# The Nonlinear and Threshold Effect of Built Environment on Ride-Hailing Travel Demand
## 1 Introduction  
Transportation Network Companies (TNCs) such as Uber, Lyft, and DiDi build service platforms based on Internet technology to match vehicles online and provide travel services for travelers in real time, also known as ride-hailing services. Amid the swift progress of information technology and the popularity of smartphones, ride-hailing as a shared travel mode has reduced passenger waiting time and improved travel efficiency, and is gradually becoming one significant mode of daily urban transportation [1]. The scale of ride-hailing users in China continues to expand, where the ride-hailing user base has surged to 453 million at the end of 2021. Although ride-hailing provides passengers with high accessibility services, research has shown that there is an alternative or complementary relationship between ride-hailing and transit [2, 3]. Some researchers have found that ride-hailing has replaced traditional modes of transportation, leading to various issues including traffic congestion, increased energy consumption, and higher vehicle mileage, which in turn contribute to additional traffic pressure [4]. As a microscopic manifestation of urban spatial form, the built environment significantly influences travel patterns [5, 6, 7]. A multitude of scholars have scrutinized the nexus between the built environment and traffic travel, and have studied different models, including the metro [8, 9], taxis [10, 11, 12], dockless bike-sharing [13, 14] and private cars [15, 16, 17]. As a rising mode of travel, ride-hailing is gradually affecting the change in residents' travel demand. The built environment factors also wield a significant influence on this phenomenon. In the pursuit of promoting green, low-carbon, and sustainable urban development, delving into the impact mechanism between the built environment and ride-hailing becomes imperative. Researchers have discussed the relationship between the built environment and the demand for ride-hailing travel. Most of them start from the characteristics of spatial attributes, including spatial autocorrelation and spatial heterogeneity. Spatial autocorrelation effects are usually explained by spatial econometric models [18]. Geographically Weighted Regression (GWR) enhances regression accuracy by creating a local spatial weight matrix to estimate spatial variations [19]. The GWR and its variations are frequently utilized to investigate the spatial diversity in how the built environment influences ride-hailing travel demand [20; 21; 22]. On the one hand, these models assume that there is a linear or generalized linear relationship between the two, and the conclusions may have some deviations. On the other hand, the machine learning method possesses the advantage of not adhering to the assumption of linear relationships between variables in multivariate fitting, allowing for more flexible modeling of complex relationships, which helps find complex nonlinear relationships [23]. Based on this, contemporary research has started to explore the nonlinear impact of the built environment on travel behavior, and the threshold effect of the built environment can also be observed [9; 24; 25]. However, there are few studies on the nonlinear correlation and threshold effect amid the built environment and ride-hailing travel demand. To address this gap, this study utilizes weekday ride-hailing travel data from Nanjing, China, and applies a machine learning method, XGBoost, to explore the complex relationship between the built environment and the ride-hailing travel demand, using the XGBoost model to identify the important built environment characteristics influencing ride-hailing travel demand. The SHAP summary plot and traditional PDPs are used to explain the threshold effect between the built environment and the ride-hailing service. It furnishes a foundation for TNCs to enhance their current ride-hailing service and has policy implications for how future urban land use and transportation strategies can effectively affect the ride-hailing service.