# Analyzing Multiscale Spatial Relationships between the House Price and Visual Environment Factors
## 3 Experiment and Results
### Spatial Scale Analysis  
The bandwidths indicating the data-borrowing range can vary across parameter surfaces. The individual optimal bandwidths specific to each parameter in the MGWR model are given in Table 5, where it can be seen that the processes being modeled operate at different spatial scales. The GWR calibration yielded an optimal bandwidth of 166 nearest neighbors in Beijing, implying fairly localized processes. As can be seen from the table, the closer the bandwidth of the variable is to the total number of samples, the more likely it is to affect the house price on a large scale or even globally.  
The parameter estimates associated with Beijing's house price, such as the D_Hospital, the D_PrimarySchool, elevator, the GVI, and the NAI, are global; the optimal bandwidth  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Beijing**} & \multicolumn{2}{c}{**Chongqing**} \\ \cline{2-5}  & \(\mathbf{R^{2}}\) & **AICc** & \(\mathbf{R^{2}}\) & **AICc** \\ \hline HPM & 0.56 & 3319.564 & 0.706 & 1221.922 \\ GWR & 0.834 & 2284.684 & 0.762 & 1168.135 \\ MGWR & 0.895 & 1815.088 & 0.831 & 1049.259 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of models.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variables**} & \multicolumn{2}{c}{**Beijing**} & \multicolumn{2}{c}{**Chongqing**} \\ \cline{2-5}  & **MGWR** & **GWR** & **MGWR** & **GWR** \\ \hline
**Covariates** & & & & \\ D\_Bus & 79 & 166 & 531 & 286 \\ D\_Subway & 968 & 166 & 332 & 286 \\ D\_Hospital & 1617 & 166 & 744 & 286 \\ D\_Kindergarten & 1635 & 166 & 248 & 286 \\ D PrimarySchool & 1518 & 166 & 97 & 286 \\ D\_MiddleSchool & 127 & 166 & 736 & 286 \\ D\_Government & 1214 & 166 & 744 & 286 \\ D\_Park & 1336 & 166 & 744 & 286 \\ Elevator & 1635 & 166 & 218 & 286 \\ Year & 120 & 166 & 744 & 286 \\ Area & 43 & 166 & 44 & 286 \\ \hline \hline
**Visual factors** & & & & \\ GVI & 1635 & 166 & 744 & 286 \\ SVI & 43 & 166 & 744 & 286 \\ WI & 43 & 166 & 733 & 286 \\ MI & 82 & 166 & 113 & 286 \\ BVI & 43 & 166 & 66 & 286 \\ NAI & 1635 & 166 & 240 & 286 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of parameter bandwidth between MGWR and GWR.  
in each case is as large as it could be (1640 nearest neighbors). The relationship between Beijing's house price and the D_Subway exhibits spatial nonstationarity, but the process varies at a broad regional scale (optimal bandwidths of 968). The other variables have impacts on Beijing's house prices that vary over relatively short distances, with the optimal bandwidths for the SVI being forty-three nearest neighbors, the MI being eighty-two nearest neighbors, and the BVI being forty-three nearest neighbors.  
The parameter estimates associated with Chongqing's house price, such as the D_hospital, the D_MiddleSchool, year, the GVI, and the SVI are global; the optimal bandwidth in each case is as large as it could be (747 nearest neighbors). The relationship between Chongqing's house price and the D_Bus exhibits spatial nonstationarity, but the process varies at a broad regional scale (optimal bandwidths of 531). The other variables have impacts on Chongqing's house price that vary over relatively short distances, with the optimal bandwidths for the area being forty-four nearest neighbors and the BVI being sixty-six nearest neighbors.