Revealing the Influence of the Fine-Scale Built Environment on Urban Rail Ridership with a Semiparametric GWPR Model

Abstract

There is a causal interaction between urban rail passenger flow and the station-built environment. Analyzing the implicit relationship can help clarify rail transit operations or improve the land use planning of the station. However, to characterize the built environment around the station area, existing literature generally adopts classification factors in broad categories with strong subjectivity, and the research results are often shown to have case-specific applicability. Taking 154 stations on 8 rail transit lines in Xi’an, China, as an example, this paper uses the data sources of multiple open platforms, such as web map spatial data, mobile phone data, and price data on house purchasing and renting, then combines urban land classification in the China Urban Land Classification and Planning and Construction La1d Standard to classify the land use in the station area using structural hierarchy. On the basis of extracting fine-grained factors of the built environment, a semi-parametric Geographically Weighted Poisson Regression (sGWPR) model is used to analyze the correlation and influence between the variation of passenger flow and environmental factors. The results show that the area of Class II residential land (called R2) is the basis for generating passenger flow demand during morning and evening peak periods; The connection intensity between rail transit station area and bus services has a significant impact on commuters’ utilization level of urban rail transit. Furthermore, two scenarios in practical applications will be provided as guidance according to the research results. This study provides a general analytical framework using urban multi-source data to study the internal relationship and impact between the built environment of urban rail transit stations and passenger flow demand.

1. Introduction

The regular heavy passenger flow of urban rail transit is a current and pressing issue faced by many densely populated cities in China. Although future operational passenger flows were assessed during the planning and design stages of rail transit lines, large deviations still exist in some lines and stations between the assessed threshold values and actual passenger volumes. The fluctuation between actual and pre-evaluated passenger volumes on a certain rail transit line (or station) is primarily attributed to the objective factor of the built environment, which is a core determinant. First, the dynamic changes in the built environment around stations are difficult to grasp upfront, even with reference to overarching urban planning as superior transportation planning. For rail transit lines, guidance from the recent 5-year plan at the urban and regional level is limited. Second, there is a lack of research that correlates increases or decreases in urban rail traffic with land use changes. The uneven level of land development along rail transit lines traversing different urban areas will result in varying passenger demands and the spatiotemporal dynamic characteristics of each station, presenting spatial heterogeneity. The above shows that the designers of rail lines cannot simply borrow some planning concepts or surveys without local characteristics to guide the empirical work. To this end, this study will develop a technical framework for analyzing the built environment of urban rail transit station catchments and how it affects passenger flow generation and spatiotemporal distribution characteristics.

In recent years, research on analyzing the relationship between the built environment of urban rail transit station catchments and their passenger flows has been conducted. The determination that drives the progress of studies at home and abroad is the accurate description and definition of the built environment and passenger flow in the station catchment. Firstly, in addition to the physical environment, the built environment also includes the activities of passengers who travel in this context. The built environment and the station are inseparable and constitute a complete system. In general, researchers have categorized built environments into several typical sets of factors, with land use following the conventional classification of residential, commercial, work, and public service areas. It is obvious that urban point-of-interest (POI) data provides an opportunity to capture land use factors. The introduction of POIs for diversity is effective; however, it is unreasonable to accurately characterize station land use. This approximate statistical classification based on POIs does not reflect the size of their land area, which is a key determinant of the generation of actual travel at stations. According to the classification of urban construction land in China’s urban land classification and planning construction land standard [1], urban land is divided into 8 major categories, 35 sub-categories, and 43 minor categories. The land use of the built environment at rail transit stations is derived from the classification in “standard”. In this paper, the subdivision of the built environment at the station level is realized for the first time according to the classification and definition of sub-categories in “standard”, and each land category is measured in terms of area. Thus, this study is not limited to local surveys or POIs sampling and is based on a “fine-grained” method to divide land use in the station-built environment. Secondly, the definition of station traffic demand in most literature focuses on the passenger flows over a certain period of time (the shortest period is daily), with statistics such as monthly station traffic, average weekly traffic, average weekday and weekend traffic, etc. Since these studies do not involve the relationship between the built environment and hourly flow fluctuations within the station, this vulnerability will be a continuing concern for researchers.

In short, this paper describes the built environment factors for the station catchment using the fine-grained land use classification. Meanwhile, indicators such as detailed economic demographics, transportation connections, and station characteristics are combined to construct a semi-parametric Geographically Weighted Poisson Regression (sGWPR) model to explore the influence of the built environment on the daily travel demand over time at urban rail transit stations. The remainder of the paper is organized as follows. Section 2 reviews the literature on the construction of impact factors and the development of analytical methods evolution. Section 3 describes the study area, the data sources, and the processing of the available data. The methodology employed is introduced in Section 4. Section 5 presents the model results and discussion, and Section 6 guides the practical scenario application of the research results. Conclusions are presented in Section 7.

2. Literature Review

Different from fares, train departure interval, train punctuality rate, and ride comfort et al, the external factors that researchers have paid attention to in the station-built environment affect passenger flow in urban rail transit systems and devoted themselves to analyzing the interaction between them. The built-environment factor sets constructed to characterize rail stations, which consist of four major categories including economic demographics, land-use category, transport connection facilities, and station attributes, are generally considered by scholars. The differential selection of variables in factor sets is reflected in different literature. When determining the population and employment density variables of the station catchment, Wang [2] took the statistical values of these two indicators from the administrative district where the station is located. Although this was regarded as an approximate sampling method, it was somewhat inappropriate. On the one hand, the area of the station catchment is far smaller than the size of the administrative district; on the other hand, the employment or population concentrated in the station catchment area may be slightly higher than the corresponding statistical average for that administrative district. When determining the land classification, Zhu et al. [3] considered only residential, office, and entertainment to characterize the land use function of the station catchment. The simple classification may not fully represent the diversity of actual station land use, and given this premise, the depth of the relationship between land use and travel is also insufficient. Sohn and Shim [4]. take employment, commercial, and office as three variables to characterize the station’s land use. To better explore more variables to study the relationship between the built environment and passenger flow, urban point-of-interest (POI) data has been used in some literature. Ma et al. [5] expanded the description of land use by sampling POIs, such as obtaining hotel density, residential building density, and service facility density. However, this method of only counting the number of facilities with different functions cannot directly obtain the area of various types of land use. Due to the limited scale of available data, much of the literature reviewed shares a common feature of less-than-ideal factor sets for constructing the built environment.

