Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West...
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Transcript of Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West...
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
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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)