## 5 Results and Analysis
### The Joint Nonlinear Effect of the Floor Area Ratio (FAR) and Accessibility on Ridership  
When the MGWR and GBDT models are used to capture the linear and nonlinear influences on local spatial heterogeneity affecting passenger flow, respectively, it is found that accessibility is one of the main factors affecting passenger flow, while the building plot ratio mainly characterises the development density of the built environment [32]. In order to deeply investigate the nonlinear effects on total passenger flow and inbound and outbound passenger flow under the condition of linkage of building volume ratio and accessibility built environment factors, this study creates three-dimensional bias dependency diagrams of total passenger flow and inbound and outbound passenger flow under the condition of linkage of the building volume ratio and accessibility built environment factors, as shown in Figure 14a-c.  
As can be seen in Figure 14a, the peaks in total passenger flow are concentrated in areas with FAR > 2 and accessibility < 25 min, indicating that the combination of high development density and short commuting time significantly attracts passenger flow. Areas with FAR > 2 and accessibility < 25 min can be targeted for further optimisation of public transport services to shorten commuting time and increase the attractiveness of these areas. As can be seen in Figure 14b, accessibility takes values from 0 to 65 min in the main, and when the building volume ratio is certain, the change in accessibility time is not significant. This indicates that, in a fixed area, or within a certain range of accessibility, metro inbound traffic is mainly influenced by building volume ratio. When the accessibility time is certain, the inbound passenger flow tends to increase and then decrease with the building volume ratio, and the peak occurs at the accessibility \(\approx\) 56 min. This indicates that, as the building density increases, more and more people tend to use the metro, but after reaching a certain peak, as the buildings become denser, the inbound passenger flow starts to decrease instead. This may be due to the fact that over-dense buildings bring problems such as traffic congestion and crowdedness, which reduces people's willingness or efficiency to use the metro. Therefore, for areas with high building density, it is necessary to consider how to alleviate traffic congestion caused by over-densification of buildings to ensure the efficient operation of the metro system. Figure 14c shows that accessibility is insensitive to changes in outbound traffic at FAR = 1.5, highlighting the stability of outbound demand in office-concentrated areas. This suggests that the distribution of office areas is relatively stable within the lower building density zones and that the demand for travelling out of these zones is not significantly affected by the time taken to reach their destinations. The attractiveness of these areas can be further enhanced by improving accessibility and public transport facilities. When the FAR is between 1.5 and 3, the combination of the building plot ratio and accessibility does not attract much outbound traffic. This suggests that, for medium building density areas, there should theoretically be more people needing to travel via the metro to reach these places, but in practice, there is not a significant increase. Possible  
Figure 14: Partial dependence of floor area ratio (FAR) and accessibility built environment factors on total ridership and inbound and outbound ridership. (**a**) On total ridership; (**b**) on inbound ridership; (**c**) on outbound ridership. reasons for this include traffic congestion and capacity constraints of public transport facilities offsetting the potential increase in travel demand due to increased building density. Traffic congestion and public transport carrying capacity issues can be focussed on to unlock potential travel demand in these areas through rational transport planning and infrastructure development.