With the increasing application of big data technology in urban planning and transportation, the amount and variety of data that can be collected are growing exponentially, thus opening up new research opportunities. In two publications by Li et al. [6,7] in 2020, although there were slight differences in methods, both of them achieved a detailed description of the built environment in the central area of Guangzhou, China, by integrating multi-source geospatial big data. Based on this, they analyzed the changes in rail transit passenger flow and its relationship with external built environmental factors. However, there are still some shortcomings in their research. On the one hand, the transport connection facilities of the station are inadequately considered, with only rough statistics of road network density and public transportation routes. On the other hand, when the amount and diversity of available data reach a certain scale, it becomes necessary to consider the hierarchy of indicators. The cases presented in the literature are all practical applications of the research, and it is clearly unreasonable to extract widely varying indicators for different cities. The hierarchical structure of urban construction land classification is provided in the China Urban Land Classification and Planning and Construction Land Standard, which is divided into 8 major categories, 35 sub-categories, and 43 minor categories. The definition of each type of urban land use is derived from the standard. Given the scope of the station catchment, the study selects 35 sub-categories of indicators based on standard specifications to achieve a fine-scale description of land use. Given the scope of the station catchment, the study selects 35 sub-categories of indicators based on standard specifications to achieve a fine-scale description of land use and combines the means of big data collection to characterize the universal indicators of the built environment (e.g., using smartphone data to extract the residential and employment population within the station catchment), thus providing support for obtaining more fine-scale research results in the case study.

In addition to the characterization and collection of the built environment, scholars have been committed to exploring methods for analyzing the relationship between the built environment of the station catchment and passenger flow. Traditional econometric models, such as Ordinary Least Squares regression [8] and Backward Stepwise regression [9], have been used to model the factors that influence station passenger flow due to their advantages of concise form and easy-to-interpret results. However, the premise assumption of these models is the independence of passenger flow between stations, making it impossible to deal with potential spatial effects associated with a geographic location in the data. Subsequently, spatial econometric models with the Spatial Lag Model (SLM), Spatial Error Model (SEM), and Spatial Durbin Model (SDM) were developed to explore the possible spatial effects of public transport passenger flow [10]. Moreover, it has been widely applied in modeling the functional relationship between the built environment and the passenger flow of urban rail stations [11,12,13]. Although spatial dependence is a concern in these models, the study area is regarded as homogeneous, while the actual observations not only exhibit spatial dependence but also spatial heterogeneity. That is, the explanatory ability or influence degree of the same variable varies with its spatial location. Therefore, a Geographically Weighted Regression (GWR) model has been proposed to study the influencing factors of station passenger flow.

The Geographically Weighted Regression (GWR) model incorporates geographic location into regression coefficients, allowing for local independent regression at each observation point. It not only has good model interpretability but also accurately reflects changes in the degree of influence spatially. This model has been widely applied in the transportation field. Li et al. [14] took Kuala Lumpur’s urban rail transit as a research case and identified the spatial heterogeneity of urban rail stations from the built environment of passenger flow through the GWR model. The results indicate that even with the same measurement variables, the impact of different station catchments varied, i.e., the coefficients of the built environment variables differed in different locations. Thus, the influence of selected indicators on passenger flow has obvious spatial heterogeneity. Cardozo et al. [15] introduced the GWR model to establish a direct model to predict boarding at Madrid metro stations. The information supplied by the GWR model regarding the spatial variation of elasticities and their statistical significance provides more realistic and useful results. By constructing GWR and mixed geographically weighted regression (MGWR), Yang et al. [16] analyzed the relationship between the built environment of urban rail stations and station-level passenger travel distances in Chengdu, China. The results show that although both the GWR and MGWR models revealed spatially varying relationships between the built environment and travel demand, the MGWR model, which could differentiate between global and local variables, had better goodness of fit compared with GWR and OLS. Besides, with the development of spatial econometric, the GWR model has evolved. Scholars have argued that all the variables are regarded as local variables, overemphasizing that variables are more affected locally than globally [16,17], and that the degree of influence of all variables varies with spatial changes, which contradicts the fact that the effects of certain impact variables are spatially stationary. To this end, Nakaya et al. [18] proposed the semi-parametric Geographically Weighted Poisson Regression (sGWPR) model, which is dedicated to considering the differences between global and local variables. Currently, the model is used to analyze the relationship construction between the built environment and traffic accidents [19], built environment and ride-hailing [20], and rarely for the analysis of factors influencing urban rail passenger flow. In reality, among the factors that influence passenger flow at rail transit stations, the variables that are inherent to a station do not change spatially as other factors do, so it is more realistic to consider them as global variables rather than local variables. Therefore, in this study, we use the sGWPR model and big data to explore the impact mechanisms of the fine-scale built environment, including land use, economic population, transportation connections, and station characteristics, on the daily passenger flow over different times at urban rail transit stations.

