Timeline for Why does including latitude and longitude in a GAM account for spatial autocorrelation?
Current License: CC BY-SA 3.0
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| Mar 2, 2018 at 15:58 | comment | added | Gavin Simpson | @Julian Values of the response are smoothed with respect to the 2 spatial coordinates. Or put another way, the spatial effect is estimated as a smooth 2-d function. By smooth we mean has some wiggliness measured by the integrated squared second derivative of the spline. The wiggliness is chosen to balance the fit and the complexity of the model. If you want to know how the smooth functions (splines) are formed then it might be worth asking a specific question. | |
| Mar 2, 2018 at 15:12 | comment | added | Funkwecker | Why smoothed? What is exactly meant by "smoothed"? | |
| Sep 1, 2012 at 20:19 | vote | accept | gisol | ||
| Sep 1, 2012 at 17:03 | comment | added | Gavin Simpson | Yes. I suspect that in the examples you have looked at either the spatial component was of interest so was modelled explicitly via a smooth of lat/lon or the spatial component was a nuisance term but needed to be modelled to leave the residuals i.i.d. If the "spatial" component is better modelled via a different variable (e.g. elevation in you comment) then a smooth of that variable would be used instead of the spatial locations. | |
| Sep 1, 2012 at 16:43 | comment | added | gisol | Thanks for your clear answer Gavin. What makes spatial autocorrelation fundamentally different from any gradient not included in the model? Say your study area was on a sloping hill, and the species of interest preferred lower habitat to higher habitat. Failing to include the elevation in the model would leave a structure in the residuals, would it not? Is it simply that spatial autocorrelation is (or was) forgotten about or not considered? (P.S. perhaps this is a poor example as inclusion of lat,long would account for this effect too). | |
| Sep 1, 2012 at 16:35 | history | answered | Gavin Simpson | CC BY-SA 3.0 |