GWR with dependent and explanatory variables in different files

Question

I have a point shapefile (let's say A) with pollution measures (let's say Y). My hypothesis is that pollution at theses locations is primarily driven by nearby industrial units and not by activities at the locations in A. I have the locations of the factories in another shapefile (let's say B) along with a host of explanatory variables (let's say X1, X2, X3).

I want to model the pollution measure Y as a function of X1, X2, X3, and the distance of the industrial unites from the points of measurements. I was planning on using a Geographically Weighted Regression (GWR), but am not certain whether it is the right choice.

In ArcMap for example, the GWR tool expects one shapefile as input with both the dependent and explanatory variables.Thus, the assumption is that Y is driven by events at that point along with some influence of nearby locations. I looked into GWR in R also and the assumption is similar since it expects only one argument with data. I know that in R I can force feed the explanatory variables and dependent variable to be from different files, like this:

gwr.sel(A$Y ~ B$X1 + B$X2 + B$X3 + B$dist, ...)

But I am not sure if this makes sense, primarily for 2 reasons:

1. My dependant and explanatory variables are not in the same file. So, I may be violating a basic assumption of GWR.
2. The dist variable only has the distance from the nearest industrial unit to the measurement location. Thus, I am loosing the effect of the industrial plants which are close to the measured location, but not the closest.

Thus, my question is what other alternative do I have to GWR that will help me model this phenomenon?

Answer 1

Geographic Weighted Regression is used to look at how a process may vary across space, shown by the varying regression coefficients. So you can use this to potentially look at how your dependent variable is influenced by the proximity to industrial unit differently depending on where it is in the study area.

So to answer your main question I would say that it would be useful to perform a regression analysis that would look at how your predictors relate to the dependent variable across all your data. Then you can look at the results and and draw conclusions about how proximity to industrial units affects pollution compared to your other predictors globally. Then apply a GWR to see if this relationship varies over space to identify if there may be other processes influencing your dependent variable that you may not have considered. This essentially takes a global regression model and compares it to the local regression models in GWR to highlight relationships at these different scales within your data.

Also to answer point 1, that when peforming GWR or other modelling methods you need a series of observations and each observation has a measure of the dependent variable and each of the predictor variables; so you need to combine your point data with your predictor variables for the model. So yes at some point you do need to join your data.

To help with point 2, I would run your analysis as is and see if you can find a link between distance and pollution. There would be many other factors you need to consider as well as distance. For example the terrain could influence air flow (is the site above or below the industrial unit etc), the position relative to prevailing winds could also be a factor. So look to see if there is a relationship based on proximity, then maybe try to derive other measures that link the position of sites and industrial units and then incorporate those.