3. Study Area and Data Sources

3.1. Study Area

By November 2021, there were eight rail lines in operation in Xi’an, with a total mileage of 258 km and 154 stations. The ridership of rail transit accounts for more than 50% of that of urban public transport. Since the area studied in this paper is mainly the downtown area, six rail lines in Xi’an were selected as the study objects. In addition, according to China’s “Guidelines for Planning and Design of Areas Along Metro Lines”, a station catchment area is defined as “an area that is approximately 500–800 m away from the station and can arrive at the station entrance within about a 15 min walk and is closely related to the metro function”. In fact, the rail network in Xi’an is not perfect, and the station density is low. Thus, the station catchment was defined as the area enclosed by a radius of 800 m with the station as the center in this paper, and the rail network in the study area is shown in Figure 1.

3.2. Data Sources

In this paper, the main datasets include smartcard data (SCD), the land use of the station catchment area, mobile signal data, house price data, road network data, and bus route data. Among them, the SCD, from 1 November to 30 November 2021, was obtained from Xi’an Metro Operation Co., Ltd. The entry/exit ridership was measured in 60-min intervals from 06:00 to 24:00. The land use data were obtained from Xi’an Urban Development Resources Information Co., Ltd., and land use types were classified at the level of sub-categories based on the Standard [1]. The mobile data were collected from the 2G, 3G, and 4G signal sources of the subscribers served by the Xi’an Unicom Communication agent, which was used to measure the population density and employed density within the station catchment. The rent/sale price of the house were acquired from Anjuke, one of the most active online platforms for housing transactions in China. The routes for the bus and the network of roads were downloaded through the API of Gaode Map and the OpenStreetMap website, respectively.

3.3. Summary of Variables

By combining the existing study results [21,22,23,24] and the data collected, the influencing factor sets of ridership are classified into four major categories: socioeconomic and demographic factors, land use characteristics, external connection facilities, and station characteristics.

Table 1. Summary of variables and descriptive statistics.

Variable Category	Variable Name	Definition	Min	Max	Mean	SD	VIF
Dependent variables	Entry ridership	Station entry ridership in 60-min period	0	6452	811.7	878.9	-
	Exit ridership	Station exit ridership in 60-min period	2	9970	816.1	938.7	-
Socioeconomic and demographics	Population density (PD) *	Number of resident population	292	134,134	35,030.5	27,388.6	5.384
	Employment density (ED)	Number of employment population	154	142,150	27,665.7	23,882.2	4.587
	House price (HP) *	Average house price (CNY/m2)	6799.6	36,027.1	16,766.5	5142.1	2.234
Land use characteristics	Class II residential (R2) *	The area of the second-level residential LU (m2)	0	1,240,517.1	572,415.6	288,016.3	7.187
	Administrative office (A1) *	The area of administrative office LU (m2)	0	152,827.7	21,652.2	34,452.6	1.834
	Cultural facility (A2) *	The area of cultural facility LU (m2)	0	294,717.3	19,396.4	46,196.6	1.939
	Educational (A3) *	The area of educational research LU (m2)	0	624,846.7	116,422.3	13,2747.1	2.916
	Sports (A4)	The area of sports LU (m2)	0	613,139.4	13,447.4	64,595.9	1.547
	Medical health (A5)	The area of medical and health LU (m2)	0	475,058.6	21,514.3	53,987.9	2.099
	Social welfare (A6)	The area of social welfare facility LU (m2)	0	17,306.9	337.0	1844.9	1.291
	Heritage sites (A7) *	The area of heritage sites LU (m2)	0	735,163.3	20,098.4	85,308.5	1.803
	Other administration and public service (A89) *	The area of other administration and public service LU (m2)	0	87,973.4	1445.9	9178.4	1.417
	Commercial and recreation (B13) *	The area of commercial, recreation and sports LU (m2)	0	63,4781.3	155,585.9	121,377.2	2.836
	Business affairs (B2) *	The area of business affairs LU (m2)	0	634,968.6	59,505.8	115,307.1	2.547
	Municipal utility outlet (B4)	The area of municipal utility outlet LU (m2)	0	20,395.3	1386.1	3065.2	1.498
	Park and greenbelt (G1)	The area of park and greenbelt LU (m2)	0	724,110.2	146,059.9	120,917.6	2.491
	Other park and square (G23) *	The area of other park and square LU (m2)	0	405,827.3	41,507.6	68,006.5	3.452
	Industrial (M) *	The area of industrial LU (m2)	0	1,103,616.1	75,547.8	203,630.4	4.184
	street and transportation (S) *	The area of street and transportation LU (m2)	0	654,855.6	25,939.5	78,612.1	3.735
	Municipal utility (U) *	The area of municipal utility LU (m2)	0	671,838.3	20,258.5	65,000.1	1.779
	Logistics and warehouse (W)	The area of logistics and warehouse LU (m2)	0	39,990.3	760.6	4782.4	1.404
	Other land (Other) *	The area of other LU (m2)	186,640.2	1,713,577.9	417,614.0	229,157.1	4.761
	FAROR(FR) *	Average floor area ratio of residential land	0	7.42	2.44	1.23	3.770
	FAROA(FA) *	Average floor area ratio of administration and public services land	0	2.38	1.13	0.68	4.190
	FAROB(FB) *	Average floor area ratio of commercial and business facilities land	0	4.80	1.94	1.41	2.584
	Entropy(E)	Land use entropy	0.16	0.69	0.54	0.08	4.146
External connection facility	Arterial density (AD) *	Sum of arterial road lengths (m)	0	24,158	7937	3969	1.706
	Secondary trunk density (STD) *	Sum of secondary trunk road lengths (m)	0	35,270	8496	6901	2.171
	Branch way density (BWD) *	Sum of branch way lengths (m)	0	22,929	7062	4430	2.330
	Intersections (IS) *	Number of motor road intersections	2	59	18.72	10.37	2.778
	Shuttle bus (SB) *	Number of shuttle bus	0	32	10.49	6.26	2.437
	Overlap bus (OB) *	Number of overlap bus	0	36	7.34	6.44	3.625
Station characteristics	Entrances/exits (EE) *	Number of station entrances or exits	2	20	4.59	2.36	7.295
	Betweenness centrality (BC) *	Betweenness centrality calculated based on rail network	0	6076	1226.1	1124.3	3.144
	Closeness centrality (CC)	Closeness centrality calculated based on rail network	0.000034	0.000103	0.000070	0.000018	1.858
	Hub station (HS) *	Hub station or not (1 = yes, 0 = no)	0	1	0.026	0.16	2.761
	Operation time (OT) *	The number of months of station operation until November 2021	11	122	59.98	40.01	2.188
	Terminal station (TS) *	Terminal station or not (1 = yes, 0 = no)	0	1	0.078	0.27	2.020

