Lab 12 - Geographically Weighted Regression

For Lab 12 we focused on Geographically Weighted Regression (GWR) to include the variations in data across geographic space. In GWR, there is a dependent variable for a study area and one or more independent variables within that area that have known locations. Based on Tobler's concept of spatial autocorrelation, greater weight is given to observations that are closer to the known locations then those that are further away. In OLS, a coefficient is created for each variable which can be used to understand the relationship between the dependent and the explanatory variables. In GWR, one coefficient is created for each feature (known location or data point) for each explanatory variable, which can provide insight into the relationship strength between the explanatory variables themselves and the dependent.

For example, in the first part of the lab we ran a GWR on 911 calls for a set of census block groups using 4 demographic variables. This was compared to the OLS run in our last lab. The OLS produced an explanatory power of 83.1%, while the GWR improved the model with an explanatory power of 85.5%. Individual variables were then be mapped, in this case population, to identify areas of strong and weak relationships between population and 911 calls in the study area. We also ran a prediction GWR model to look at potential future year 911 calls based on the four variables. Using GWR we not only can see the predicted calls, but the way the calls vary across the study area. These types of results can be useful in policy making decisions as the models provide more insight into the spatial variation of data. 

In the second part of the lab we again ran an OLS and a GWR for a dataset, selecting explanatory variables from a larger demographic dataset based on high correlation coefficients in the correlation matrix and the dependent variable of hit and run crimes (also considered were the exclusion of one variable if it suggested collinearity with another, such as rent and median income). Using 3 variables- residents of black race & residents of hispanic ethnicity as a total percent of population and renter occupied housing units as a % of all housing units-I created OLS and GWR models, ran Moran's I tool to determine spatial autocorrelation between the standardized residuals, and selected the independent variable with the highest regression coefficient in my GWR to map individually. 

My OLS and initial GWR were similar, with no real improvement in explanatory power in the GWR compared to the OLS (both 19.4%). However, by adjusting the kernel parameter (or how the model selects sample points) to be adaptive, the model was slightly improved, with 21.7% explanatory power of the independent variables. Renter occupied housing units as a % of all housing units produced the highest regression coefficients of all selected variables. Notice the variation in the map indicating areas where the relationship between the explanatory variable was stronger (darker) or weaker (lighter) to the dependent variable (hit and run crimes).

Screenshot of adaptive kernel GWR results showing relationship pattern between renter occupied housing as a % of all housing units and hit and run crime rates within the study area tracts.