## 1 Introduction
One is the scale effect, that is, different area unit sizes; the other is the zoning effect, that is, area elements with different shapes, such as a square grid [20], traffic analysis zone [21; 22; 23], Voronoi diagram [14; 21; 23; 24; 25], etc. Previous work selected a spatial scale. For example, [PERSON] et al. selected a 200 \(\times\) 200 m square grid as the basic unit to study the impact of the built environment on ride-hailing [15]; [PERSON] et al. selected a 500 \(\times\) 500 m square grid as the basic unit of land use classification in Shanghai [26]; and [PERSON] et al. selected a 200 \(\times\) 200 m square grid as the basic unit of land use classification in Singapore [27]. The methods for determining the optimal scale include the nugget-sil ratio (NSR) [18], the optimal parameter-based geographical detector (OPGD) [28], and comparison of the coefficient of determination \(R^{2}\) values from multiple regressions [29] at different scales. The NSR determines the best scale by comparing the ratio of intra-unit variance and inter-unit variance, because variance represents how much information is lost in the process of aggregation [16], and the NSR only considers dependent variables [18]; the OPGD compares the 90% quantiles of the \(q\) value results of the geographical detectors at different scales and selects the scale corresponding to the maximum 90% quantile of the \(q\) value of all explanatory variables as the best scale, and independent and dependent variables are also considered [28]. The existingresearch on ride-hailing mostly uses grids as area units [15], and there are few studies on the optimal scale of impact for the built environment on the ridership of ride-hailing. This paper mainly summarizes related studies about ride-hailing from the aspects of variable selection, the size of the analysis unit, and modeling methods, as shown in Table 1. In terms of modeling methods, OLS [30; 31], GWR [14; 15; 30; 32], GTWR [33], MGWR [25; 34], a nonlinear regression model [35], and other models [36; 37; 38; 39] have often been used in the research investigating built-environment impacts on the ridership of ride-hailing, and the global impact or local spatial heterogeneity of each built-environment variable on ride-hailing is analyzed separately. The geographical detector can detect the influence of a single variable and the interaction of variables, and eliminate the influence of the multicollinearity of variables [40]. The geographical detector model has been widely used in research in various fields, such as health risk assessments [40; 41; 42; 43; 44; 45; 46], crime prediction [47; 48], land health assessments [49; 50], carbon emission influencing factors [51; 52], etc. To the best of our knowledge, the geographical detector model has not been used in the impact of the built environment on the ridership of ride-hailing. These studies have shown that the built environment has an important impact on the ridership of ride-hailing. However, few studies have considered the impact of the modifiable areal unit problem (MAUP) on the ride-hailing analysis results. In addition, existing studies have not analyzed the interaction effects from built-environment factors on ride-hailing ridership. To fill the above gaps, this study utilized the nugget-sill ratio (NSR) [18] method and the optimal parameter-based geographical detector (OPGD) [28] model to explore the relative importance and interactive impacts of the explanatory variables of the built environment on ride-hailing ridership, mainly solving the following four questions: (1) What is the optimal grid scale for the aggregation of the built environment and the ridership of ride-hailing? (2) What is the optimal data discretization method of the explanatory variables for the geographic detector model? (3) What is the ranking of the impact importance of the built-environment variables? (4) How effective is the interaction of variable combinations?