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).
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 multiscalegwr
print(x, ...)A list of class “psdmgwr”:
a SpatialPointsDataFrame (may be gridded), or SpatialPolygonsDataFrame object (see package “sp”), or sf object (see package “sf”) 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.
a list class object including the model fitting parameters for generating the report file
a list class object including the diagnostic information of the model fitting
an object of class inheriting from “lm”, see lm.
bandwidths used for all the parameters within the back-fitting procedure
starting and ending time.
the function call used.
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
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
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 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.
maximum number of iterations in the back-fitting procedure
threshold value to terminate the back-fitting iterations
a list of distance matrices used for estimating each specific parameter
index corresponds to a specific distance matrix for each exploratory variable, if dMats is provided
a collection of positive numbers used as the power of the Minkowski distance
a collection of values used as angles in radians to rotate the coordinate system
if TRUE, great circle distances will be calculated
a vector of initializing bandwidths for the back-fitting procedure, of which the length should equal to the number of paramters if specified
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.
specified by CV for cross-validation approach or by AIC corrected (AICc) approach
threshold values to define whether the bandwidth for a specific parameter has converged or not
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;
if TRUE and bandwidth selection is undertaken, the bandwidth searches are reported
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.
if TRUE the hatmatrix for the whole model will be calculated, and AICc, adjusted-R2 values will be returned accordingly.
the minmum number of nearest neighbours if an adaptive kernel is used
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
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.
if TRUE, use the original RcppArmadillo implementation instead of the new RcppEigen implementation. Only matters if parallel.method = F or parallel.method = "omp".
an object of class “multiscalegwr”, returned by the function gwr.multiscale
arguments passed through (unused)
Binbin Lu binbinlu@whu.edu.cn
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.
data(LondonHP)
EUDM <- gw.dist(coordinates(londonhp))
#No bandwidth is selected, and bws0 values are used
if (FALSE) {
###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))
}
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