## 3 Data and Methodology
### MGWR Model
Additionally, the R\({}^{2}\) improvement for MGWR during the overnight period is especially significant workdays: 0.739; holidays: 0.721), further indicating that this model provides stronger explanatory power during periods of complex demand distribution. Regarding model selection metrics, the results for the AIC and log-likelihood further confirm these findings. The AIC for the OLS model is the highest in all the periods, indicating poor performance in balancing goodness of fit and model complexity. For instance, in the workday overnight period, the AIC for OLS is 1810.895, while, for SLM and MGWR, it drops to 1660.456 and 1616.246, respectively, with the latter being the best among all the models. Furthermore, the log-likelihood for MGWR is the highest in all the periods, such as \(-1327.596\) during the holiday morning peak, higher than GWR (\(-1402.475\)) and SLM (\(-1400.562\)), suggesting that MGWR not only significantly improves model fit but also demonstrates greater robustness in accounting for model complexity. Additionally, the impact of time periods on model performance shows significant differences. During peak hours, the spatial autocorrelation in ride-hailing demand is stronger, and models like SLM, GWR, and MGWR perform better, while OLS is unable to capture these features effectively. Particularly during the overnight period, whether on workdays or holidays, the spatial concentration of demand is most significant, further highlighting the advantages of the MGWR model, which shows optimal performance in the AIC and log-likelihood. This suggests that MGWR has a significant advantage in capturing the spatial heterogeneity of variable effects across different regions, especially during periods of complex and fluctuating demand distribution. For local models like GWR and MGWR, bandwidth is an important indicator of the spatial effect range of variables [73]. GWR uses a single bandwidth, meaning all the variables share the same spatial scale, while MGWR allows different variables to have different bandwidths, making it more flexible in capturing spatial heterogeneity. In this study, by comparing the bandwidths of MGWR and GWR, we further explore the spatial variation in the impact of variables and analyze the characteristics of ride-hailing demand in different time periods. Table 7 shows that the bandwidth for GWR is mostly between 181 and 305, indicating that a larger smoothing window is applied to all the variables, averagingtheir spatial variation and potentially ignoring some spatial heterogeneity. In contrast, the bandwidth distribution for MGWR is more diverse, ranging from 49 to 610, indicating significant differences in the spatial effects of variables at different scales. This is the key reason why MGWR outperforms GWR in capturing spatial heterogeneity. Examining the variables themselves, there are significant differences in their spatial effects. For example, the bandwidth for bus stop density is consistently small (MGWR: 49-54), indicating that its impact is limited to a smaller range. Ride-hailing primarily serves as a short-distance connector, complementing surrounding public transportation facilities. The bandwidth for distance from the city center reaches 610 during overnight periods, indicating that late-night travel has a broader spatial impact and is more influenced by the overall urban structure than by local facilities. Additionally, the bandwidth for financial POIs is smaller during workdays (76-115) but significantly expands during holidays, suggesting that financial districts may have a greater impact on a wider range of travel due to commercial and leisure activities. At the same time, the spatial effect range of ride-hailing demand is dynamic. During peak periods, spatial dependency is more localized, with smaller MGWR bandwidths for variables such as road and building density, reflecting the direct influence of local conditions on commuting demand.