gwr.multiscale {GWmodel}R Documentation

Multiscale GWR

Description

This function implements multiscale GWR to detect variations in regression relationships across different spatial scales. This function can not only find a different bandwidth for each relationship but also (and simultaneously) find a different distance metric for each relationship (if required to do so).

Usage

gwr.multiscale(formula, data, kernel = "bisquare", adaptive = FALSE,
                 criterion = "dCVR", max.iterations = 2000, threshold =
                 1e-05, dMats, var.dMat.indx, p.vals, theta.vals,
                 longlat = FALSE, bws0, bw.seled, approach = "AIC", bws.thresholds, 
                 bws.reOpts = 5, verbose = F,
                 hatmatrix = T, predictor.centered = rep(T,
                 length(bws0) - 1), nlower = 10, parallel.method = F,
                 parallel.arg = NULL, force.armadillo = F)
## S3 method for class 'multiscalegwr'
print(x, ...)

Arguments

formula

Regression model formula of a formula object

data

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

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)

criterion

criterion for determining the convergence of the back-fitting procedure, could be "CVR" or "dCVR", which corespond to the changing value of RSS (CVR) and the differential version (dCVR), respectively; and "dCVR" is used as default.

max.iterations

maximum number of iterations in the back-fitting procedure

threshold

threshold value to terminate the back-fitting iterations

dMats

a list of distance matrices used for estimating each specific parameter

var.dMat.indx

index corresponds to a specific distance matrix for each exploratory variable, if dMats is provided

p.vals

a collection of positive numbers used as the power of the Minkowski distance

theta.vals

a collection of values used as angles in radians to rotate the coordinate system

longlat

if TRUE, great circle distances will be calculated

bws0

a vector of initializing bandwidths for the back-fitting procedure, of which the length should equal to the number of paramters if specified

bw.seled

a vector of boolean variables to determine whether the corresponding bandwidth should be re-selected or not: if TRUE, the corresponding bandwiths for the specific parameters are supposed to be given in bws0; otherwise, the bandwidths for the specific parameters will be selected within the back-fitting iterations.

approach

specified by CV for cross-validation approach or by AIC corrected (AICc) approach

bws.thresholds

threshold values to define whether the bandwidth for a specific parameter has converged or not

bws.reOpts

the number times of continually optimizing each parameter-specific bandwidth even though it meets the criterion of convergence, for avoiding sub-optimal choice due to illusion of convergence;

verbose

if TRUE and bandwidth selection is undertaken, the bandwidth searches are reported

predictor.centered

a logical vector of length equalling to the number of predictors, and note intercept is not included; if the element is TRUE, the corresponding predictor will be centered.

hatmatrix

if TRUE the hatmatrix for the whole model will be calculated, and AICc, adjusted-R2 values will be returned accordingly.

nlower

the minmum number of nearest neighbours if an adaptive kernel is used

parallel.method

FALSE as default, and the calibration will be conducted traditionally via the serial technique, "omp": multi-thread technique with the OpenMP API, "cluster": multi-process technique with the parallel package, "cuda": parallel computing technique with CUDA

parallel.arg

if parallel.method is not FALSE, then set the argument by following: if parallel.method is "omp", parallel.arg refers to the number of threads used, and its default value is the number of cores - 1; if parallel.method is "cluster", parallel.arg refers to the number of R sessions used, and its default value is the number of cores - 1; if parallel.method is "cuda", parallel.arg refers to the number of calibrations included in each group, but note a too large value may cause the overflow of GPU memory.

force.armadillo

if TRUE, use the original RcppArmadillo implementation instead of the new RcppEigen implementation. Only matters if parallel.method = F or parallel.method = "omp".

x

an object of class “multiscalegwr”, returned by the function gwr.multiscale

...

arguments passed through (unused)

Value

A list of class “psdmgwr”:

SDF

a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package “sp”) integrated with data locations,coefficient estimates from the PSDM GWR model,predicted y values,residuals, coefficient standard errors and t-values in its "data" slot.

GW.arguments

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

GW.diagnostic

a list class object including the diagnostic information of the model fitting

lm

an object of class inheriting from “lm”, see lm.

bws.vars

bandwidths used for all the parameters within the back-fitting procedure

timings

starting and ending time.

this.call

the function call used.

