# Spatiotemporal Heterogeneous Effects of Built Environment and Taxi Demand on Ride-Hailing Ridership
## 3 Methodology
### Modeling Approach  
In this study, the MGWR model is used to examine the correlation between built environment characteristics and ride-hailing ridership. The main reason is that, as mentioned in the previous sections, the global model is difficult to measure the spatial variation relationship. In addition, GWR is a local regression model that can address spatial heterogeneity by allowing the parameters to vary across spatial units with a fixed spatial scale. However, the fixed spatial scale for each exogenous variable in GWR may cause misspecification of scales for some factors and unnecessary noise. The MGWR model reflects the influence scale of different independent variables. Thus, it is necessary to apply this method to estimate the spatial and temporal heterogeneity and spatial scale effects of the impact of the built environment on ride-hailing ridership. Ordinary least squares (OLS)  
The OLS linear regression is a global regression modeling approach, which is commonly used to regress an endogenous variable on exogenous variables. In OLS regression, it is assumed that the link between the endogenous variable and exogenous variables is stationary and constant over space [32]. In this study, the link between ride-hailing ridership (\(y\)) and its influencing factors (\(x_{1},~{}x_{2},\dots,~{}x_{n}\)) is presented as a line of best fit. The OLS can be shown as follows:  
\[y=\beta_{0}+b_{1}x_{1}+b_{2}x_{2}+\dots+b_{n}x_{n}+\varsigma, \tag{2}\]  
where \(x_{1},x_{2},\dots,x_{n}\) represent the built environment variables and taxi ridership; \(\beta_{0}\) represents the intercept; \(b_{1},b_{2},\dots,b_{n}\) represent the corresponding parameters; \(\varsigma\) represents the random error term. GWR \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Description** & **Mean** & **S.D.** \\ \hline Density & & & \\ Population density & Population size divided by the grid area & & \\ (thousand persons/km\({}^{2}\)) & 12.641 & 19.460 \\ Housing price & Average housing prices in the grid (thousand & & \\  & yuan/m\({}^{2}\)) & 16.904 & 19.683 \\ Diversity & & & \\ Land use mix & The entropy value of thirteen categories of POIs & 0.793 & 0.208 \\ Design & & & \\ Road density & Road lengths divided by the grid area (km/km\({}^{2}\)) & 7.891 & 4.601 \\ Bike lane density & & Bike lane lengths divided by the grid area & 0.821 & 2.047 \\ Distance to transit & & & \\ Bus stop density & Number of bus stops divided by the grid area & & \\  & (/km\({}^{2}\)) & 3.92 & 4.510 \\ Metro station density & Number of metro stations divided by the grid & & \\  & area (/km\({}^{2}\)) & 0.25 & 0.987 \\ Distance to the nearest bus stop & Distance from the grid centroid to the nearest & & 0.307 & 0.214 \\ Distance to the nearest metro station & Distance from the grid centroid to the nearest & & 1.442 & 1.363 \\ Destination accessibility & & & \\ Distance to CBD & Distance from the grid centroid to CBD (km) & 10.155 & 5.735 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical descriptions of the built environment variables. In traditional global regressions, it is assumed that the link between the endogenous variable and exogenous variables is stationary across the study area. This assumption may lead to biased estimations because the link varies over space in spatial relationships [33]. The GWR relaxes assumptions and allows parameters to vary across space [34]. Aiming to reduce errors caused by spatial non-stationary effects, it estimates a local parameter for each spatial unit separately. Thus, GWR can effectively address the spatial heterogeneity in the link between ride-hailing ridership and its influencing factors in this study.