gwr.mixed {GWmodel}

Mixed GWR

Description

This function implements mixed (semiparametric) GWR

Usage

gwr.mixed(formula, data, regression.points, fixed.vars,
                     intercept.fixed=FALSE, bw, diagnostic=T, kernel="bisquare", 
                     adaptive=FALSE, p=2, theta=0, longlat=F,dMat, dMat.rp)

Arguments

formula

Regression model formula of a formula object

data

a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp

regression.points

a Spatial*DataFrame object, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp

fixed.vars

independent variables that appeared in the formula that are to be treated as global

intercept.fixed

logical, if TRUE the intercept will be treated as global

bw

bandwidth used in the weighting function, possibly calculated by bw.gwr;fixed (distance) or adaptive bandwidth(number of nearest neighbours)

diagnostic

logical, if TRUE the diagnostics will be calculated

kernel

function chosen as follows:

gaussian: wgt = exp(-.5*(vdist/bw)^2);

exponential: wgt = exp(-vdist/bw);

bisquare: wgt = (1-(vdist/bw)^2)^2 if vdist < bw, wgt=0 otherwise;

tricube: wgt = (1-(vdist/bw)^3)^3 if vdist < bw, wgt=0 otherwise;

boxcar: wgt=1 if dist < bw, wgt=0 otherwise

adaptive

if TRUE calculate an adaptive kernel where the bandwidth (bw) corresponds to the number of nearest neighbours (i.e. adaptive distance); default is FALSE, where a fixed kernel is found (bandwidth is a fixed distance)

p

the power of the Minkowski distance, default is 2, i.e. the Euclidean distance

theta

an angle in radians to rotate the coordinate system, default is 0

longlat

if TRUE, great circle distances will be calculated

dMat

a pre-specified distance matrix, it can be calculated by the function gw.dist

dMat.rp

a distance matrix when an individual set of regression points are adopted

Value

A list of class “mgwr”:

GW.arguments

a list class object including the model fitting parameters for generating the report file

aic

AICc value from this calibration

df.used

effective degree of freedom

rss

residual sum of squares

SDF

a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package “sp”) integrated with coefficient estimates in its "data" slot.

timings

starting and ending time.

this.call

the function call used.

Note

For an alternative formulation of mixed GWR, please refer to GWR 4, which provides useful tools for automatic bandwidth selection. This windows-based software also implements generalised mixed GWR.

The mixed GWR in the latest release of GWmodel (2.0-0) has been revised by Dr. Fiona H Evans from Centre for Digital Agriculture, Murdoch and Curtin Universities in terms of its computational efficiency.

Author(s)

Binbin Lu [e-mail]

References

Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.

Brunsdon C, Fotheringham AS, Charlton ME (1999) Some notes on parametric signficance tests for geographically weighted regression. Journal of Regional Science 39(3):497-524

Mei L-M, He S-Y, Fang K-T (2004) A note on the mixed geographically weighted regression model. Journal of regional science 44(1):143-157

Mei L-M, Wang N, Zhang W-X (2006) Testing the importance of the explanatory variables in a mixed geographically weighted regression model. Environment and Planning A 38:587-598

Nakaya T, Fotheringham AS, Brunsdon C, Charlton M (2005) Geographically Weighted Poisson Regression for Disease Association Mapping, Statistics in Medicine 24: 2695-2717

Nakaya T et al. (2011) GWR4.0, http://gwr.nuim.ie/.