Note

This function implements multiscale GWR to detect variations in regression relationships across different spatial scales. This function can not only find a different bandwidth for each relationship, but also (and simultaneously), find a different distance metric for each relationship (i.e. Parameter-Specific Distance Metric GWR, i.e. PSDM GWR). Note that multiscale GWR (MGWR) has also been referred to as flexible bandwidth GWR (FBGWR) and conditional GWR (CGWR) in the literature. All are one and the same model, but where PSDM-GWR additionally provides a different distance metric option for each relationship. An MGWR model is calibrated if no “dMats” and “p.vals” are specified; a mixed GWR model will be calibrated if an infinite bandwidth and another regular bandwidth are used for estimating the global and local parameters (again when no “dMats” and “p.vals” are specified). In other words, the gwr.multiscale function is specified with Euclidean distances in both cases. Note that the results from this function for a mixed GWR model and gwr.mixed might be different, as a back-fitting algorithm is used in gwr.multiscale, while an approximating algorithm is applied in gwr.mixed. The gwr.mixed function performs better in computational efficiency, but poorer in prediction accuracy.

Author(s)

Binbin Lu binbinlu@whu.edu.cn

References

Yang, W. (2014). An Extension of Geographically Weighted Regression with Flexible Bandwidths. St Andrews, St Andrews, UK.

Lu, B., Harris, P., Charlton, M., & Brunsdon, C. (2015). Calibrating a Geographically Weighted Regression Model with Parameter-specific Distance Metrics. Procedia Environmental Sciences, 26, 109-114.

Lu, B., Brunsdon, C., Charlton, M., & Harris, P. (2017). Geographically weighted regression with parameter-specific distance metrics. International Journal of Geographical Information Science, 31, 982-998.

Fotheringham, A. S., Yang, W. & Kang, W. (2017). Multiscale Geographically Weighted Regression (MGWR). Annals of the American Association of Geographers, 107, 1247-1265.

Yu, H., A. S. Fotheringham, Z. Li, T. Oshan, W. Kang & L. J. Wolf. 2019. Inference in multiscale geographically weighted regression. Geographical Analysis(In press).

Leong, Y.Y., & Yue, J.C. (2017). A modification to geographically weighted regression. International Journal of Health Geographics, 16 (1), 11.

Lu, B., Yang, W. Ge, Y. & Harris, P. (2018). Improvements to the calibration of a geographically weighted regression with parameter-specific distance metrics and bandwidths. Forthcoming Computers, Environment and Urban Systems.

Wolf, L.J, Oshan, T.M, Fotheringham, A.S. (2018). Single and multiscale models of process spatial heterogeneity. Geographical Analysis, 50(3): 223-246.

Murakami, D., Lu, B., Harris, P., Brunsdon, C., Charlton, M., Nakaya, T., & Griffith, D. (2019) The importance of scale in spatially varying coefficient modelling. Forthcoming Annals of the Association of American Geographers.

Examples

data(LondonHP)
EUDM <- gw.dist(coordinates(londonhp))
#No bandwidth is selected, and bws0 values are used
## Not run: 
###Similar as the basic GWR
res1<-gwr.multiscale(PURCHASE~FLOORSZ+PROF, data=londonhp, criterion="dCVR",kernel="gaussian", 
adaptive=T, bws0=c(100, 100, 100),bw.seled=rep(T, 3), dMats=list(EUDM,EUDM,EUDM))
#FBGWR
res2<-gwr.multiscale(PURCHASE~FLOORSZ+PROF, data=londonhp, criterion="dCVR",kernel="gaussian",
adaptive=T, bws0=c(100, 100, 100), dMats=list(EUDM,EUDM,EUDM))
#Mixed GWR
res3<-gwr.multiscale(PURCHASE~FLOORSZ+PROF, data=londonhp, bws0=c(Inf, 100, 100, Inf),
               bw.seled=rep(T, 3),kernel="gaussian", dMats=list(EUDM,EUDM,EUDM))
#PSDM GWR
res4<- gwr.multiscale(PURCHASE~FLOORSZ+PROF, data=londonhp, kernel="gaussian", p.vals=c(1,2,3))

## End(Not run)
[Package GWmodel version 2.3-3 Index]