# How Does the Built Environment Affect Drunk-Driving Crashes? A Spatial Heterogeneity Analysis
## 4 Results
### Results of the GWPR Model  
As shown in Table 4, different spatial GWPR models were constructed based on the spatial kernel functions of the adaptive bi-square and adaptive Gaussian models. The AICc values in GWPR models were all smaller than those in the MLR model, which indicated that the crash models considering spatial heterogeneity had better fitting accuracy. Moreover, the AICc value of GWPR models dropped after removing the entertainment density and restaurant density. Among the GWPR models, the SGWPR model based on the adaptive Gaussian function had the smallest AICc value and the best fitting accuracy. The best bandwidth of the SGWPR model was 237.62. The global variables of the model were residential density and intersection density, and the local variables were population density, retail density, company density, hotel density, residential density, intersection density, and road density. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model** & **MLR** & \multicolumn{2}{c}{**GWPR**} & \multicolumn{2}{c}{**GWPR**} & \multicolumn{2}{c}{**SGWPR**} \\ \hline
**Kernel** & **-** & **Adaptive** & **Adaptive** & **Adaptive** & **Adaptive** & **Adaptive** & **Adaptive** \\
**Functions** & **-** & **Bi-Square** & **Gaussian** & **Bi-Square** & **Gaussian** & **Bi-Square** & **Gaussian** \\ \hline Best & - & 1386 & 215 & 1172 & 147 & 303.14 & 237.62 \\ bandwidth size & & & & & & \\ AICc & 1385.20 & 1355.79 & 1350.56 & 1348.00 & 1339.52 & 1312.80 & 1307.91 \\ Number of & 9 & 9 & 9 & 7 & 7 & 7 & 7 \\ variables & & & & & Other & & Residential\_den \\ Global Variables & All variables & - & - & - & Explanatory & & Intersection\_den \\  & & & & All Explanatory variables & & & Other \\ Local Variables & & All Explanatory variables & & except Entertainment\_den & Company\_den & Explanatory \\  & & & & and Restaurant\_den & & variables \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fitting results of GWPR model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Coefficients** & **\(t\)-Statistic** & **\(p\)-Value** \\ \hline Pop\_den & 0.193 & 7.779 & 0.001 \\ Retail\_den & 0.483 & 9.918 & 0.001 \\ Entertainment\_den & \(-\)0.018 & \(-\)0.381 & 0.704 \\ Restaurant\_den & 0.006 & 0.110 & 0.913 \\ Company\_den & \(-\)0.680 & \(-\)24.348 & 0.001 \\ Hotel\_den & \(-\)0.108 & \(-\)4.190 & 0.001 \\ Residential\_den & \(-\)0.105 & \(-\)2.911 & 0.004 \\ Intersection\_den & 0.074 & 1.927 & 0.048 \\ Road\_den & 0.103 & 2.959 & 0.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coefficient estimation of MLR model. Table 5 lists the descriptive statistics of the regression coefficient of the local variables. The regression coefficients of population density, hotel density, and road density were positive in some areas but negative in other areas, indicating significant spatial heterogeneity. Retail density had a positive effect, while company density had a negative effect for all the TAZs. By comparing the standard deviations, it could be found that the value of company density had the most dispersed regression coefficient, which indicated that the difference in influence from company density in different regions was more significant than other variables. Table 6 shows descriptive statistics for the regression coefficient of the global variables. The residential density and intersection density were positively correlated with the drunk driving crashes. The results were consistent with existing literature [13]. As shown in Figure 2, the local pdev values were all greater than 0.23. The spatial distribution of the local pdev indicated that the SGWPR model fitted to the data. It is noteworthy that the size and spatial distribution of the local pdev value in the urban area and the core area of the BH district were basically the same. A major reason for this phenomenon might be that the BH district is not an ordinary outer suburb area but an economic and technological development zone.