This function implements the Minkovski approach to select an 'optimum' distance metric for calibrating a GWR model.
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)A list of:
a data frame with four columns (p, theta, bandwidth, AICc/CV), each row corresponds to a calibration
a list class object including all the estimated coefficients
Regression model formula of a formula object
a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp, or a sf object defined in package sf
the criterion used for distance metric selection, AICc ("AICc") or cross-validation ("CV") score; default is "AICc"
bandwidth used in the weighting function, possibly calculated by bw.gwr;fixed (distance) or adaptive bandwidth(number of nearest neighbours)
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
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)
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
a collection of positive numbers used as the power of the Minkowski distance
if TRUE, Chebyshev distance is tried for model calibration, i.e. p is infinity
a collection of values used as angles in radians to rotate the coordinate system
if TRUE and bandwidth selection is undertaken, the bandwidth searches are reported
the minmum number of nearest neighbours if an adaptive kernel is used
Binbin Lu binbinlu@whu.edu.cn
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.