1. West Virginia University
Advantages of Geographically Weighted Regression for Modeling Substrate in Streams
Ken Sheehan
West Virginia University
Dept. of Wildlife & Fisheries
June 9th, 2010

3. Establishment of Need Habitat Study and Assessment
Integral to (overall) stream health
Management (present and future)
Fish and aquatic organism health
Needs improvement
Non-spatial analysis typically used
Assessment is an Expensive Endeavor

4. Spatial Data and Streams
Commonly Collected Variables
Substrate
Flow
Depth
Spatial autocorrelation (Legendre 1993)
Red herring (Diniz 2003)
Or effective new tool ?
Let’s use it to our advantage…
Geographically Weighted Regression

5. Depth
Flow
Substrate
Flow Direction

6. Traditional Linear Regression…
Fitting a line to a stream variable 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
Independent variables to predict dependent variables

7. Geographically Weighted Regression
Fotheringham and Brunsden (1998)
Modification of linear regression formula to include spatial attributes of data.
Standard regression formula
GWR regression formula

9. `
Study Sites
Research on Grayling and Wapiti Creeks, Greater Yellowstone ecosystem (Montana)
Elk River and Aaron’s Creek, WV

10. Depth
Flow
8,580 x,y coordinates
33 meters
Substrate
Flow Direction
* Each dot represents an x,y coordinate with depth, flow, and substrate values

13. Results

14. Visual Comparison
Predicted
Actual

15. Conclusions
Geographically Weighted Regression models stream substrate more effectively
Supported by AIC, adjusted R2, percent match, and visual comparison
Better assessment of streams
Management
Guides future study and
Economically efficient

16. Acknowledgements
Dr.’s Stuart Welsh, Mike Strager, Steve Kite, Kyle Hartman
WVDNR
West Virginia University
West Virginia Cooperative Fish and Wildlife Research Unit (USGS)