# Spatial regression with overlapping areas

Is it statistically correct to calculate a regression with overlapping areas? I have market areas as the spatial unit with different sociodemographic and (macro)economic variables and I´m examining their influence on insurance demand. The market areas are overlapping in some areas. According to the spatial distribution I suppose there´s a spatial autocorrelation. Firstly I can calculate simple multiple linear reg. and then run the Moran I. test to check for spatial autocorrelation. But I´m not sure if I can do so when lots of my market areas are overlapping? (I cannot aggregate the data up to a higher level because then I´d have too few cases (about 50)). I´ve just found some papers dealing with overlapping observations in time models: https://pdfs.semanticscholar.org/c830/33c957f103b6561038589682ab807bba8c3b.pdf https://pdfs.semanticscholar.org/3d59/d8106ae0ff9310ce5ac95e19f4e9ab6d505a.pdf but I haven´t found anything dealing with spatial overlapping. Do you know some methods, useful transformations etc. how to solve this problem with spatial overlapping or is it possible at all? I´d really appreciate any comment or help! Thank you in advance!

Edit: @whuber: Thank you for your quick response. But in my understanding the approaches presented in the above mentioned papers are applicable only to time-regression models (cf. e.g. Britten-Jones & Neuberger, 2011, p. 2) (first paper). Or do you think that the presented methods can also be applied to regression models with spatial overlays, although these were not mentioned in the papers?

I haven´t calculated the regression yet so I cannot surely say that the error terms are spatial correlated (independently from other necessary OLS-assumptions like the normal distribution of standardised error terms or the homoscedasticity) but I when I look at the spatial distribution of the variables values I´m pretty sure the spatial autocorrelation is present (e.g. urban areas vs. rural areas).

But the general question is: Is it possible to calculate the regression with SPATIALLY overlapping areas at all? How the spatial weighting matrix (weighting of the neighbours) can be calculated when the spatial units are overlapping? Right now I cannot imagine how this should be done. I calculate the regression in R. For the Moran I. test I simply load the .shp files into R for calculating the weighting matrices.

I´m interested if someone knows an implementation in R environment for this (NOT for time regressions) (OLS-regression with Newey-West error terms for spatial autocorrelation?) OLS regression with Newey-West error term

Overlapping market areas is surely a common problem. Solving this “statistical” problem would help in many ways (Does the spatial distribution of location factors determine the economic success? Which firm-endogenous / exogenous factors determine the demand for a product in a market area X etc. …).

• +1 for recognizing this might be an issue and researching relevant papers. Indeed, the approaches taken in these papers do apply to spatial data. The complication is that you won't obtain the nice covariance matrices they do: yours will depend on the details of the overlaps as well as your assumptions about the responses (insurance demands) in the overlapping areas are related to their containing areas. – whuber Sep 21 '18 at 19:12
• @whuber Thank you for your reaction again. I´ve just updated my question. – Mapos Sep 23 '18 at 10:47