gwr.mink.approach: Minkovski approach for GWR

In GWmodel: Geographically-Weighted Models

Minkovski approach for GWR

Description

This function implements the Minkovski approach to select an 'optimum' distance metric for calibrating a GWR model.

Usage

gwr.mink.approach(formula, data, criterion="AIC", bw, bw.sel.approach = "AIC",adaptive=F, 
              kernel="bisquare", p.vals=seq(from=0.25, to=8, length.out=32), p.inf = T,
                          theta.vals = seq(from=0, to=0.5*pi, length.out=10), verbose=F, 
                          nlower = 10)

Arguments

formula	Regression model formula of a formula object
data	a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp, or a sf object defined in package sf
criterion	the criterion used for distance metric selection, AICc ("AICc") or cross-validation ("CV") score; default is "AICc"
bw	bandwidth used in the weighting function, possibly calculated by bw.gwr;fixed (distance) or adaptive bandwidth(number of nearest neighbours)
bw.sel.approach	approach used to seclect an optimum bandwidth for each calibration if no bandwidth (bw) is given; specified by CV for cross-validation approach or by AIC corrected (AICc) approach
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)
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
p.vals	a collection of positive numbers used as the power of the Minkowski distance
p.inf	if TRUE, Chebyshev distance is tried for model calibration, i.e. p is infinity
theta.vals	a collection of values used as angles in radians to rotate the coordinate system
verbose	if TRUE and bandwidth selection is undertaken, the bandwidth searches are reported
nlower	the minmum number of nearest neighbours if an adaptive kernel is used

Value

A list of:

diag.df	a data frame with four columns (p, theta, bandwidth, AICc/CV), each row corresponds to a calibration
coefs.all	a list class object including all the estimated coefficients

Note

The function “mink.approach” (in the early versions of GWmodel) has been renamed as “gwr.mink.approach”, while the old name is still kept valid.

Author(s)

Binbin Lu [e-mail]

References

Lu, B, Charlton, M, Brunsdon, C & Harris, P(2016). The Minkowski approach for choosing the distance metric in Geographically Weighted Regression. International Journal of Geographical Information Science, 30(2): 351-368.

GWmodel documentation built on Sept. 11, 2024, 9:09 p.m.