I am using observation data from several countries to develop maps that predict the concentration of trace elements in soils. I have ~20,000 observations and have several rasters that describe the environment (e.g., climate, precipitation, temperature, etc.). All of this data is highly correlated spatially and observations are not independent (i.e., data from pixels/observations are more likely to be similar if they are closer in proximity). In order to account for this, I was hoping to use ArcMAPs (10.2) geographically weighted regression (GWR) analysis.
I am having trouble finding documentation on the assumptions of the GWR analysis and how the model selection works. For example, if you do a quick search for linear regression assumptions, you will easily find that linear regression requires as linear relationship between dependent and independent variables, constant variance, independence of samples, etc. I have not found a list of corresponding assumptions for GWR. I suspect they are the same, but I need to be able to cite a source that describes the assumptions so I can adequately show that each assumption was addressed. Does anyone know where I can find a list of these assumptions? For example, can GWR handle parabolic relationships or does the data need to be linearized first before entered into the model?
Also, it seems to me that GWR is more of a "black box" tool. When I enter multiple independent or explanatory variables, does GWR enter all the variables at once, or does it enter the variables stepwise, and hence the use of AICc? Is there documentation on the criteria for how a model is entered into the model (e.g., F to Enter & F to Remove)?
Finally, I would like to use GWR to predict how concentrations will change as the input variables change. With OLS, this is easy given the global regression equation. Since GWR calculates parameters locally instead of globally, how can I use a GWR in ArcMAP to predict how changes in input variables will affect the output, similar to a traditional linear model?
Thank you very much for your time and help. I greatly appreciate it.