Bus ridership and its determinants in Beijing: A spatial econometric perspective

Beijing, as a populous megacity, has a population size of 21.7 million, inducing enormous travel demand. In 2018, the total number of weekday bus riders in the urban areas of Beijing was 6.3 million, accounting for 16.06% of the total number of weekday trips. Geographically, bus ridership is mainly distributed in the central urban areas of Beijing, especially within the Six-Ring Road, where there were 3616 bus stations in 2015. The smart card data (SCD) for a single week of 2015 were obtained from the Beijing Transportation Information Center, and they account for 85% of the total trips in the system (Zhong et al. 2016). The SCD is widely used to explore the commute mode preference (Wang et al. 2020), the transit-based health seeking patterns (Du et al. 2020), and the Job-worker dynamics (Huang et al. 2019). These data include information on the boarding station, alighting station, boarding time, alighting time, and many other items of all bus riders. Since there might be several bus stations at the crossroads, and these stations might serve the same residents in the nearby community, so we adopt community as the basic unit for analysis in this paper. For example, at the crossroad of Beitucheng West Road and Huayuan East Road, there are four bus stations, named Mudanyuan East, Mudanyuan West, Mudanyuan South, and Mudanyuan North stations, located at the different directions of the crossroad. To better understand the spatial patterns and the influential factors of bus riders, the OD-linked transit trips are aggregated to a certain spatial area (community level).

A community, one kind of continuous area in cities, is a mass self-government organization under the leadership of community residents to implement self-management, self-service, and self-monitoring. In China, most transport services are distributed by taking the community as the smallest unit. Thus, the 3049 communities located within the Six-Ring Road of Beijing are chosen as the objects of study in this study, as shown in Fig. 1. The travel demand of communities is calculated according to the bus ridership at the station level. Considering that the demand for persons might decrease with an increase in the distance to bus stations, the inverse distance weight (IDW) method is introduced to transfer the bus ridership at each bus station to that in each community in this study. The formulas for the IDW are written as:where \({z_i}\) are the observed data points noted as i and d_iu is the distance from observed data i to pixel u. The bandwidth used in the IDW is set as 500 m, which is the access distance for walking.

To better understand the temporal nonstationarity of bus ridership determinants, the average bus alighting ridership per day in a week, on weekdays, and weekends is chosen as the dependent variable to explore the determinants across a week. The average bus alighting ridership per hour during morning peak hours, afternoon peak hours, daytime off-peak hours, and night-time off-peak hours is chosen as the dependent variable to explore the determinants across the course of a day. According to the temporal dynamics of bus ridership (refer to Sect. 3.1), the morning peak, evening peak, daytime off-peak, and night-time off-peak hours are respectively set as 6:30 -10:00, 16:30 -20:00, 10:00 -16:30, and 20:00 -6:30.

According to previous studies (Kuby et al. 2004; Chakour and Eluru 2016; Zhu et al. 2018; Chiou et al. 2015), the independent variables in this study include the transport endowment indicators, socio-economic attributes, and built environment attributes of each community.

The transport endowment of a community reflects how well a community is positioned in the transport network, which refers to the indicators related to the bus infrastructure and service network of the bus network, its alternative transport modes, and the intercity transport location endowment. The transport endowment related to the bus network includes the indicators reflecting its scale, accessibility, and connectivity characteristics, which includes the density of bus stations (bus stations), the distance to the nearest bus stations (Dist_to_bus stations), and the betweenness centrality in the bus service network (Betw_bus). The alternative transport indicators include the density of subway stations (subway stations), the shortest distance to the subway stations (Dist_to_subway stations), the density of the road network (Road density), and the betweenness centrality in the road network (Betw_road). Traditionally, having more subway stations, more convenient subway stations, higher road network density, and larger road network connectivity means having lower bus ridership. The intercity transport locational endowment is reflected by the distance to the airport (Dist_to_airport) and railway stations (Dist_to_rail station). Amongst, betweenness centrality measures the extent to which a particular node lies between other nodes in a bus network or road network, which reflects the inter-change role of the node (Jiao et al. 2017). The betweenness centrality of each station in the bus network and each road intersection in the road network are calculated according to the previous work by Wang et al. (2011), and then the betweenness centrality of each community in the bus and road network is calculated using IDW. The distance to bus stations, subway stations, airports, and rail stations is calculated using the software ArcGIS. The other data are mostly calculated according to the raw data sourced from a web mapping service application “Baidu Map”.

