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)