Spatial regression

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07-02-2012 09:34 AM
DjurdjicaIvkovic
New Contributor
Hello everyone,

I have a question regarding performing spatial regression on data which residuals are spatially correlated. If the residuals are spatially autocorrelated due to the presence of trend, how should I account for the existence of spatial autocorrelation? And what about if there is no trend, but rather spatial autocorrelation in random variation (in residuals left after detrending)? And what about if there are both trend and spatially autocorrelated random variation in my data? Can I in both cases apply this formula to account for spatial autocorrelation no matter if it is the result of trend or random variation correlation:

y*=y-ρ???(w_ij*y_j)
x*=x-ρ???(w_ij*x_j)

Thanks!
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2 Replies
JeffreyEvans
Occasional Contributor III
I can think of no instance where your equation would account for autocorrelation and there is no "one size fits all" approach. It is dependent on your data, desired inference and type of autocorrelation. The first decision that you need to make is if you want to detrend spatial effects or incorporate them into your model. This will dictate the appropriate model.     

If you have a first order spatial trend that can be fit to a simple polynomial then is is easy to detrend an OLS regression (plenty of literature on this). Another way to dismiss spatial effects in a regression is to treat them as a random effect in a mixed effects model. If you want your inference to incorporate spatial effects, then look into methods such as spatial and conditional autoregressive regression. There are also nonparametric and semiparametric methods available.   

Geographically Weighted Regression (GWR) should be reserved for instances where you have a strong 2nd (nonstationarity) order spatial effect. An additional caveat on GWR is that it has come under serious criticism in the literature and the authors have yet to provide any response. The observed behavior of GWR on simulated data and the lack of response by the authors calls into question the validity of this method.

Perhaps it is time to seek out a statistician to help guide you in selecting the appropriate model.
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DjurdjicaIvkovic
New Contributor
Hello Jeffrey,

Thank you a lot for your reply.

But is it necessary first to remove or account for trend in the data and then deal with spatial autocorrelation, since I plan to include spatial effects in covariates by using spatial lag regression? If I plan to include in regression equation coordinates as covariates (in order to adjust for existing trend), but I expect, for example, to have quadratic trend, then I will have to include also x sqaured and y squared as variables, right? What if I get p-values for  x squared and y high (so that I have to exclude them) and thus only able to keep y squared and x. What kind of trend is there in my data in that case? Or I do not have to focus on that too much, but just include those forms of coordinate variables (along with outer independent variables) that appear significant in my regression?
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