Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West...
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![Page 1: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/1.jpg)
Advantages of Geographically Weighted Regression for Modeling
Substrate in Streams
Ken Sheehan
West Virginia University
Dept. of Wildlife & Fisheries
June 9th, 2010
![Page 2: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/2.jpg)
![Page 3: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/3.jpg)
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
![Page 4: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/4.jpg)
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
![Page 5: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/5.jpg)
Flow DirectionSubstrate
DepthFlow
![Page 6: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/6.jpg)
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
![Page 7: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/7.jpg)
Geographically Weighted Regression
• Fotheringham and Brunsden (1998)
• Modification of linear regression formula to include spatial attributes of data.
Standard regression formula
GWR regression formula
![Page 8: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/8.jpg)
Depth +
= Substrate?Flow +
![Page 9: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/9.jpg)
`Study Sites
• Research on Grayling and Wapiti Creeks, Greater Yellowstone ecosystem (Montana)
• Elk River and Aaron’s Creek, WV
![Page 10: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/10.jpg)
Flow DirectionSubstrate
DepthFlow
* Each dot represents an x,y coordinate with depth, flow, and substrate values
33 m
eter
s8,580 x,y coordinates
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![Page 12: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/12.jpg)
![Page 13: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/13.jpg)
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
![Page 14: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/14.jpg)
Visual Comparison
Actual
Predicted
![Page 15: Advantages of Geographically Weighted Regression for Modeling Substrate in Streams Ken Sheehan West Virginia University Dept. of Wildlife & Fisheries June.](https://reader035.fdocuments.us/reader035/viewer/2022062516/56649daa5503460f94a9859f/html5/thumbnails/15.jpg)
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
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Acknowledgements
• Dr.’s Stuart Welsh, Mike Strager, Steve Kite, Kyle Hartman
• WVDNR
• West Virginia University
• West Virginia Cooperative Fish and Wildlife Research Unit (USGS)