The socio-economic attributes contain the Gross Domestic Product (GDP), population, employment, and average housing price in each community, which respectively measures the scale of GDP, population and employment divided by the areas of the community, and the average listing price of each residential quarter in each community. Considering that there is high collinearity between GDP and population-scale of communities, only the population scale, employment, and housing price are introduced in the models. The population and employment data are respectively sourced from Beijing population census data in 2010 and Beijing economic census data in 2014 (available at < http://​gis.​bjhgk.​gov.​cn/​visual/​main/​base.​html?​gallery > . accessed on 4 May 2016). The listing price of each residential quarter within the Six-Ring Road is collected from the website of Soufang (http://​bj.​fang.​com/​, accessed in December 2013), which is one of the famous real estate network media and information service enterprises.

The land use and built environment are evaluated using the density of education, catering, commercial facilities, financial spots, tourist spots, and healthcare, which are calculated using their number and the areas of the community where they are located in. Amongst, the number of these facilities is also sourced from “Baidu Map”, while the area of each community is calculated using the software ArcGIS. Details about the dependent and independent variables are shown in Table 1.

Spatial econometric models are widely used to capture spatial autocorrelation, which is referred to as the neighborhood effect or spatial autocorrelation (Jiao et al. 2020). Three widely used spatial econometric models, including the SEM, SLM, and SDM, are introduced. Specifically, the SDM accommodates the spatial interaction effect from the dependent variable and all explanatory variables, whereas the SLM and the SEM accommodate the spatial interaction effect only from the dependent and residual variables, respectively (Elhorst 2010). The formulas for the baseline, SDM, SEM, and SLM are as follows:where \(y\) is the dependent variable, including the indicators reflecting the demand for bus ridership; X represents the constant and independent variables, including the external and internal factors influencing bus ridership; β represents the corresponding parameters of each variable; and ε is the residual of the model. \(\mathrm{W}\) is the spatial weight matrix, which is set as the inverse distance matrix, measuring the reciprocal of Euclidean distance between two communities. \(\mathrm{Wy}\) represents the spatial lag in the dependent variable, indicating the spatially weighted average value of bus ridership from i’s neighboring regions; \(\mathrm{WX}\) is a spatial lag in the independent variables, which is the weighted average value of the independent from the neighbors. The coefficients \(\uprho\) and \(\uptheta\) represent the effects of the dependent and independent variables for the neighboring regions, respectively, and \(\lambda\) represents the spatial lag of the associated residual.

The selection of spatial econometric models is based on the following tests. First, the Lagrange multiplier (LM) diagnostics, including the Lagrange multiplier (LM) error test, LM-lag test, robust LM-error test, and robust LN-lag test, are used to judge whether spatial lag dependence or spatial error dependence exists in the model. Second, whether the SDM could be simplified, the SLM and SEM should be examined according to the values of \(\uprho\) and \(\lambda\) (Elhorst, 2010; LeSage and Pace, 2009). When \(\uprho \ne 0\mathrm{ and \theta }=\lambda =0\), SLM should be chosen; when \(\uprho =\uptheta =0\mathrm{ and }\lambda \ne 0\), SEM should be chosen; when hypotheses of H₀:θ=0 and H₁:θ+ρλ=0, tested using the Wald test, are rejected, the SDM is preferred over the spatial lag model (SLM) and the SEM.

Figure 2 shows the aggregated hourly dynamics of bus usage concerning alighting ridership. The patterns are quite distinct on weekdays and weekends as well as at different time slots of the day. During weekdays, bus usage has shown stationarity patterns with two commuting peaks in the morning (6:30–10:00) and evening (16:30–20:00), indicating that most bus ridership occurs for commuters during the weekdays. Normally, bus ridership in the morning peak is higher than that in the evening peak. On weekends, both the morning and evening peaks still exist, but the total bus ridership during peak hours is much lower than that on weekdays, possibly because some commuters still work on weekends. The total bus ridership during off-peak hours on weekends is slightly higher than that on weekdays, indicating that more people choose to travel during off-peak hours on the weekends.

Figure 3 shows the spatial patterns of average bus ridership per day during a week (Fig. 3a), weekday (Fig. 3b), and weekend (Fig. 3c) and the spatial disparity in bus ridership on weekdays and weekends (Fig. 3d), which is set as the difference between the average daily bus ridership on weekdays and that on weekends.

