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Using AIC to compare Ordinary Least Squares and Geog. Weighted Regression models

Question asked by stevedugdale on Jul 19, 2010
Latest reply on Oct 5, 2010 by lscott-esristaff
I have produced some Ordinary Least Squares (OLS) and Geographically Weighted Regression (GWR) regression models and I want to identify which model is better. 

According to http://resources.esri.com/help/9.3/arcgisengine/java/Gp_ToolRef/spatial_statistics_tools/interpreting_gwr_results.htm "Comparing the GWR AICc value to the OLS AICc value is one way to assess the benefits of moving from a global model (OLS) to a local regression model (GWR)".

However, whereas the OLS tool in ARCMAP 9.3 outputs straightforward AIC (NOT AICc), the GWR tool appears to output AICc (i.e. a "corrected" version of AIC).    According to Fotheringham, A.S., Brunsdon, C. & Charlton, M. (2002) Geographically Weighted Regression - the analysis of spatially varying relationships John Wiley & Sons, Chichester. (page 96) "direct comparisons should NOT be made between AIC and AICc".

I'm therefore wondering how I can validly compare my OLS and GWR models when the diagnostics appear to give me incompatible outputs for that purpose.  I'm rather confused.

Please could someone advise whether the outputs are comparable after all and if not, why have they been "programmed" in this way?  I'm a non-statistician so I don't understand the nuts and bolts of the underlying calculations. 

Any assistance would be appreciated.

Thanks
Steve

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