To investigate dependencies between the variables the Local Moran's I-analysis was performed in addition to the raw and the spatially smoothed rates. The Local Moran's I provides a possibility to check spatially distributed attributes in its context. As we are interested in the connection between the interventions and the origin of the population, we have chosen the Bivariate method. It enables a comparison of the values for the variables with its neighbors and presents the correlation of the two variables at the same time. When working with Local Moran's I, the value of each cell is associated to its specific location and not with the global context.
Local Indicators of Spatial Association (LISA) measures the association for each spatial unit and identifies the type of spatial correlation. For instance, the Bivariate Local Moran's I gives an indication of the sign of linear association (positive or negative) between the averaged value of the first variable at a given location and the averaged value of another variable at neighboring locations \cite{mirzaie2013a}.
As Figure 3b shows, cells with relatively high values for both variables end up in the top-right quadrant "HH". Cells with relatively low values for both variables end up in the "LL"-quadrant (positive association) . Cells with a high and a low value for the variables are located in the "LH" or "HL"-quadrant respectively (negative association). In case the variables of a cell are not significantly high or low the cell is categorized as non significant using a threshold for significance (p-value).
Results
Regarding the hotspots, a simple representation of the variables over the area has been applied. To observe existing neighboring effects and to include a smoothening filter, the SRS was applied for both parameters using a Queen's 2 weights file. To be able to compare the results for raw and smoothed data directly, the images are represented aside each other. The cells are organized in 5 quantiles, with the darkest being the highest and the lightest being the lowest quantile. Figure 4 shows the interventions per population, while Figure 5 represents the percentage of foreigners per cell.