Bus ridership is mainly aggregated around transport hubs and residential areas (see Fig. 3). Specifically, the communities with high bus ridership align well with the intercity transport hubs (i.e., Beijing West station, Beijing South station, and Lianhuachi intercity bus station), the urban transport hubs (i.e., Dongzhimen station, Xizhimen station), and the central business district (CBD) and residential area (i.e., Huilongguan). This pattern is most explicit in Fig. 3a, which depicts bus usage on weekdays. This finding indicates that on weekdays, people are likely to commute by bus or travel to transport hubs by bus for transfer during a commuting journey.

To further investigate spatial disparity, the difference in average bus ridership between weekdays and weekends is explored (as shown in Fig. 3d). Of 3049 communities within the Six-Ring Road of Beijing, 2801 have more bus ridership on weekdays than weekends, which indicates that approximately 91.87% of communities have higher travel demand on weekdays than on weekends. These communities with large differences in average bus ridership between weekdays and weekends are mostly located near the CBD, transport hubs, and residential areas. The remaining 8.13% of communities have higher travel demand on weekends and are mainly located around tourist spots (i.e., South Luogu Lane, Tian’an Men, Happy Valley, Longtan Park) and some industrial parks.

We further explore the spatial dynamics of bus ridership at peak and off-peak hours on weekdays. Figure 4 illustrates the spatial dynamics of average bus ridership hourly during morning peak hours (Fig. 4a), evening peak hours (Fig. 4b), daytime off-peak hours (Fig. 4c), and night-time off-peak hours (Fig. 4d) on weekdays.

The bus ridership during morning and afternoon peak hours share large similarities with the total on weekdays, and communities located around transport hubs or with large residential populations have larger volumes of bus ridership than other places. According to the difference between the hourly bus ridership during morning and afternoon peak hours, we find that most communities have larger bus ridership during morning peak hours than during afternoon peak hours, indicating that residents are apt to use bus services for commuting in the morning. Possible reasons are that in Beijing, most people go to work at the similar times, but they finish work at different times in the afternoon since some of them work overtime. Moreover, elderly people in Beijing, who are free to take the bus, are more likely to go shopping or go to the park in the early morning, which might also increase bus ridership during morning peak hours. The alighting ridership during morning peak hours is mainly concentrated at the transport hubs and job centers of Beijing (Zhongguancun, Guomao, etc.), while that in residential communities are concentrated during afternoon peak hours.

Figure 5 shows the coefficients of the transport endowment and their spatial lag, which respectively reflect how the transport endowment of a community and its neighbors impact its bus ridership; thus, a positive coefficient for the density of bus stations and subway stations, betweenness centrality in road and bus network, and road density, and a negative coefficient for distance to bus stations, subway stations, rail stations, and airports, meaning that the transport endowment in a community and its neighbors have a negative influence on its bus ridership.

The betweenness centrality in the bus network and road network and the distance to subway stations and rail stations had a significant influence on bus ridership at all the selected time slots (Fig. 5). The elasticities of these indicators were higher than the other significant indicators at all the selected time slots. That is, there might be more bus ridership in the communities with higher betweenness centrality, and lower distance to the subway station, which respectively reflected the transferring role in bus and road network, and the accessibility to subway stations. The positive influence of betweenness centrality in bus and road network and negative influence of the distance to subway stations and rail station indicated that persons are more likely to transfer from one bus to another bus, or even to subway or railway. Except for the distance to subway stations, the impact magnitude of the other three indicators on weekdays was higher than that on weekends. On both weekdays and weekends, bus ridership was also influenced by the distance to bus stations and road density, and the magnitude of the impact of these two indicators on weekdays was lower than that on weekends. That’s to say, the transport connectivity, reflected by the betweenness centrality, had generated a larger influence on the bus ridership on weekdays, while the density and accessibility respectively donated by the road density and distance to bus stations had generated a larger affect on the bus ridership on weekends.

Concerning the four-time slots on weekdays, the betweenness centrality in the road network, the distance to subway stations and rail station generated the largest influence on bus ridership during morning peak hours but the smallest influence at night-time off-peak hours or afternoon peak hours; the betweenness centrality in the bus network generated the largest influence on bus ridership during afternoon peak hours but the smallest influence at night-time off-peak hours. Additionally, the density of subway stations and road density had a significantly positive influence on bus ridership during morning peak hours, but the density of subway stations had a negative influence during daytime off-peak hours. Overall, the bus ridership during morning peak hours were more impacted by the betweenness centrality in the road network, the distance to subway stations and rail station, and subway density than the other time slots, while that during afternoon peak hours were more likely to be influenced by the betweenness centrality in the bus network.

