## 3 Data and Methodology
### MGWR Model
This indicates that the spatial correlation in ride-hailing demand primarily arises from the spatial lag of the dependent variable rather than the spatial correlation of the error terms. In other words, ride-hailing demand is influenced not only by local factors but also by spillover effects from neighboring areas, and this spatial effect cannot be captured by OLS. Therefore, SLM is more appropriate for fitting this demand. Additionally, spatial effects are generally stronger on workdays than on holidays, particularly during the overnight period, where the LM-Error and LM-Lag values are the highest (workdays: 139.838 and 182.903; holidays: 165.068 and 209.493), indicating that ride-hailing demand is highly concentrated during this time, with significant interaction between regions. This may be due to the imbalance of ride-hailing supply and demand during late-night hours, making the demand highly dependent on neighboring areas' spillover effects. In contrast, during daytime and evening peak hours, spatial effects are still significant, but the spatial correlation is weaker on holidays, indicating that holiday travel patterns are more dispersed, \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Time Period**} & \multicolumn{2}{c}{**LM-Error**} & \multicolumn{2}{c}{**LM-Lag**} & \multicolumn{2}{c}{**RLM-Error**} & \multicolumn{2}{c}{**RLM-Lag**} \\ \cline{2-9}  & **Value** & \(p\) & **Value** & \(p\) & **Value** & \(p\) & **Value** & \(p\)** \\ \hline Workday & & & & & & & \\ Morning Peak & 69.079 & 0.000 & 110.439 & 0.000 & 0.842 & 0.3590 & 42.201 & 0.000 \\ Morning Day & 55.470 & 0.000 & 113.420 & 0.000 & 0.981 & 0.3221 & 58.931 & 0.000 \\ Evening Peak & 72.385 & 0.000 & 112.630 & 0.000 & 0.363 & 0.5468 & 40.608 & 0.000 \\ Evening & 43.843 & 0.000 & 77.088 & 0.000 & 0.457 & 0.4991 & 33.702 & 0.000 \\ Overnight & 139.838 & 0.000 & 182.903 & 0.000 & 3.042 & 0.0811 & 46.107 & 0.000 \\ \hline Holiday & & & & & & & \\ Morning Peak & 44.950 & 0.000 & 79.194 & 0.000 & 0.056 & 0.8126 & 34.300 & 0.000 \\ Morning Day & 30.343 & 0.000 & 66.847 & 0.000 & 1.365 & 0.2426 & 37.869 & 0.000 \\ Evening Peak & 25.515 & 0.000 & 47.373 & 0.000 & 0.874 & 0.3498 & 22.733 & 0.000 \\ Evening & 24.279 & 0.000 & 43.471 & 0.000 & 1.324 & 0.2498 & 20.515 & 0.000 \\ Overnight & 165.068 & 0.000 & 209.493 & 0.000 & 3.276 & 0.0703 & 47.700 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of Lagrange multiplier (LM) diagnostics. with less impact between regions. Therefore, during workday peak hours and overnight periods, the focus should be on the spillover effects between regions, while, on holidays, due to more random demand distribution, a more nuanced analysis considering other spatial factors is needed. #### 4.4.2 Local Model Results

Although SLM effectively addresses the spatial autocorrelation issue in ride-hailing demand and significantly improves model fit, it assumes consistent regression coefficients across the entire study area, which fails to capture the spatial heterogeneity of variable effects between regions. In reality, ride-hailing demand is influenced by several factors, including population density, commercial activities, and public transportation accessibility, which may have significantly different effects in different spatial locations. This spatial heterogeneity cannot be accurately captured by global models such as SLM, so local models are necessary to analyze the spatial variation in the influence of variables, thereby improving the model's explanatory power and prediction accuracy. Compared to the global models, the GWR and MGWR models outperform in terms of goodness of fit and spatial adaptability. In all the time periods, the R\({}^{2}\) values for MGWR are higher than for both GWR and SLM. For instance, during the holiday evening peak period, the R\({}^{2}\) for MGWR reaches 0.767, significantly higher than GWR (0.708) and SLM (0.575), indicating that MGWR is better at capturing spatial heterogeneity in variable effects.