# Geographically Weighted Regression with overlapping polygons

Is it statistically correct (or possible at all) to calculate a spatial regression with (partly) overlapping spatial areas?

I have market areas as the spatial unit with different sociodemographic, economic and other (firm-endogenous) variables and I´m examining their influence on the economic success (demand). To examine necessary regression assumptions a firstly need to calculate a simple OLS-regression to check for spatial autocorrelation (Moran I. test), homoscedasticity, normal distribution of standardized error terms etc. …Only from the visual perspective, when I look at the spatial distribution of my regression variable values I suppose a strong spatial autocorrelation so I probably need to implement spatial lag variables in my model. I´m using R for my calculations. To calculate the spatial weighting matrix of the neighbours I need to read the SHP-files to T. But how the spatial weighting matrix can be calculated when the areas are overlapping?

Aggregating my data to a higher level to avoid the overlapping effect is in my case not possible (too few cases for the regression analysis). I´ve only found some papers dealing with overlapping observations in time models:

Improved Inference and Estimation in Regression With Overlapping Observations

The Overlapping Data Problem

but I haven´t found anything dealing with spatial overlapping.

Do you know some methods, useful transformations etc. to solve this problem with spatial overlapping or is it possible at all?

## 1 Answer

Most spatial weight matrix schemes are ad-hoc structures and don't have much bearing on the final model.

So you could try various things, as long as they have the right properties. For examples: weight>0 for any two adjacent or overlapping regions; a weight>0 dependent on distance between region centroids; a weight>0 for N nearest centroids.

You could then either have those as weight=1 or do some sort of weight scaled from 0 to 1 based on degree of overlap or adjacency, or centroid distance.

Try all of those, and then write a paper on the effects of different weighting schemes for overlapping spatial data. You may find it makes less difference than you think, in which case it doesn't matter much which you use...