# The Nonlinear and Threshold Effect of Built Environment on Ride-Hailing Travel Demand
## 5 Results and Discussion
### Marginal Effects Analysis  
The above results help determine the importance and positive/negative feedback of each built environment variable in influencing ride-hailing travel demand. To further clarify the nonlinear relationship between individual built environment variables and the demand for ride-hailing travel, partial dependence plots can be utilized to visualize the marginal impacts of built environment features on model predictions [45]. This allows capturing the effective scope of influence and threshold impacts on ride-hailing travel demand. Figure 3 illustrates the non-linear relationship between density variables and ride-hailing travel demand. Dining, finance, company, medical, shopping, accommodation, and leisure POI facilities positively influence ride-hailing travel demand. As the density of POI facilities rises, so does the demand for ride-hailing. However, the range of influence and thresholds vary among different types of POI facilities. For example, the influence of dining  
Figure 2: SHAP summary plot of independent variables. facility density on ride-hailing travel demand gradually increases between 0 and 700, and stabilizes after exceeding 700. Similarly, for financial facilities, the impact stabilizes after surpassing 100. Scenic spots have a negative impact on ride-hailing travel demand, as illustrated in Figure 3i. A noticeable decrease in demand occurs within the range of 0 to 20. This could be attributed to the fact that scenic spots are typically located near public transportation hubs, making it convenient for tourists to travel without relying on ride-hailing services. Additionally, these scenic spots may often be situated in suburban areas, where the cost of utilizing ride-hailing services is relatively higher. The influence of commercial residence areas and science, education, culture areas on ride-hailing travel demand exhibits a trend of rising and then declining, as shown in Figure 3f,h. This indicates that there are certain advantageous intervals for influencing ride-hailing travel demand. Commercial residence areas are most attractive to ride-hailing travel demand within the range of 20 to 90, while science, education, and culture areas exhibit peak influence between 50 and 150. Figure 3: Nonlinear effect of density variables on ride-hailing travel demand. As shown in Figure 3, population density generally impacts ride-hailing travel demand positively. Within the range of 0 to 20,000 person/km\({}^{2}\), there is significant fluctuation in ride-hailing travel demand. The lowest demand for ride-hailing occurs when the population density is 5000 person/km\({}^{2}\). This suggests that areas with either sparse or excessively dense populations exhibit higher ride-hailing travel demand. This could be attributed to several factors: in regions with low population density, public transportation accessibility may be poor while road connectivity is high, making ride-hailing a preferred mode of transportation due to the lack of viable alternatives. Additionally, in densely populated areas, where the separation between residential and commercial areas is pronounced, ride-hailing becomes more favorable. Figure 4 illustrates a noticeable positive impact of road length on ride-hailing travel demand within the grid, particularly within the range of 0 to 4. As road length increases, there is a clear rise in ride-hailing travel demand, which stabilizes once the road length surpasses this range. In Figure 4, when the length of slow roads within the grid reaches 1 km, there is a sharp decrease of approximately 500 ride-hailing travel trips. Figure 4 illustrates that the influence of the number of road nodes on ride-hailing travel demand is most significant within the range of 0 to 3. As the number of road nodes increases from 3 to around 40, there is a gradual increase in demand. However, this impact stabilizes once the number of road nodes exceeds approximately 40 per grid. As illustrated in Figure 5, the demand for ride-hailing remains constant when the land use mix is between 0 and 0.4.