## 2 Materials and Methods
The model also assumes locally stationary relationships, which may not account for social or cultural dynamics, so we supplemented our analysis with contextual knowledge. Additionally, MGWR does not capture temporal dynamics, highlighting the need for future research to incorporate longitudinal data. These measures were taken to ensure the robustness and reliability of our findings. The MGWR modeling performs a regression for each spatial unit under analysis, in this case, the Voronoi polygons indicated above, relative to the other surrounding spatial units and the local values that make up the information for each spatial unit analyzed. This allows us to capture the \(p\)-value of each set of relationships within the map and thus define how statistically significant this group of relationships is. Figure 3: Food deserts in the Santiago metropolitan area. As mentioned above, the data used for this analysis is aggregated at the Census Zone Level. The location data is projected, ensuring that the spatial relationships are measured on a plane rather than a sphere, thus reducing potential distortions that might arise from spherical measurements. The MGWR approach was adopted because it extends the traditional Geographically Weighted Regression (GWR) by allowing each covariate to have its own bandwidth, thus capturing the multiscale effects of the covariates on the dependent variable. An adaptive bisquare kernel was employed to determine the spatial weighting scheme. The adaptive kernel ensures that each regression point uses a consistent number of nearest neighbors, which is particularly useful in areas with varying densities of observations. Also, the model used a bisquare function to ensure that weights decline smoothly to zero at the bandwidth distance, reducing the influence of distant observations. Bandwidth for each covariate was determined using the golden section search method, which optimizes the bandwidth selection by minimizing the corrected Akaike Information Criterion (AICc). AICc is an adjustment of the Akaike Information Criterion (AIC) that corrects for small sample sizes, providing a more reliable model selection metric in datasets with fewer observations. The general formulation of the MGWR model is as follows:  
\[y_{i}=\beta_{0}(u_{i},v_{i})+\sum_{k=1}^{p}\beta_{k}(u_{i},v_{i})x_{ik}+ \epsilon_{i}\]  
where \(y_{i}\) is the dependent variable (number of cardiovascular patients) at location \(i\); \((u_{i}\),\(v_{i})\) represents the coordinates of location i; \(\beta_{0}\) (\(u_{i}\),\(v_{i}\)) is the intercept, which can vary spatially; \(\beta_{k}(u_{i}\),\(v_{i})\) are the coefficients for the \(k\)-th covariate _xik_, which can also vary spatially; and \(ei\) is the error term. The spatial variability of each coefficient \(\beta_{k}(u_{i}\),\(v_{i})\) is captured by allowing each covariate to have a different bandwidth. This process of analysis allows a comparative review of whether the MGWR study improves in relation to a global regression and, specifically, allows us to see whether there is a statistical relationship between food deserts and cardiovascular health problems in patients in the public health system of the Metropolitan Area of Santiago, Chile.