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
Flow DirectionSubstrate
DepthFlow
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
Depth +
= Substrate?Flow +
`Study Sites
• Research on Grayling and Wapiti Creeks, Greater Yellowstone ecosystem (Montana)
• Elk River and Aaron’s Creek, WV
Flow DirectionSubstrate
DepthFlow
* Each dot represents an x,y coordinate with depth, flow, and substrate values
33 m
eter
s8,580 x,y coordinates
Results
Site R-Squared Adjusted R-Squared AIC Model
Little Wapiti 0.69 0.69 10637.48 3
0.55 0.55 11980.46 2
0.52 0.52 12214.06 1
Grayling 0.63 0.63 12924.04 1
0.63 0.63 12925.88 3
0.49 0.49 17901.21 2
1
Location
Adjusted
R-squared R-squared AIC Value Model
Search
Radius
Kernal
Type Bandwidth Method
Little Wapiti 0.93 0.98 5742.72 1 8 neighbor Adaptive Bandwidth Parameter
0.92 0.98 6005.73 2 8 neighbor Adaptive Bandwidth Parameter
0.94 0.99 6982.44 3 8 neighbor Adaptive Bandwidth Parameter
0.82 0.82 8637.95 3 default (30) Fixed AICc
0.80 0.81 8947.01 1 default (30) Fixed AICc
0.75 0.76 9756.02 2 default (30) Fixed AICc
Grayling 0.83 0.95 3226.54 3 8 neighbor Adaptive Bandwidth Parameter
0.85 0.94 4789.01 1 8 neighbor Adaptive Bandwidth Parameter
0.78 0.9 6668.95 2 8 neighbor Adaptive Bandwidth Parameter
0.85 0.86 8444.63 1 default (30) Fixed AICc
0.84 0.84 8879.35 3 default (30) Fixed AICc
0.8 0.81 9948.32 2 default (30) Fixed AICc
1
Visual Comparison
Actual
Predicted
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)
