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:
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?