residential, employment, and mixed-use—by combining built environment, station attributes, and network characteristics [15]. Chen L. et al.used station characteristics and nearby building functions to categorize 30 stations in Xi’an into six types [16].

1.1.2 Study on the influence mechanism of passenger flow.

Regression analysis is a common method to determine how different indicators affect passenger flow at rail stations. Traditional models such as Ordinary Least Squares (OLS) have been widely used. For example, Loo et al. used the OLS model to analyze rail transit stations in Hong Kong and New York, concluding that various indicators within the service areas significantly impacted station passenger flow [17]. An et al. employed Ordinary Least Squares (OLS) regression analysis and found that commercial land use, bus stations, and tourist attractions have significant positive impacts on Shanghai’s rail transit passenger flow, independent of weekdays [18]. However, with the deepening of research, some scholars argue that the OLS method lacks consideration of spatial spillover effects. The Geographically Weighted Regression (GWR) model addresses this by visualizing how independent variables affect dependent variables across different spatial locations. For instance, Qian et al. found that the GWR model offered better explanatory power when studying the dynamic demand for cabs in New York City [19].

The GWR model, however, assumes that all independent variables affect the dependent variable at the same spatial scale, ignoring spatial heterogeneity. To address this limitation, researchers introduced the MGWR model. Jun et al.applied the MGWR model to Seoul’s rail stations, finding that it effectively accounted for both global and local variables [20]. Zahratu et al. highlighted that the MGWR model allows each independent variable to have a specific bandwidth, reflecting the differentiated scales of influence [21]. Tak et al. used the MGWR model to analyze passenger flow in Beijing’s rail stations, concluding that it provided more reliable estimates compared to the classical OLS and GWR models [22].

In summary, while considerable progress has been made in classifying rail transit stations and understanding passenger flow mechanisms, further improvements are necessary. First, much of the existing research focuses on plain areas, overlooking the unique geographic conditions of mountainous cities. Additionally, many studies fail to consider differences in the factors affecting passenger flow across various types of stations. Therefore, it is critical to develop a reasonable classification system for rail stations and examine the passenger flow mechanisms of different station types, considering the spatial and geographic characteristics of mountainous cities, to enhance the rail transit share in such areas.

2.1.1 Selection of station classification indicators.

Based on station functionality, service capacity, and environmental impacts of surrounding areas, and considering data accessibility, quantifiability, and comprehensiveness, we propose four categorized indicators as classification criteria.Development intensity indicator--reflecting urbanization levels and economic activity density in station-adjacent areas;Transfer convenience--indicating accessibility to other zones and the station’s functional role within the transportation network;Walking accessibility--measuring passenger convenience in reaching stations;Passenger flow--capturing distinct temporal characteristics of ridership during morning/evening peak periods.

1. (1). Development intensity indicator. POI data contain spatial information of the urban fabric, including attributes such as names, category classifications, and geographical coordinates (latitude and longitude). These data can effectively reveal the density and distribution of developments around these stations. The types of facilities and service functions within a 500-meter radius around the stations significantly influence the attractiveness and vitality of the transit stations [26]. This study employs Gaode Map to obtain POI data within a 500-meter radius around rail transit stations in nine districts of Chongqing, namely Yuzhong, Shapingba, Jiangbei, Yubei, Nan’an, Jiulongpo, Dadukou, Banan, and Beibei. Based on the “Urban Land Use Classification and Planning and Construction Land Use Standards,” a total of 298,035 POIs were extracted from the core station area [27]. This includes 138,887 POIs for commercial land use, 72,878 for residential land use, 40,215 for public administration and services, and 23,766 for transportation purposes.
2. (2). Transfer convenience indicator. The number of bus lines within 500 meters of the station is calculated based on Gaode POI data to measure the ease of transferring between buses and rail transit [28]. Additionally, the number of parking lots is used to reflect the convenience of Park + Ride (P + R) modes. A total of 3,585 bus lines and 3,316 parking lots around the stations are extracted.
3. (3). Walking accessibility indicators [29]. The 500-meter radius around rail transit stations is generally regarded as the core area for pedestrian accessibility. Within this range, residents and passengers can conveniently reach the stations on foot without relying on other transportation modes. The characteristics of roads and buildings within this range directly influence the walking experience and travel efficiency of passengers, making it a focal area for research. Using Open Street Map data, walking accessibility is measured by the length of the road network within a 500-meter radius around the station area. The degree of zigzagging and elevation differences in the terrain are reflected by the road growth coefficient and average longitudinal slope, as shown in equations (1 and 2). A total of 3,842 road segments were extracted, allowing the calculation of road length, growth coefficient, and average slope.

