## 3 Results
### High/Low Clustering: Getis-Ord General G statistic  
The geostatistical correlations obtained in the previous section using the Anselin Local Moran's I (LISA) global approach are quite interesting, since they allow us to know which indicators have a greater global degree of spatial correlation with the level of damage in buildings. However, this two-dimensional evaluation of the statistical correlation has certain limitations when working with average values to simplify the numerical analysis. Therefore, we shall graphically represent the distribution of those couples of the LISA analysis performed that present higher levels of bivariate correlation to analyze their spatial distribution through a two-dimensional Low-High statistical map. Using the whole set of values of the LISA bivariate statistics we can identify High-High clusters (a high value surrounded primarily by high values) and Low-Low clusters (a low value surrounded primarily by low values) and map them spatially at a local level. In addition, spatial outliers, either High-Low (high values surrounded primarily by low values) or Low-High (low values surrounded primarily by high values) can also be mapped and analyzed numerically. The geoprocessing tool of ArcGIS Getis-Ord \(Gi^{*}\) Hot Spot Analysis measures the degree of clustering for either high values or low values using the Getis-Ord General G statistic. Given incident points or weighted features (geolocated points for discrete values or interpolated surfaces for areas), it creates a map of statistically significant hot and cold spots using the Getis-Ord \(Gi^{*}\) analysis. Thus we can distinguish the spatial distribution in detail areas where high values of an indicator imply a high level of damage in buildings, areas where low values of an indicator imply low values of building damage and the level of both kinds of outliers. The results obtained for the different couples can be observed in the spatial hot spot analysis of Figure 12 and the detailed numerical data for the different levels of damage in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**GIS Indicators** & \(I_{SS}\) **- \(I_{LDB}\)** & \(I_{SC}\) **- \(I_{LDB}\)** & \(I_{SAC}\) **- \(I_{LDB}\)** & \(I_{IIUC}\) **- \(I_{LDB}\)** \\ \hline \multicolumn{5}{c}{**Bivariate Anselin Local Moran’s I**} \\ \hline Global Moran’s & 0.54 & 0.61 & 0.47 & 0.42 \\ Index & 37.2 & 55.0 & 34.8 & 28.8 \\ \(p\)-value & 0.01 & 0.01 & 0.01 & 0.01 \\ \hline \multicolumn{5}{c}{**Bivariate Anselin Local Moran’s I**} \\ \hline Global Moran’s & 0.44 & 0.12 & 0.15 & \\ Index & 35.2 & 0.09 & 11.3 & \\ \(p\)-value & 0.01 & 0.01 & 0.01 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Bivariate Anselin Local Moran’s I statistics for spatial correlation between indicators and damage level in buildings. The brief observation coefficient B in Table 3 indicate that the red codes are clearly associated with the phenomena of short columns, while the driving mechanisms in the rest of the phenomena indicators are more heterogeneous and complex. Red codes tend to be found in areas with well-defined characteristics. The model obtained for this code, therefore, has a relatively high explanatory capacity (R2 Adj. : 0.52, the rest of the codes reflect a much smaller adjustment in their models, which explains less than 25% of their distribution). In the cases of the green and yellow codes, it is also quite interesting to observe that there is a strong presence of soft story phenomena, being very numerous in the overall quantity yet not particularly relevant in terms of the level of damage. Figure 12: Hot spot spatial analysis for LISA bivariate results for (**a**) \(I_{\text{SS}}\) - \(I_{\text{LDB}}\), (**b**) \(I_{\text{SC}}\) - \(I_{\text{LDB}}\), (**c**) \(I_{\text{SAC}}\) - \(I_{\text{LDB}}\), (**d**) \(I_{\text{IUC}}\) - \(I_{\text{LDB}}\), (**e**) \(I_{\text{IARSD}}\) - \(I_{\text{LDB}}\), (**f**) \(I_{\text{BA}}\) - \(I_{\text{LDB}}\), and (**g**) \(I_{\text{SF}}\) - \(I_{\text{LDB}}\).