gwr.mink.pval: Select the values of p for the Minkowski approach for GWR

In GWmodel: Geographically-Weighted Models

Select the values of p for the Minkowski approach for GWR

Description

These functions implement heuristics to select the values of p from two intervals: (0, 2] in a 'backward' direction and (2, Inf) in a 'forward' direction.

Usage

gwr.mink.pval(formula, data, criterion="AIC", bw, bw.sel.approach = "AIC",
                       adaptive=F, kernel="bisquare", left.interval=0.25,
                       right.interval=0.5,drop.tol=3, theta0=0,verbose=F,nlower = 10)
gwr.mink.pval.forward(formula, data, bw, bw.sel.approach = "AIC",
                       adaptive=F, kernel="bisquare", p.max=Inf,p.min=2,
                       interval=0.5,drop.tol=3, theta0=0,verbose=F,nlower = 10)
gwr.mink.pval.backward(formula, data, bw, bw.sel.approach = "AIC",
                       adaptive=F, kernel="bisquare", p.max=2,p.min=0.1,
                       interval=0.5,drop.tol=3, theta0=0,verbose=F,nlower = 10)
## S3 method for class 'pvlas'
plot(x, ...)
                       

Arguments

formula	Regression model formula of a formula object
data	a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp
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
left.interval	the step-size for searching the left interval (0, 2] in a 'backward' direction
right.interval	the step-size for searching the right interval (2, Inf) in a 'forward' direction
p.max	the maximum value of p
p.min	the minimum value of p
interval	the step-size for searching the given interval in a 'backward' or 'forward' direction
drop.tol	an AICc difference threshold to define whether the values of p to be dropped or not
theta0	a fixed rotation angle in radians
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
x	an object of class “pvlas”, returned by these functions
...	arguments passed through (unused)

Value

A list of:

p.vals	a vector of tried values of p
cretion.vals	a vector of criterion values (AICc or CV) for tried values of p
p.dropped	a vector of boolean to label whether a value of p to be dropped or not: TRUE means to be dropped and FALSE means to be used for the Minkowski approach

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.