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GWmodel (version 2.2-9)

gwr.mink.pval: 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 pvlas
plot(x, ...)

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

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)

Author

Binbin Lu binbinlu@whu.edu.cn

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.