Note: LU means land use; * means that the variable is retained after multicollinearity and spatial autocorrelation test.

provides descriptive statistics regarding all variables considered in this study. In order to reflect the diversity of land use and the accessibility of the station, specific formulas (1)–(3) are made to define the indicators: land use entropy, closeness, and betweenness centrality of the station.

$$E=\left[\frac{{\sum }_j{p}_j\ln \left(p_j\right)}{\ln \left(J\right)}\right]$$

(1)

$$C_i^C=\frac{n-1}{{\sum }_{\forall r}{d}_{ir}}$$

(2)

$$C_i^B=\sum _{i\ne k\ne m}{\varnothing }_{km}\left(i\right)$$

(3)

where $E$ is the land use entropy, $p_j$ is the proportion of the area of land use category j within the station catchment area, $J$ is the total number of land use categories (19 in this study), $C_i^C$ and $C_i^B$ represent the closeness centrality and betweenness centrality of station $i$, respectively, and $n$ is the number of stations. $d_{ir}$ defines the shortest topological distance between stations $i$ and $r$, and ${\varnothing }_{km}\left(i\right)$ is the number of passing stations $i$ in the number of shortest paths from station $k$ to station $m$.

4. Methodology

4.1. Multicollinearity and Spatial Autocorrelation

In regression analysis, if there is a high correlation between independent variables, distortion can occur in the model assessment [8,25]. Therefore, to ensure the accuracy of the model evaluation, it is necessary to perform a multicollinearity test on all independent variables. Currently, there are two common methods used to test for multicollinearity: the Pearson correlation coefficient and the variance inflation factor (VIF). When the absolute value of the Pearson correlation coefficient is higher than 0.7 or the VIF value is higher than 10, a high correlation is indicated between the two variables.

For the GWR model, being spatially nonstationary is another key issue in selecting independent variables. Spatial autocorrelation analysis is used to determine whether a variable is spatially nonstationary. The Global Moran’s I test is often used to assess the spatial autocorrelation of variables. Thus, this paper uses this method to validate the spatial autocorrelation of variables. The formula (4) is shown as follows.

$$I=\frac{n}{{\sum }_{i=1}^n{\sum }_{j=1}^n{\omega }_{ij}}\frac{{\sum }_{i=1}^n{\sum }_{j=1}^n{\omega }_{ij}\left(y_i-\overline{y}\right)\left(y_j-\overline{y}\right)}{{\sum }_{i=1}^n{\left(y_i-\overline{y}\right)}^2}$$

(4)

where $n$ is the number of stations, $y_i$ and $y_j$ are the actual values of the observed attribute at stations $i$ and $j$, respectively, and $\overline{y}$ is the average value of the observed attribute. ${\omega }_{ij}$ represents the spatial weights matrix of stations $i$ and $j$.

4.2. Semi-Parametric Geographically Weighted Poisson Regression

The Poisson distribution is defined before understanding the Geographically Weighted Poisson Regression model, which is mainly used to analyze count data (e.g., entry passenger flow per hour). The Poisson regression model is shown as formula (5), where $x_{ik}$ denotes the $k_{th}$ local variable at station $i$, ${\beta }_k$ denotes the coefficient of the $k_{th}$ variable, $t_i$ is the offset variable at station $i$, ${\beta }_0$ is the constant term.

$$y_i~Poisson\left[t_i\exp \left({\beta }_0+\sum _k{\beta }_k{x}_{ik}\right)\right]$$

(5)

By adding spatial location to model (5), a Geographically Weighted Poisson distribution regression is constructed, as in Equation (6), which allows the parameters to vary with geographic location, clearly capturing some important local variations in the relationship between the dependent and explanatory variables. Where, $\left(u_{i,}{v}_i\right)$ denotes the two-dimensional coordinates of station $i$, ${\beta }_0\left(u_{i,}{v}_i\right)$ indicates the constant term at station $i$, ${\beta }_k\left(u_{i,}{v}_i\right)$ represents the coefficient of the $k_{th}$ local variable at station $i$. Suppose $\mathsf{\beta }=({\beta }_0,{\beta }_1,···,{\beta }_k)$, then β is a matrix, the specific form is shown in Equation (7).

$$y_i~Poisson\left[t_i\exp \left({\beta }_0\left(u_{i,}{v}_i\right)+\sum _k{\beta }_k\left(u_{i,}{v}_i\right)x_{ik}\right)\right]$$

(6)

$$\mathsf{\beta }=\left[\begin{array}{cc}\begin{array}{cc}{\beta }_0\left(u_{1,}{v}_1\right)& {\beta }_1\left(u_{1,}{v}_1\right)\\ {\beta }_0\left(u_{2,}{v}_2\right)& {\beta }_1\left(u_{2,}{v}_2\right)\end{array}& \begin{array}{cc}\cdots & {\beta }_k\left(u_{1,}{v}_1\right)\\ \cdots & {\beta }_k\left(u_{2,}{v}_2\right)\end{array}\\ \begin{array}{cc}⋮& ⋮\\ {\beta }_0\left(u_{n,}{v}_n\right)& {\beta }_1\left(u_{n,}{v}_n\right)\end{array}& \begin{array}{cc}\ddots & ⋮\\ \cdots & {\beta }_k\left(u_{n,}{v}_n\right)\end{array}\end{array}\right]$$

