topic Re: negative R2 in GWR in Spatial Statistics Questions
https://community.esri.com/t5/spatial-statistics-questions/negative-r2-in-gwr/m-p/755251#M2391
<HTML><HEAD></HEAD><BODY><SPAN>Hi Jochen,</SPAN><BR /><BR /><SPAN>First "hello from Baltimore" - Andr3w T1ml3ck here (was in your class at UMD with Maurice C.)... </SPAN><BR /><BR /><SPAN>Not sure if I can help at all, been messing with this stuff too....</SPAN><BR /><BR /><SPAN>In Fischer & Getis' </SPAN><SPAN style="font-style:italic;">Handbook of Applied Spatial Analysis</SPAN><SPAN> (2010) Wheeler & Paez have a chapter on what works and what doesn't in GWR (see esp. pp 486-469). In it they note that bandwith and number of neighbors selection can be highly problematic - too many neighbors, too far a reach and of course you get no spatial variability. Too few neighbors, too close and you end up with spatial autocorrelation and you get wild, local, swings in regression coefficients - which sounds like what you're describing.</SPAN><BR /><BR /><SPAN>Cheers,</SPAN><BR /><SPAN>Andrew (Andy)</SPAN><BR /><BR /><BLOCKQUOTE class="jive-quote">Clearly, if the bandwidth is such as to include a large <BR />number of observations, there will be relatively little or no spatial variation in the <BR />coefficients, and if the bandwidth is small, there will potentially be large amounts <BR />of variation. A natural concern emerges that some variation or smoothness in the <BR />pattern of estimated coefficients may be artificially introduced by the technique <BR />and may not represent true regression effects. This situation is at the heart of the <BR />discussion about the utility of GWR for inference on regression coefficients and is <BR />not answered by existing statistical (Leung et al. 2000a) or Monte Carlo (Fother- <BR />ingham et al. 2002) tests for significant variation of GWR coefficients because <BR />these tests do not consider the source of the variation. This is important because <BR />one source of regression coefficient variability in GWR can come from collinear- <BR />ity, or dependence in the kernel-weighted design matrix. Collinearity is known in <BR />linear models to inflate the variances of regression coefficients (Neter et al. 1996), <BR />and GWR is no exception (Griffith 2008). Collinearity has been found in empiri- <BR />cal work to be an issue in GWR models at the local level when it is not present in <BR />the global linear regression model using the same data (Wheeler 2007). In addition <BR />to large variation of estimated regression coefficients, there can be strong depend- <BR />ence in GWR coefficients for different regression terms, including the intercept, at <BR />least partly attributable to collinearity. Wheeler and Tiefelsdorf (2005) show in a <BR />simulation study that while GWR coefficients can be correlated when there is no <BR />explanatory variable correlation, the coefficient correlation increases systemati- <BR />cally with increasingly more collinearity. <BR /></BLOCKQUOTE></BODY></HTML>Tue, 28 Jun 2011 18:23:39 GMTAndrewTimleck2011-06-28T18:23:39Znegative R2 in GWR
https://community.esri.com/t5/spatial-statistics-questions/negative-r2-in-gwr/m-p/755250#M2390
<HTML><HEAD></HEAD><BODY><SPAN>I have been struggling with my attempt to regress global greenhouse gas emissions on a bunch of social and environmental variables such as population density, GDP, distance to coast, elevation, heating degree days, and so on. With standard regression techniques I am getting rather low R-squares, and with GWR, I managed to raise it to some .25 using four variables (a brownie if you guess which ones). The results of my latest attempt threw me a bit though: I am now getting negative R-squares in the .3 range. Obviously something went wrong - but what? I am attaching a screen shot of the results window.</SPAN><BR /><SPAN>Btw, this is still exploratory. I will eventually move to spatial regression techniques but first wanted to get a feel for the spatial effects, which are far more local than I would have thought given that I am working with global data sets.</SPAN><BR /><SPAN>Cheers,</SPAN><BR /><SPAN> Jochen</SPAN><BR /><A href="http://giscience.hunter.cuny.edu/GWR/GWRresults.PNG"><IMG src="http://giscience.hunter.cuny.edu/GWR/GWRresults.PNG" /></A></BODY></HTML>Fri, 24 Jun 2011 02:35:17 GMThttps://community.esri.com/t5/spatial-statistics-questions/negative-r2-in-gwr/m-p/755250#M2390JochenAlbrecht2011-06-24T02:35:17ZRe: negative R2 in GWR
https://community.esri.com/t5/spatial-statistics-questions/negative-r2-in-gwr/m-p/755251#M2391
<HTML><HEAD></HEAD><BODY><SPAN>Hi Jochen,</SPAN><BR /><BR /><SPAN>First "hello from Baltimore" - Andr3w T1ml3ck here (was in your class at UMD with Maurice C.)... </SPAN><BR /><BR /><SPAN>Not sure if I can help at all, been messing with this stuff too....</SPAN><BR /><BR /><SPAN>In Fischer & Getis' </SPAN><SPAN style="font-style:italic;">Handbook of Applied Spatial Analysis</SPAN><SPAN> (2010) Wheeler & Paez have a chapter on what works and what doesn't in GWR (see esp. pp 486-469). In it they note that bandwith and number of neighbors selection can be highly problematic - too many neighbors, too far a reach and of course you get no spatial variability. Too few neighbors, too close and you end up with spatial autocorrelation and you get wild, local, swings in regression coefficients - which sounds like what you're describing.</SPAN><BR /><BR /><SPAN>Cheers,</SPAN><BR /><SPAN>Andrew (Andy)</SPAN><BR /><BR /><BLOCKQUOTE class="jive-quote">Clearly, if the bandwidth is such as to include a large <BR />number of observations, there will be relatively little or no spatial variation in the <BR />coefficients, and if the bandwidth is small, there will potentially be large amounts <BR />of variation. A natural concern emerges that some variation or smoothness in the <BR />pattern of estimated coefficients may be artificially introduced by the technique <BR />and may not represent true regression effects. This situation is at the heart of the <BR />discussion about the utility of GWR for inference on regression coefficients and is <BR />not answered by existing statistical (Leung et al. 2000a) or Monte Carlo (Fother- <BR />ingham et al. 2002) tests for significant variation of GWR coefficients because <BR />these tests do not consider the source of the variation. This is important because <BR />one source of regression coefficient variability in GWR can come from collinear- <BR />ity, or dependence in the kernel-weighted design matrix. Collinearity is known in <BR />linear models to inflate the variances of regression coefficients (Neter et al. 1996), <BR />and GWR is no exception (Griffith 2008). Collinearity has been found in empiri- <BR />cal work to be an issue in GWR models at the local level when it is not present in <BR />the global linear regression model using the same data (Wheeler 2007). In addition <BR />to large variation of estimated regression coefficients, there can be strong depend- <BR />ence in GWR coefficients for different regression terms, including the intercept, at <BR />least partly attributable to collinearity. Wheeler and Tiefelsdorf (2005) show in a <BR />simulation study that while GWR coefficients can be correlated when there is no <BR />explanatory variable correlation, the coefficient correlation increases systemati- <BR />cally with increasingly more collinearity. <BR /></BLOCKQUOTE></BODY></HTML>Tue, 28 Jun 2011 18:23:39 GMThttps://community.esri.com/t5/spatial-statistics-questions/negative-r2-in-gwr/m-p/755251#M2391AndrewTimleck2011-06-28T18:23:39Z