(1)

Where:

I is the average longitudinal slope, H is the station elevation, H_o is the passenger departure point’s elevation within 500m, and L_t is the length of the passenger trip within 500m.

(2)

Where:

C_r is the road growth factor, L_r is the length of the passenger walk within 500m, and L_s is the straight-line distance from the start to the end of the passenger walk.

1. (4). Station Passenger Flow Indicator: The station passenger flow data from the urban rail transit automatic fare collection system in 2021. The morning and evening peak inbound and outbound passenger flow of each station is selected to reflect the passenger flow changes of passengers in different periods [30]. The station passenger flow indicators are derived from the AFC data in 2021.

Thirteen indicators were selected to classify stations based on four categories of factors. To reduce inconsistencies in scale between different indicators, data were standardized using the Z-score method. The Z-score method standardizes data by subtracting the mean of each variable and dividing by its standard deviation. This process ensures that all variables have a mean of 0 and a standard deviation of 1, thus eliminating the influence of scale differences (as shown in Table 1).

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Table 1. Indicators for station classification.

https://doi.org/10.1371/journal.pone.0323937.t001

2.1.2 Determination of the number of clusters.

Before conducting cluster analysis, it is necessary to determine the appropriate number of clusters. This study applies the “elbow method” to determine the optimal number of clusters by analyzing the sum of squares of errors (SSE) for various cluster sizes and identifying the elbow point where the marginal improvement in SSE diminishes (i.e., the inflection point). The optimal number of clusters is identified by observing the largest reduction in SSE, corresponding to the inflection point. The basic principle behind the “elbow rule” is that as the number of clusters (k) increases, the clustering becomes more granular, and the cohesion within each cluster improves, causing the SSE to decrease. However, after a certain point, further increases in k result in diminishing improvements in cohesion, causing the SSE reduction to slow. This produces an “elbow” shape on a graph plotting SSE against k, and the k-value corresponding to this elbow is considered the optimal number of clusters. The SSE is calculated using the following formula:

(3)

where:

K is the current number of clusters; C_i is the ith subset in the clustering; p is the sample points within the subset; and m_i is the average of all sample points within the subset.

2.2.1 Selection of indicators for passenger flow impact mechanisms.

1. (1). Station functional attributes

The operational and geographical attributes of urban rail transit stations influence passenger flow [31]. Based on passenger flow statistics, this study designates stations with particularly high passenger volumes at transfer points as large transfer stations. The geographical location of the station is used to determine whether it serves as an external transportation hub and whether it is in proximity to a large commercial area. These three indicators are collectively referred to as the station functional attributes indicators of the station.

1. (2). Built environment

In addition to the previously mentioned indicators, the land use mix index was also considered, reflecting the diversity of land use types in the station area [32].

(4)

Where:

H_(X) is the land use mix index at station X; P_i is the percentage of the number of types i POIs at station X to the total number of POIs at that station.

This paper analyzes two dimensions: the built environment and the station’s attributes. Among them, three indicators, whether the station is an interchange station, whether it is an external transportation hub, and whether it is adjacent to a large business district, are discrete, while the rest are continuous variables. Table 2 presents an overview of these potential influences. The characteristics of the station itself were obtained through observation and the compilation of web resources, while the built environment was based on categorical data with the addition of a land use mixing rate, as shown in Table 2.