(7)

The parameter estimation of the GWPR model belongs to the local regression analysis. For each observation, a local range selection is first performed to determine the range used for local regression, and the parameter estimate of each observation can be obtained by regressing the observation data points using the local data within the range. By applying this method of regression analysis to each observation data in a loop, the fitting coefficients with spatial variation can be obtained. Therefore, assuming that $y_1,y_2,y_3,···,y_n$ are independent of each other and each $y_i$ obeys the Poisson distribution, the parameter $\beta \left(u_{i,}{v}_i\right)$ for each station can be estimated by solving the problem of maximizing the geographically weighted log-likelihood as in Equation (8). Where, $y_j$ is the actual ridership of station j, ${\widehat{y}}_j\left(\widehat{\beta }\left(u_{i,}{v}_i\right)\right)$ is the predicted ridership for station j using the parameters of station $i$. $d_{ij}$ represents the Euclidean distance between station $i$ and j, $w_{ij}$ is the weight value of station j to $i$. For any given station $i$, the parameter $\beta \left(u_{i,}{v}_i\right)$ can be calculated by formula (9), where Y is the dependent variable, X is the matrix $n\times (k+1)$ of explanatory variable, and W is the diagonal weighted matrix of station $i$.

$$\max L\left(u_{i,}{v}_i\right)=\sum _j^N\left(-{\widehat{y}}_j\left(\widehat{\beta }\left(u_{i,}{v}_i\right)\right)+y_{j}log{\widehat{y}}_j\left(\widehat{\beta }\left(u_{i,}{v}_i\right)\right)\times w_{ij}{d}_{ij}\right)$$

(8)

$$\begin{gathered} \widehat{\beta }\left(u_{i,}{v}_i\right)={\left({\mathbf{X}}^T\mathbf{W}\left(u_{i,}{v}_i\right)\mathbf{X}\right)}^{-1}{\mathbf{X}}^T\mathbf{W}\left(u_{i,}{v}_i\right)\mathbf{Y} \\ \mathbf{X}=\left(\begin{array}{cc}\begin{array}{cc}1& x_{11}\\ 1& x_{21}\end{array}& \begin{array}{cc}\cdots & x_{1k}\\ \cdots & x_{2k}\end{array}\\ \begin{array}{cc}⋮& ⋮\\ 1& x_{n1}\end{array}& \begin{array}{cc}\ddots & ⋮\\ \cdots & x_{nk}\end{array}\end{array}\right)\hspace{1em}\mathbf{Y}=\left[\begin{array}{c}\begin{array}{c}{y}_1\\ y_2\end{array}\\ \begin{array}{c}⋮\\ y_n\end{array}\end{array}\right]\hspace{1em}\mathbf{W}=\left(\begin{array}{cc}\begin{array}{cc}{w}_{i1}& 0\\ 0& w_{i2}\end{array}& \begin{array}{cc}\cdots & 0\\ \cdots & 0\end{array}\\ \begin{array}{cc}⋮& ⋮\\ 0& 0\end{array}& \begin{array}{cc}\ddots & 0\\ \cdots & w_{in}\end{array}\end{array}\right) \end{gathered}$$

(9)

whereas, not all variables have spatial heterogeneity in reality, and there may be no obvious geographic variation in the estimation of some parameters. In this context, variations of the GWPR model are involved. To explore the influence of the built environment on ridership, this paper employs the sGWPR model, which considers local variables that vary spatially and global variables with inherent properties, such as station characteristics. The mathematical expression is shown as Equation (10), where ${\gamma }_m$ represents the coefficient of the $m_{th}$ global variable, which h means that this coefficient has no geographical variation across the study area, and $x_{im}$ represents the $m_{th}$ global variable at station $i$.

$$y_i~Poisson\left[t_i\exp \left({\beta }_0\left(u_{i,}{v}_i\right)+\sum _k{\beta }_k\left(u_{i,}{v}_i\right)x_{ik}+\sum _m{\gamma }_m{x}_{im}\right)\right]$$

(10)

Furthermore, a combination of parametric and nonparametric methods was used to estimate global and local coefficients [26]. Thus, for any given station $i$, the numerical solution ${\beta }_k\left(u_{i,}{v}_i\right)$ can be calculated by the formula (9) above. In the sGWPR model, the weighting matrix is calculated from the spatial kernel function. An appropriate spatial kernel function and the optimal bandwidth in the kernel function are crucial to the fitting effect of the model. Several spatial kernel functions have been developed to define spatial weighting matrixes, such as the Gauss function and the Bi-square function. In this paper, the adaptive bi-square function was selected as the spatial kernel function. For the optimal bandwidth, this study employs the golden-section search method to find the optimal bandwidth size by minimizing the modified Akaike information criterion.

5. Results and Discussion

5.1. Comparison of Model Performance

The multicollinearity among the variables was tested according to both the Pearson coefficient and VIF values (Table 1), and two variables, employment density and closeness centrality, were excluded. The remaining variables were used as alternative independent variables. In addition, according to the results of the global Moran’s I test, seven variables, namely, sports (A4), medical health (A5), social welfare (A6), municipal utility outlet (B4), park and greenbelt (G1), logistics and warehouse (W), and entropy, were also excluded. The remaining 29 variables were considered independent variables.

It is necessary to select the key factors that have a significant impact on ridership before formulating the sGWPR model. Therefore, first, an OLS model is employed to select the built environment factors that have a significant impact on entry/exit ridership during different periods of the day. Then, a sGWPR model is formulated, which considers both local and global variables. The global variables are station characteristics, and the local variables are socioeconomic, demographic, land use characteristics, and external connection facilities. Finally, the ArcGIS 10.3.0.4322 platform is used to visualize and capture the spatial variation in these key impact factors on ridership.