The spatial lag of the betweenness centrality in the bus network and road network and road density generated a significantly negative influence on bus ridership at all the selected time slots, indicating that an increase in these indicators of a community’s neighbors had a negative influence on its bus ridership (Fig. 5). The spatial lag of the distance to subway stations, airport, and rail stations had a significant positive influence on bus ridership at all the selected time slots, indicating that an increase in the distance to subway stations, airport and rail station of a community’s neighbors might have an overall positive influence on bus ridership. Bus ridership on weekdays was more sensitive to a decrease in betweenness centrality in the bus network and road network, a decrease in road density, and an increase in the distance to the airport than on weekends. Bus ridership was more sensitive to an increase in the density of subway stations and a decrease in the distance to bus stations and rail stations on weekends than on weekdays. Concerning the four-time slots on weekdays, bus ridership during afternoon peak hours was most sensitive to the increased betweenness centrality in the bus network and road network and the road density of its neighbors than the other three time slots. Bus ridership at daytime off-peak hours was most sensitive to the increased distance to subway stations and airports. Bus ridership at all the time slots was more influenced by the betweenness centrality in the bus network of its neighbors than by the other `indicators.

Figure 6 shows the coefficients of the social-economic attributes (including housing price, employment, and population) and their spatial lag, which respectively represent the impacts of social-economic attributes of a community and its neighbors on its bus ridership; thus, a positive coefficient means that the housing price, employment, and population of a community and its neighbors have a positive influence on its bus ridership.

Housing price, employment, and population all had positive impacts on bus ridership on weekends and weekdays. The impact magnitude of housing price and the population was greater on weekends than on weekdays, but the impact magnitude of employment was greater on weekdays than on weekends. Specifically, the elasticities of housing price and population were respectively 0.5097 and 0.0180 on weekdays, which were lower than those on weekends (0.6569 and 0.0267), indicating that housing prices and the population had generated a larger influence on the bus ridership on weekends than that on weekdays. The elasticity of employment was 0.0225 on weekdays, 0.0195 in a week, and 0.0145 on weekends. The impact magnitude on weekdays was higher than that on weekends, indicating that employment had generated a larger influence on the bus ridership on weekdays than that on weekends.

Concerning the time slots on weekdays, both housing price and employment generated the largest influence on bus ridership during afternoon peak hours but the smallest influence at night-time off-peak hours; population generated the largest influence on bus ridership during morning peak hours but the smallest influence at daytime off-peak hours. Specifically, the elasticities of housing price and employment during afternoon peak hours (0.3676 and 0.0159) were slightly higher than those during morning peak hours (0.3450 and 0.0143), daytime off-peak hours (0.3410 and not significant), and much higher than those during night-time off-peak hours (0.2845 and 0.0099), indicating that housing prices and employment had a larger influence on bus ridership during afternoon peak hours than during the other time slots. The elasticity of the population during morning peak hours (0.0290) was higher than that during afternoon peak hours (0.0277) and at daytime off-peak hours (0.0189), indicating that the population had a larger influence on the bus ridership during morning peak hours than during the other time slots.

Concerning the spatial neighbouring effects, the housing price in a community’s neighbors generated a negative influence on bus ridership in a week, weekdays, weekends, and all four-time slots. The population in a community’s neighbors had a negative influence on bus ridership on weekends, during morning peak hours, and daytime off-peak hours on weekdays, but a positive effect on bus ridership during afternoon peak hours. The employment in a community’s neighbors had a positive influence on bus ridership on weekends and during night-time off-peak hours, but a negative influence on bus ridership during morning peak hours and daytime off-peak hours.

Figure 7 shows the coefficient related to the built environment attributes and their spatial lag, which respectively represent the impacts of density indicators in a community and of its neighbors on its bus ridership; thus, a positive coefficient means that the density indicators in a community and its neighbors have a positive influence on its bus ridership.

Education and catering had a significant influence on bus ridership on both weekends and weekdays, but the impact magnitude on bus ridership on weekends was higher than that on weekdays. Specifically, the elasticities of education and catering on weekends were respectively 0.0102 and 0.0167, which were higher than the values of −0.0082 and 0.0137 on weekdays. Possible reasons might be that during the weekends, people have more spare time to visit catering and that university students are more likely to go off campus for shopping and entertainment. Healthcare had a positive influence on bus ridership on weekdays but no significant influence on weekends. That is, healthcare was one of the key determinants of bus ridership on weekdays instead of weekends, possibly because most hospital departments are closed on weekends. Commercial facilities and financial spots had a significantly positive influence on bus ridership on weekends but no significant influence on bus ridership on weekdays. Specifically, the elasticities of commercial facilities and financial spots were respectively 0.0096 and −0.0148 on weekends, which indicated that the higher the commercial facilities and the lower the financial spots, the higher the bus ridership of a community on weekends. The density of tourism spots had no significant influence on bus ridership on either weekdays or weekends.