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Table 2. Factors affecting passenger flow.

https://doi.org/10.1371/journal.pone.0323937.t002

2.2.2 Selection of key variables.

Only if there is no strict collinearity between the independent variables can the model analysis be conducted. The collinearity test is represented by the variance inflation factor (VIF). The greater the VIF, the higher the collinearity probability between the independent variable and other variables.VIF within 10 indicates that there is no serious collinearity [33].

The VIF of the jth independent variable is:

(5)

Where:

VIF_j is the variance inflation factor of the jth independent variable; R_j² is the determination coefficient of the jth independent variable as the dependent variable, and the other independent variables are used as linear regression.

There may be spatial dependence between neighboring stations, and this influence cannot be explained by OLS regression, so it is necessary to test the spatial correlation between stations. In this study, Moran’s I was selected as the test index, and the spatial projection coordinates and influencing factors of each station were imported into Arc GIS for the spatial autocorrelation test [34]. Prior to the calculation of the Moran’s I index, the concept of a spatial weights matrix must be introduced. This matrix reflects the spatial proximity between multiple locations by representing the relationships among different spatial units. In the context of the Moran’s I index, the spatial weights matrix is often constructed using Euclidean distance as the basis for assigning weights. The product of the weight matrix γ and the explanatory variable indicators, as shown in Equation (10), reflects the degree of similarity between spatial units. Euclidean distance, which measures the straight-line distance between two points, provides an accurate representation of the actual distance between them in geographical space and thus serves as a valid basis for assigning weights.

The calculation formula of Moran’I is as follows:

(6)

(7)

Where:

m’ is the total number of rail transit stations;γ_ij is the weight between stations; e_i and e_j are represented as independent variable indicators for the i and j stations; is the mean value of station- independent variable indicator e; S² is the variance of the station-independent variable index e; d_ij is the Euclidean distance between stations i and station j; b is the bandwidth, which refers to the non-negative decay parameter of a weighted remote function.

When the sample space distribution is relatively uniform, equal bandwidth is often used, and the opposite is used.The value of Moran’I is usually [-1, 1]. Under certain significance tests, the Moran index is 0. That is, there is no spatial autocorrelation. A value greater than 0 indicates that the variable has agglomeration, while a value less than 0 indicates that the variable has dispersion (spatial negative correlation) [35]. Generally, normalized statistical Z-value is used to conduct a significance test, and its expression is as follows:

(8)

Where:

E (Moran’I) is the theoretical mathematical expectation of the Moran’I; is the theoretical variance.

The reliability of Moran’I can be evaluated by the Z-value and P-value of significance. If the significance P value is less than 0.05 (through a 95% confidence test) the absolute value of the Z score exceeds the critical value of 1.96, indicating that the results of Moran’I are credible, and more than 95% of the certainty is that the data are spatially correlated. When the value of Moran’I is greater than 0, the spatial correlation is positive; when the value of Moran’I is less than 0, the correlation is negative [36].

2.2.3 Passenger flow impact regression modeling.

The OLS, GWR, and MGWR models are commonly used to handle continuous dependent variables. When analyzing the factors influencing station passenger flow in regression models, passenger flow data can be treated as a continuous variable.In the regression models, the dependent variables include the total daily passenger flow, morning peak inbound passenger flow, morning peak outbound passenger flow, evening peak-hour inbound passenger flow, and evening peak outbound passenger flow. The independent variables are the station functional attributes and built environment indicators introduced in the previous section.

1. (1). OLS Regression Model [37]

(9)

Where:

X₁, X₂,..., X_n are the independent variables; α₀ is the intercept term of the OLS model, α₁, α₂,..., α_n are the regression coefficients for the nth independent variable; Y is the dependent variable; and ε is the residual, which follows a normal distribution with a mean of zero.

1. (2). GWR regression model [38]

(10)

Where:

(U_i, V_i) is the coordinates of station i; Y_i is the dependent variable at location i; β_{0 (Ui, Vi)} is the intercept of station i; β_{j (Ui,Vi)} is the regression coefficient of the jth independent variable at (U_i,V_i); and ε_i is the residuals of station model i.