Figure 2 shows a comparison of the $R^2$ values of the sGWPR model and the OLS model for different periods of the day. The results show that the determination coefficient $R^2$ is larger based on the sGWPR model, indicating that the sGWPR model has better goodness of fit and a smaller bias. Moreover, compared with the OLS model, the $R^2$ of the sGWPR model varies much less over time. The goodness of fit of entry ridership is better than that of exit ridership before 16:00. However, after 16:00, the goodness of fit of entry ridership starts to decrease and is lower than that of exit ridership. In addition, another more important aspect, according to the characteristics of the independent variables, is that the sGWPR model can consider both independent variables with and without spatial nonstationary, i.e., local and global variables. It is more practical to set the station characteristics, such as the terminal station and the number of station entrances/exits, as global variables.

5.2. Spatial Analysis of Coefficients from the sGWPR Model

After obtaining the results based on the sGWPR model, the mechanism of the spatial imbalance characteristics of ridership and its intrinsic relationship with the built environment are further analyzed in the spatial dimension. Considering the space limitation, this paper only selects some important variables from the factors influencing ridership in some specific periods to analyze the spatial characteristics. Demographics have been discussed in many studies [3,10,15], so the spatial characteristics of the demographics will not be examined in this section. For the land use characteristics, since many studies use POI data instead, this paper uses the actual area, Class II residential (R2), and average floor area ratio of commercial and business facilities (FAROB) for the spatial characteristics analysis. For the external connection facility, this paper selects the most typical shuttle bus as the object of spatial analysis. For the station characteristics, there is no spatial variability because the sGWPR model treats them as global variables.

According to the results of the OLS model (

Table 2. Results of OLS model for entry ridership.

	Constant	PD	R2	A1	A7	S	FB	FR	IS	SB	OB	BC	EE	OT	ES
6	−183.5 **	2.4 **	383.8 **		475.7 *					7.1 *				2.7 **	164.6 *
7	−649.9 **	9.6 **	1945.5 **		1796.3 *			123.8 *	−20.9 **	34.4 **				8.7 **	573.9 *
8	−836.6 **	12.9 **	2120.1 **		2243.7 *					36.7 **				9.6 **	600.9 *
9	−342.0 **	3.4 **	471.9 **		795.2 **			72.4 **		12.9 **				5.6 **	351.8 **
10	−214.8 **		219.2 **	1537.9 **		912.5 **	44.6 **			11.3 **		6.3 **		4.4 **	189.1 *
11	−167.4 **			1762.7 **		1128.8 **	59.8 **			12.3 **		7.2 **		4.4 **	181.7 *
12	−208.3 **						89.5 **			15.8 **			20.3 *	5.2 **	285.2 **
13	−224.7 **						90.5 **			18.8 **			20.5 *	5.7 **	274.2 **
14	−287.7 **						82.7 **			16.3 **		5.8 *	27.5 *	5.7 **	307.1 **
15	−380.8 **					1564.2 **	86.8 **			14.8 **		9.1 **	44.4 **	5.2 **
16	−446.8 **						108.1 **			16.5 **		10.7 **	56.3 **	6.2 **	398.7 **
17	−361.4 *						327.3 **			29.2 **			99.2 **	7.1 **
18	−472.6 **						358.9 **			57.4 **	53.3 **		132.8 **
19	−492.6 **						181.7 **			26.7 **			108.2 **	4.7 **
20	−426.0 **						136.5 **			15.6 **			94.1 **	3.2 **
21	−403.9 **						133.6 **			15.5 *			109.2 **
22	−317.7 **						106.5 **						96.4 **
23	−92.8 **						16.3 **						17.8 **	0.7 **

Note: * p ≤ 0.05; ** p ≤ 0.01; 6 means 6:00~7:00, and so on, 23 means 23:00~24:00.

and

Table 3. Results of OLS model for exit ridership.

	Constant	PD	R2	A3	A7	B2	S	FB	FR	SB	OB	BC	EE	OT	HS	ES
6	0											3.6 **		1.0**
7	0			1028.1 *								30.5 **		7.1 **		661.4 **
8	0					3096.9 **		576.9 **			70.5 **		138.1 **
9	−504.7 **					961.9 *		217.3 **		26.5 **	27.4 **		82.4 **	3.1 *
10	−324.4 **						1390.2 **	96.7 **		11.5 **		8.4 **	42.7 **	4.3 **
11	−302.8 **							89.4 **		10.3 *			59.2 **	4.6 **
12	−327.7 **							97.3 **		11.2 **			59.1 **	4.8 **
13	−365.3 **							108.0 **		12.4 **			66.8 **	5.1 **
14	−450.8 **							111.6 **		12.8 *			86.7 **	5.4 **
15	−359.1 **							81.2 **		17.0 **			66.4 **	5.3 **
16	−403.8 **		212.8 *					76.1 **		18.9 **			49.2 **	5.9 **		237.5 **
17	−580.2 **	4.4 **	542.4 **		866.2 *			84.9 **		22.8 **			54.3 **	6.9 **		382.2 **
18	−1220.2 **	9.9 **	1564.5 **		2137.3 **				136.8 *	44.6 **			71.9 *	11.5 **		531.9 **
19	−673.6 **	6.1 **	1059.1 **		1172.6 *					39.2 **			48.7 *	8.2 **
20	−471.6 **	3.9 **	509.9 **		710.2 *				45.2 *	20.6 **			24.1 *	4.7 **	−486.4 **	288.3 **
21	−251.0 **	3.9 **	404.6 **		492.1 *					18.8 **				3.9 **	−442.1 **	224.9 **
22	−236.1 **	3.2 **	337.1 **		420.5 *					13.8 **				3.4 **	−244.1 *	191.7 **
23	−85.4 **	1.1 **	105.1 **							4.7 **				1.5 **	−91.3 *	83.3 **

Note: * p ≤ 0.05; ** p ≤ 0.01; 6 means 6:00~7:00, and so on, 23 means 23:00~24:00.

