GWR v.2.0 - LOCALREGRESSION MODELLING:takingspatial...

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COMPUTATIONAL ASPECTS OF  COMPUTATIONAL ASPECTS OF  LOCAL REGRESSION  LOCAL REGRESSION  MODELLING: taking spatial  MODELLING: taking spatial  analysis to another level analysis to another level Stewart Fotheringham  Martin Charlton Chris Brunsdon Spatial Analysis  Spatial Analysis  Research Group Research Group Department of Geography, University of Newcastle upon  Department of Geography, University of Newcastle upon  Tyne, Tyne, Newcastle upon Tyne, ENGLAND NE1 7RU Newcastle upon Tyne, ENGLAND NE1 7RU
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GEOGRAPHICALLY  GEOGRAPHICALLY  WEIGHTED REGRESSION WEIGHTED REGRESSION The mechanics of GWR  New software for GWR: GWR 2.0 GWR in practice: an example of the  determinants of London house prices
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Some Definitions Some Definitions Spatial nonstationarity  Spatial nonstationarity  exists when the  same stimulus provokes a different response  in different parts of the study region Global models  Global models  are statements about  processes which are assumed to be  stationary and as such are location  independent Local models  Local models  are spatial disaggregations  of global models, the results of which are  location-specific
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Local versus Global Local versus Global Local Local  versus  global global   data data the example  of US climate data Local Local  versus  global global   relationships relationships the  example of house price determinants Local Local  versus  global global   models models the  example of regression
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Why might relationships vary  Why might relationships vary  spatially? spatially? Sampling variation Relationships intrinsically different across  space   e.g. differences in attitudes, preferences or  different administrative, political or other contextual  effects produce different responses to the same  stimuli Model misspecification -  suppose a global  statement can ultimately be made but models not  properly specified to allow us to make it. Local   models good indicator of how model is misspecified. Can all contextual effects ever be removed?  Can all significant variations in local  relationships be removed?
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Regression Regression In a typical linear regression model  applied to spatial data we assume a  stationary process: y i  =  β 0  +  β 1 x 1i  +  β 2 x 2i  +…  β n x ni  +  ε i
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so that. .. so that. .. The parameter estimates obtained in the  calibration of such a model are constant  over space: β β ’   ’   =  ( =  ( X X T T  X  X ) ) -1  -1  X X T T  Y  Y which means that any spatial variations in  the processes being examined can only  be measured by the error term
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Consequently. .. Consequently.
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This note was uploaded on 02/15/2012 for the course GEO 4167 taught by Professor Staff during the Spring '12 term at University of Florida.

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GWR v.2.0 - LOCALREGRESSION MODELLING:takingspatial...

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