1. (3). MGWR regression model [39]

(11)

Where:

β_{0 (Ui,Vi)} is the intercept for the station i; ε_l is the lth global indicator for the station; β_l is the regression coefficient for the global indicators, which are the first k indicators; and β_{l (Ui,Vi)} is the regression coefficient for the local indicators, i.e., the k + 1 to n’ indicators, which vary with each station.

3.2.1 Results of key variables selection.

The covariance test results and spatial autocorrelation of the factors influencing the passenger flow characteristics of Chongqing rail transit stations are shown in the Table 3.

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Table 3. Factors affecting passenger flow.

https://doi.org/10.1371/journal.pone.0323937.t003

The data show that the VIF values of the 13 indicators studied are all below 10, which means that there is no serious multicollinearity among these indicators and they have good validity. The Moran’I of the 13 indicators of the influencing factors are all positive. The Z-values of the 12 indicators are above 1.96, achieving the level of significance, which meets the conditions for establishing a regression model.

3.2.2 Comparison of regression models.

The independent variables are regarded as global indicators in the OLS, while they are regarded as local indicators in the GWR, and the MGWR is a comprehensive model that integrates the global and local characteristics of the two models of OLS and GWR [42,43]. In this paper, we intend to take Chongqing metro stations as the research object, choose the same independent explanatory variables, and establish three methods of OLS, GWR, and MGWR to regress and analyze the passenger flow characteristics respectively.

The smaller the value of RSS, AIC, and AICc indicators, the larger the value of R² and adjusted R², the better the model fitting effect is [44]. As can be obtained from Table 4, the results of the three types of regression models show that: RSS, AIC, and AICc index values MGWR < GWR < OLS, R² and corrected R² values are MGWR> GWR > OLS, indicating that the MGWR and GWR models considering spatial correlation have a better fitting effect. Taking the AICc index as the bandwidth optimization criterion, it is found that the AICc index value of the MGWR model regression is significantly smaller than that of the GWR model in different periods, which indicates that the MGWR model realizes further optimization based on the GWR model.

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Table 4. Comparative analysis of passenger flow regression models.

https://doi.org/10.1371/journal.pone.0323937.t004

3.2.3 Influence mechanisms of passenger flow characteristics at stations based on MGWR.

To investigate the heterogeneous effects of mountain track characteristics, interchange convenience, and pedestrian accessibility on the passenger flow of different types of stations, based on the results of station classification, the MGWR model is used to study the influence mechanisms of all-day weekday passenger flow, morning peak inbound passenger flow, morning peak inbound and outbound passenger flow, evening peak inbound passenger flow and evening peak outbound passenger flow of different types of stations, respectively [45]. Take the employment class mountain type as an example, as shown in Table 5:

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Table 5. MGWR model regression results of passenger flow characteristics for employment type hill type stations.

https://doi.org/10.1371/journal.pone.0323937.t005

Table 5 shows that: (1) the coefficients of influence on the positive effect on the all-day passenger flow in the employment category of mountain-type stations are, in descending order, neighboring business districts (0.857)> commercial POIs (0.685)> parking lots (0.362)> public administration POIs (0.269)> traffic and transportation POIs (0.24)> external transportation hubs (0.121). It indicates that the commercial land use of this type of station and the neighboring business districts attract a large number of passengers and employment; (2) the coefficients of influence on the negative effect of all-day passenger flow are, in descending order, road growth coefficients (-0.613)>residential POIs (-0.429)>transit routes (-0.33)>mixed rate of land use (-0.281)>average longitudinal slopes of roadways (-0.181)>roadway network length (-0.1)> interchange (-0.033). The road growth coefficient has the largest negative impact, indicating that passengers at these stations are very sensitive to the length of the walk near rail stations, and has the second largest impact on residential POI, with the opposite travel behavior characteristics of the residential and employment class of stations having a large negative impact on employment hill traffic.