), the period in which R2 has a significant effect on the entry ridership is from 6:00 to 11:00, while the period after 16:00 for exit ridership indicates that R2 has a significant effect on the ridership during the morning and evening peak hours. The area of R2 is the main source of entry ridership in the morning peak and exit ridership in the evening peak. The entry ridership generated during the morning peak hours is dominated by many residents going to work, and during the evening peak hours, exit ridership is dominated by many residents returning home, which is consistent with commuting trips. Figure 3a,b, and c represent the area of R2, the entry ridership from 7:00 to 8:00, and the coefficient values of R2, respectively. According to Figure 3a,b, stations with more R2 areas also have more entry ridership in the morning peak hour, such as the stations of Line 2 in the southern area. According to the spatial distribution of the coefficients in Figure 3c, the R2 area has a positive effect on the entry ridership at different stations. However, the stations with more R2 areas are not necessarily more sensitive to the R2 area. Moreover, the spatial distribution of coefficients is not random. The coefficients are higher in suburban areas and show a trend of gradual increase from urban areas to suburban areas, indicating that suburban stations (both ends of the line) are more sensitive to the R2 area than urban stations.

People living in R2 belong to the middle-income group, and rail travel dominates the trips of this group. In addition, suburban areas have unique advantages in terms of cost of living and convenience of travel; as their housing prices are lower than those in urban areas, functional facilities are gradually improved, and the distance to urban areas is shorter. People in this group prefer to live in suburban areas, which inevitably increases the demand for ridership in these areas [5,27]. Therefore, increasing the R2 area within suburban stations has a greater potential to enhance entry ridership in the morning peak hour and exit ridership in the evening peak hour than that within urban stations, which suggests that planners need to focus more on R2 planning.

Figure 4a–c show the values of FAROB, exit ridership from 8:00 to 9:00, and the coefficients of FAROB in the same period, respectively. According to Figure 4a,b, the FAROB decreases gradually from the urban areas to the suburban areas, and stations with a higher FAROB will also have more exit ridership during the 8:00–9:00 period, such as the urban stations. The results of Figure 4c show that the stations with a higher FAROB values are less sensitive to the FAROB values. The FAROB values for suburban stations have a slightly greater impact on exit ridership in the morning peak than those for urban stations, especially stations in the eastern area. The station in the east is closer to the urban area, with better regional function and more convenient transportation. However, its FAROB is much lower than that of the urban area, so the FAROB has a greater impact in this area. In addition, this paper compares the R2 values in Figure 3a and the values of FAROB in Figure 4a and finds that there is still a large difference in the spatial distribution between them, which implies that there may be an imbalance between work and residence in Xi’an.

The spatial distribution of the coefficients of the shuttle bus for entry ridership during the 8:00–9:00 period and exit ridership during the 18:00–19:00 period are shown in Figure 5a,b, respectively. The results show that improving the shuttle bus within the station catchment area will significantly increase ridership. In terms of distribution location, the shuttle bus coefficients are larger in suburban areas than in urban areas, and the impact is more significant and positively correlated, implying that ridership at suburban stations is highly sensitive to the number of shuttle buses. This phenomenon may arise because the number of transportation facilities in suburban areas is not as well developed as that in urban areas, the road network density is smaller, the convenience of transportation is not adequate, and the density of stations is lower than that in urban areas, so passengers prefer to take the bus to the station. In addition, since the land use in suburban areas is mostly dominated by residential land, the more bus lines there are for passengers with demand, the stronger the willingness to take the bus to the station will be.

Figure 5c shows the spatial distribution of shuttle bus coefficients for entry ridership during the 18:00–19:00 period. During this period, the shuttle bus coefficients at urban stations are negative, indicating that there is competition between shuttle buses and urban rail during this period. Not all commuters return home following the same route they took to work in the morning, but there are other entertainment activities. In addition, because the rail network density is lower and cannot meet the travel demand, the bus becomes the choice for travel.

6. Scenario Application

The results of the model play a very important role in guiding practice. In response to the above analytical results, it is of great value to apply them in practice. The relationship between ridership and impact factors requires not only an analysis of its spatial-temporal characteristics but also, more importantly, how to apply it in practice. With the rapid development of urban rail, many problems have gradually become prominent; for example, limiting ridership has become a regular practice at some stations, and some stations have insufficient ridership due to lagging land development. There is an interactive relationship between station ridership and fine-scale built environment factors. These problems can be solved from two perspectives. On the one hand, rail operators suggest solving the problem from the perspective of traffic engineering. On the other hand, urban planners suggest solving the problem from the perspective of urban planning.

Based on the above analysis, the modeling results in this study can be applied to the following two scenarios. In the first scenario, the impact of stations on the built environment factors is still changing. When the land use type of a parcel within the station catchment area changes or the number of traffic connection facilities changes, the change in entry/exit ridership can be quickly calculated according to the function relationship formulated in this paper. It provides a reference for rail operators to optimize and adjust operation services. In another scenario, since the scale of stations is built according to the design ridership, when urban areas need to update the land use type within the station catchment area or allocate resources, planners can propose land use update strategies based on the threshold value of the design ridership, optimize the land use within the station catchment area through the functional relationship, and provide a reference for how to adjust the land use type and determine the threshold range for adjustment to achieve synergistic development between ridership and the built environment.

