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
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 +
Flow +
= Substrate?
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
Substrate
* Each dot represents an x,y coordinate with depth, flow, and substrate values
Results
Adjusted
Site
Location
Little Wapiti
R-squared
Little Wapiti
0.93
Grayling
AIC Value
0.98
5742.72
0.69
0.98
0.94
0.99
0.55
Radius
AdjustedModel
R-Squared
6005.73
6982.44
0.82
8637.95
0.80
0.81
0.52
8947.01
0.75
0.76
9756.02
0.83
0.95
0.63
3226.54
0.85
0.94
4789.01
0.78
0.63
0.9
6668.95
0.86
8444.63
0.84
0.49
0.84
0.8
0.81
9948.32
0.85
1
R-squared
R-Squared
0.92
0.82
Grayling
Search
8879.35
1
0.69
2
3
0.55
3
1
0.52
2
3
0.63
1
0.63
2
1
0.49
3
2
Kernal
Method
AICBandwidth
Model
Type
8 neighbor
Adaptive
8 neighbor
Adaptive
8 neighbor
Adaptive
default (30)
Fixed
default (30)
Fixed
AICc
default (30)
Fixed
AICc
8 neighbor
Adaptive
8 neighbor
Adaptive
8 neighbor
Adaptive
default (30)
Fixed
Bandwidth Parameter
10637.48
3
Bandwidth Parameter
Bandwidth Parameter
11980.46
2
AICc
12214.06
1
Bandwidth Parameter
12924.04
1
Bandwidth Parameter
12925.88
3
Bandwidth Parameter
AICc
default (30)
17901.21
Fixed
default (30)
Fixed
AICc
AICc
2
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)