Concerning the time slots on weekdays, bus ridership at daytime off-peak hours was more sensitive to catering and tourist spots than the other time slots, while the bus ridership during morning peak hours and afternoon peak hours were more sensitive to the healthcare and commercial facilities, respectively. Specifically, the elasticities of catering and tourist spots during daytime off-peak hours (0.0171 and 0.0066) were higher than those during morning peak hours (0.0135 and 0.0027), afternoon peak hours (0.0091 and not significant), and night-time off-peak hours (0.0052 and 0.0061), indicating that having higher catering and tourist spots of a community had the largest influence on bus ridership during daytime off-peak hours. Healthcare had a significantly positive influence on bus ridership during the morning peak hours but was not significant during the other time slots. The elasticity of commercial facilities during afternoon peak hours was 0.0032, which was higher than that during daytime off-peak hours (0.0026).

The spatial lag of the built environment indicators all had a significant influence on bus ridership in a week, but the impact varied across different time slots. Specifically, the average bus ridership in a community was positively impacted by the education, commercial facilities, and tourist spots of its neighbors but negatively influenced by the catering, financial spots, and healthcare. Thus, the increased education, commercial facilities, and tourist spots of neighbors generated a positive influence on bus ridership, but the large catering, financial spots, and healthcare of neighbors generated a negative influence. Similar results could be found for the selected time slots, except that there was no significant influence of education during morning peak hours and daytime off-peak hours, of commercial facilities on weekends, or financial spots on weekday and daytime off-peak hours; there was a negative influence of tourist spots during daytime off-peak hours and a positive influence of healthcare during morning peak hours. The magnitude of the impact of the catering, financial spots, and tourist spots of neighbors was higher on weekends than on weekdays, while that of the education, commercial facilities, and healthcare of neighbors was higher on weekdays than on weekends. Bus ridership during morning peak hours was more sensitive to the catering, commercial facilities, and healthcare of neighbors than bus ridership in the other three-time slots on weekdays, while that during afternoon peak hours was most sensitive to the education and tourist spots of neighbors.

The estimation of spatial econometric models might be influenced by the setting of the weight matrix. Commonly, the weight matrix can be built based on the adjacency matrix, the inverse distance, the transport distance, or the travel time (e.g., Bottasso et al. 2014; Feng et al. 2019). Since the transport distance and the travel time could be reflected by the transport indicators in our model, this study adopts the adjacency matrix as a substitution for inverse distance. Thus, the robustness test is implemented by replacing the inverse distance matrix with the adjacent matrix.

After replacing the inverse distance square matrix with the adjacent matrix in the SDM, the results showed that the betweenness centrality in the bus network, distance to subway stations, betweenness centrality in the road network, road density, housing price, employment, education, commercial facilities, tourist spots and healthcare all had similar influences on bus ridership (see Table 2). That is, the influence of these indicators on bus ridership was not influenced by the matrix setting. There were also some indicators with different influences on bus ridership after replacing the inverse distance square matrix with the adjacent matrix in the SDM. In the model with an adjacent matrix, the bus stations had a positive influence on the bus ridership on weekends and a negative influence on that in a week; the distance to bus stations has a negative influence on bus ridership in a week and daytime off-peak hours; the distance to the airport has a positive influence on bus ridership in a week, on weekends and weekdays, and during three-time slots; the distance to rail station had a positive influence on bus ridership on weekends, while financial spots had a positive influence on bus ridership on weekends; population and catering had a negative influence on bus ridership in a week, and financial spots had a positive influence on bus ridership on weekends. All these indicators showed different influences on bus ridership compared with the baseline model.

To test for potential endogeneity problems, the Hausman specification test and over-identification are introduced. First, the Hausman specification test is employed to detect whether endogeneity has a significant impact on the results by comparing the estimation results with and without instrumental variables (IVs). If the estimations are not significantly different, this reveals significant endogeneity that affects the robustness of the estimation results. According to the data availability and indicator characteristics, the revenue income of each community is chosen as the IV for the population. The results of the Hausman test show that all the variables in our models are exogenous. Second, the over-identification test is employed to detect whether the IVs and the corresponding variables are strictly exogenous, and the results show that the revenue income is strictly exogenous and could thus be chosen as the IV for the population (Table 3). Overall, there are no endogeneity problems in the model.