Since this paper focuses on traffic engineering, the Nanshaomen (NSM) station of Line 2 is an example used to illustrate the practical application of the first scenario. The land use within the station catchment area of the NSM station is shown in Figure 6a. Suppose there is an R2 area (28,200 m²) located in the northeast area of the station, and this site now needs to be updated because the building is relatively old. However, the land use type will be changed to B13 after the update. Moreover, after completion of this site, the floor area ratio is higher, increasing the FAROB for this station by 0.01. Figure 6b shows the updated land use within the station catchment area. Based on the above assumptions, it is necessary to understand how the entry/exit ridership will change after the land parcel is updated to guide the rail operators in adjusting their operation services.

To address the above issues, with the model formulated in this paper,

Table 4. Ridership of the NSM Station.

Period	Entry Ridership				Exit Ridership
	CAR	CPR	Error	UPR	CAR	CPR	Error	UPR
6:00–7:00	308	443	135 (43%)	431	166	301	135 (81%)	301
7:00–8:00	1555	1881	326 (20%)	1827	1871	2411	540 (28%)	2411
8:00–9:00	2179	2067	112 (5%)	2018	5754	5304	450 (7%)	5317
9:00–10:00	1204	1233	29 (2%)	1218	2742	2619	123 (4%)	2622
10:00–11:00	998	1073	75 (7%)	1062	1450	1637	187 (12%)	1640
11:00–12:00	1050	1168	118 (11%)	1170	1212	1405	193 (16%)	1407
12:00–13:00	1169	1241	72 (6%)	1242	1200	1477	277 (23%)	1479
13:00–14:00	1214	1291	77 (6%)	1293	1351	1614	263 (19%)	1617
14:00–15:00	1319	1533	214 (16%)	1535	1408	1766	358 (25%)	1769
15:00–16:00	1428	1724	296 (20%)	1728	1266	1492	226 (17%)	1494
16:00–17:00	1677	2089	412 (24%)	2093	1242	1434	192 (15%)	1424
17:00–18:00	3327	3382	55 (1%)	3388	1676	1892	216 (12%)	1882
18:00–19:00	4081	3724	357 (8%)	3730	3010	3067	57 (2%)	3025
19:00–20:00	2117	2310	193 (9%)	2311	1994	1829	165 (8%)	1812
20:00–21:00	1684	1747	63 (3%)	1748	1083	1149	66 (6%)	1129
21:00–22:00	1457	1347	110 (7%)	1351	836	760	76 (9%)	755
22:00–23:00	1024	1089	65 (6%)	1095	628	582	46 (7%)	577
23:00–24:00	317	276	41 (13%)	277	264	228	36 (13%)	228

provides the current actual ridership (CAR), the current predicted ridership (CPR), the error between actual and predicted ridership, and the updated predicted ridership (UPR) based on the above assumptions. According to the results in Table 4, the model formulated is more accurate in predicting the entry/exit ridership at the NSM station during the morning peak and evening peak hours and has the worst accuracy during 6:00–7:00, especially the exit ridership during 6:00–7:00. Through the analysis, the only significant impact factors in this period are the station characteristics, which are global variables in the model. On the other hand, the exit ridership during this period is the lowest during the day, and these reasons may account for the poor quality of fit in this period.

Therefore, when the built environment changes, the formulated model is used to quickly calculate the changes in the entry/exit ridership, which provides a reference for the rail operator to adjust the operation services and allocate resources.

7. Conclusions

In this paper, the sGWPR model is employed to study the impact of the built environment on entry/exit ridership during different periods of the day. In terms of quantitative impact factors, different from previous studies that used POI data to calculate land use types within the station catchment areas, this study uses the actual area of land use type obtained to represent land use characteristics. The POI only clarifies the type and number of facilities while ignoring the land use area that may affect ridership. In this study, by using the national urban land use classification standard to refine the land use classification and obtain the corresponding actual area, we formulate the relationship between the fine-scale built environment factors and entry/exit ridership, which provides the theoretical basis and practical significance for adjusting rail operation services and optimizing the land use of station catchment areas.

First, the model can consider both independent variables with and without spatial nonstationary, namely, local variables and global variables, which is more in line with practical significance. According to the results of the model, the sGWPR model has better goodness of fit, which means that the proposed model can provide an effective tool for ridership prediction.

Then, according to the results of the OLS model, each impact factor presents a different impact during different periods of the day. The R2 has a significant impact on entry ridership from 6:00 to 11:00 and on exit ridership from 16:00 to 24:00. R2 is the main source of entry ridership in the morning peak and exit ridership in the evening peak. The regression coefficient is higher in suburban areas and shows a trend of gradual increase from urban areas to suburban areas, indicating that suburban stations are more sensitive to R2 than urban stations. In addition, by comparing the R2 and FAROB values, there may be an imbalance between work and residence in Xi’an. On the other hand, shuttle buses make a significant contribution to improving commuter ridership, and shuttle capacity improvements will significantly increase commuter ridership. According to the spatial characteristics of shuttle bus coefficients, the value is larger in suburban areas than in urban areas, which means that the impact is more significant and positively correlated.

Finally, based on the relationship between ridership and the formulated fine-scale built environment factors, two practical application scenarios are proposed, and the first scenario is illustrated. When the built environment within the station catchment areas changes, the formulated model can be used to quickly calculate the changes in entry/exit ridership, which verifies the practical application scenarios of this study. There are some shortcomings in this study. First, the hierarchical construction of the influencing factor set failed to consider the connection facilities of bicycles. Previous studies have mostly focused on the docked bicycles within the station area. However, the popularity of shared bicycles makes it impossible to fully characterize the station area bicycle connections based solely on the number of docked bicycles. Second, this paper analyzed the passenger flow on weekdays. However, the impact of the built environment on passenger flow over time periods on the weekend is also worth studying. Third, this paper takes Xi’an as a case study for analysis and draws on the research methodology to explore the interactive relationship between the generation of rail transit passenger flow and station environmental factors in other cities in a fine-scale built environment in the future.