I'm looking for advice/opinion on whether the co-efficient(s) resulting from a geographically weighted regression analysis can subsequently be entered into an OLS regression as the dependent variable (i.e. to test for factors influencing the observed spatial variation). Are any major assumptions violated in doing so and, if so, are there any acceptable work-around?

  • $\begingroup$ I don't really understand your scenario but you could look at mixed-effects (multilevel, hierarchical) models. I've heard they're sometimes known as slopes-as-outcomes models. $\endgroup$ – Patrick Coulombe Apr 29 '17 at 0:13
  • $\begingroup$ I cannot understand: "a geographically weighted regression analysis" means one model in the first step. Then you get estimates of one intercept and several slops. Just one observation, how to do regression again? $\endgroup$ – user158565 Apr 29 '17 at 6:30
  • $\begingroup$ See andrewgelman.com/2005/03/07/the_secret_weap $\endgroup$ – kjetil b halvorsen Apr 29 '17 at 8:29
  • $\begingroup$ Thanks for the responses. To clarify, the geographically weighted regression produces local coefficients for each IV for each case (1673 in total). In order to explore the causes of the variation I'm considering using a standard OLS regression with the co-efficients from the first step (the GWR) as the DV (n = 1673). I get meaningful estimates as a result but I'm unsure whether results from a geographically weighted model are suitable for subsequent inclusion in a linear model. $\endgroup$ – Matthew Dennis Apr 30 '17 at 5:53

Regressing on OLS estimates runs against the (classical) assumptions of the model, which hold that the estimates are unknown constants that are estimated with data (which are random). So, if I understand the regression you are suggesting running, you would get some estimates but they would not have a formal interpretation. (Bayesians have the opposite view, that our estimates are random variables given the data.) Depending on the type of patterns you wish to test for, you may wish to look at spatial autocorrelation models (http://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-how-can-i-detectaddress-spatial-autocorrelation-in-my-data/) or hierarchical models (https://www.r-bloggers.com/hierarchical-linear-models-and-lmer/).

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