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

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

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

Depth Flow Substrate Flow Direction

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

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

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

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

Results

Visual Comparison Predicted Actual

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

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