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Geographically Weighted Regression

Geographically Weighted Regression. Use and application of spatially weighted regression for environmental data analysis. Ken Sheehan - April 5, 2010. - John Muir in “My first summer in the Sierra”. Some data has inherent spatial qualities Ignore, or address?.

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Geographically Weighted Regression

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  1. Geographically Weighted Regression Use and application of spatially weighted regression for environmental data analysis Ken Sheehan - April 5, 2010

  2. -John Muir in “My first summer in the Sierra” • Some data has inherent spatial qualities • Ignore, or address? • Marveled that “one could run down the boulder field at full speed and the rocks were perfectly spaced for such an endeavor”

  3. Progression of ideas at WVU • Spatial analysis for resource management • Advanced spatial analysis • Can’t find the fish? Study it’s habitat… • Important because • stream habitat dictates stream biota • Principle of “What’s there” is dictated by “what’s there” (which goes for many systems, not just environmental).

  4. Spatial Data and Streams • Likely to be autocorrelated • Geology • Substrate • Flow • Depth • Sheehan and Welsh (2009)

  5. Most Recently • Research on Grayling and Wapiti Creeks, Greater Yellowstone ecosystem.

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  7. Before Delving into GWR… • Background on linear regression • Fitting a line to a data set • Assumes homoskedacity • Static (flat variance) • Great for predicting relationships • Heavily used, perhaps most dominant type of statistical analysis in environmental and other fields • Classic examination of observed versus expected

  8. Progression of ideas • Spatial autocorrelation (Legendre 1993) • Red herring (Diniz 2003) • or sweet new tool ? • Yes and no

  9. Background Continued.. • Fotheringham and Brunsden (1998) • Modification of linear regression formula to include spatial attributes of data. Standard regression formula GWR regression formula

  10. Concepts • Different than adding x,y coordinates to ordinary linear regression analysis datasets • Creates a moving variance for data with non-stationarity (regional variation). • Not all data is appropriate for Geographically Weighted Regression. • Still a work in progress- econometrics

  11. Demonstration of GWR • Wapiti and Grayling • Deceptively complex process

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