# The Nonlinear and Threshold Effect of Built Environment on Ride-Hailing Travel Demand
## 2 Literature Review
### Nonlinear Effects between Traffic Travel and Influencing Factors  
Analyzing the connection between influencing factors and travel behavior can be approached using various methods. In recent years, machine learning-based techniques such as Random Forests, Gradient Boosting Decision Trees (GBDT), and XGBoost have been extensively utilized to investigate such matters. For example, in investigating key factors influencing mode choice, [PERSON] et al. [34] utilized GBDT models and considered the built environment factors of residential and workplace areas to investigate the impact of built environment and commuting plans on the choice for mode of commuting. The results suggest that built environment variables of residential areas are more significant than those of workplace areas, and most built environment variables exhibit nonlinear relationships with the car mode choice. [PERSON] et al. (2018), through a survey of car users, defined 4 km as the threshold for short-distance travel and employed Random Forests to examine the essential factors influencing transportation mode selection for short-distance travelers. They analyzed the complex relationships and found significant threshold effects for key influencing factors on mode choice. Specifically, they pinpointed 1.2 km as the tipping point for car and active mode selection, with a notable surge in the likelihood of car usage beyond this threshold. Regarding the study of the nonlinear relationship between travel distance and influencing factors, [PERSON] et al. (2018) utilized bicycle travel survey data from Xi'an, China, utilizing the XGBoost model to investigate the nonlinear and interplay effects between the built environment and cycling distance. They utilized SHAP for interpretation. The results indicated that the road network structure pattern contributed the most, and bicycle lane infrastructure also played an important role. They also analyzed the interaction effects of key variables in the road network structure, such as average geodesic distance, and other variables on cycling distance. [PERSON] and [PERSON] (2018) constructed their analysis using regional travel data from the Twin Cities, US, and utilized GBDT to examine the non-linear correlation between the built environment and travel distance across driving, public transit, and active modes. The results revealed nonlinear and threshold effects between the built environment and travel distance, with different transportation modes exhibiting different impact effects. Numerous scholars have also focused on the nonlinear impacts of influencing factors on travel demand. For instance, [PERSON] et al. (2018) segmented the ride-hailing trip data into single/shared trips based on a carpooling identification algorithm, and utilized the GBDT model to investigate the relationship between the built environment and carpooling origin-destination points. The findings revealed that proximity to the city center, land use diversity, and road density are pivotal factors influencing travel behavior, and threshold effects were analyzed using partial dependence plots. [PERSON] et al. (2018) aimed to identify determinants of subway ridership and applied the GBRT model to explore the nonlinear impact that accessibility has on subway ridership from a spatiotemporal perspective. They found that accessibility indicators collectively contributed over 60% to predicting subway ridership at different times. [PERSON] et al. (2018) utilized LightGBM to study the nonlinear, threshold, and synergistic effects of last-mile facilities on subway ridership. The results showed that last-mile facilities made the largest contribution to predicting subway ridership and needed to reach a threshold to maximize subway ridership. Through 2D-PDP analysis of their synergistic effects, they found that the influence of last-mile facilities on subway ridership may vary depending on the provision of public transit and built environment factors.