gwer.multiscale: Multiscale Geographically Weighted Elliptical Regression
In gwer: Geographically Weighted Elliptical Regression

Description Usage Arguments Value References See Also Examples

The function fit geographically weighted elliptical regression model to explore the non-stationarity relationshps across differente spatial scales.

gwer.multiscale(
  formula,
  data,
  kernel = "bisquare",
  approach = "CV",
  adaptive = FALSE,
  criterion = "dCVR",
  family = Normal,
  threshold = 1e-05,
  dMats,
  p.vals,
  theta.vals,
  longlat = NULL,
  bws0,
  bw.seled = rep(F, length(bws0)),
  bws.thresholds = rep(0.1, length(dMats)),
  bws.reOpts = 5,
  spdisp = "local",
  verbose = F,
  weights,
  dispersion = NULL,
  na.action = "na.fail",
  hatmatrix = T,
  control = glm.control(epsilon = 1e-04, maxit = 100, trace = F),
  model = FALSE,
  x = FALSE,
  y = TRUE,
  contrasts = NULL,
  parplot = FALSE,
  max.iterations = 2000,
  subset,
  offset,
  predictor.centered = rep(T, length(bws0) - 1),
  nlower = 10,
  ...
)

`formula`	regression model formula as in `glm`.
`data`	model data frame, or may be a 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
`approach`	specified by CV for cross-validation approach or by AIC corrected (AICc) approach
`adaptive`	defines the type of bandwidth used. either NULL (default) or a proportion between 0 and 1 of observations to include in weighting scheme (k-nearest neighbours).
`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.
`family`	a description of the error distribution to be used in the model (see `family.elliptical` for details of family functions).
`threshold`	threshold value to terminate the back-fitting iteration.
`dMats`	a list of distance matrices used for estimating each specific parameter
`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`	TRUE if point coordinates are longitude-latitude decimal degrees, in which case distances are measured in kilometers. If x is a SpatialPoints object, the value is taken from the object itself.
`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.
`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;
`spdisp`	if TRUE dispersion parameter varies geographically.
`verbose`	if TRUE (default) reports the progress of search for bandwidth.
`weights`	an optional numeric vector of weights to be used in the fitting process.
`dispersion`	an optional fixed value for dispersion parameter.
`na.action`	a function which indicates what should happen when the data contain NAs (see `glm`).
`hatmatrix`	if TRUE, return the hatmatrix as a component of the result.
`control`	a list of parameters for controlling the fitting process. For `elliptical` this is passed by `glm.control`.
`model`	a logical value indicating whether model frame should be included as a component of the return.
`x`	a logical value indicating whether the response vector used in the fitting process should be returned as components of the return.
`y`	a logical value indicating whether model matrix used in the fitting process should be returned as components of the return.
`contrasts`	an optional list. See the `contrasts.arg` of `model.matrix.default`.
`parplot`	if TRUE the parameters boxplots are plotted.
`max.iterations`	maximum number of iterations in the back-fitting procedure.
`subset`	an optional numeric vector specifying a subset of observations to be used in the fitting process.
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting as in `glm`.
`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.
`nlower`	the minmum number of nearest neighbours if an adaptive kernel is used
`...`	arguments to be used to form the default control argument if it is not supplied directly.

returns an object of class “gwer”, a list with follow components:

`SDF`	a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package sp) with fit.points, weights, GWR coefficient estimates, dispersion and the residuals in its `data` slot.
`coef`	the matrices of coefficients, standard errors and significance values for parameters hypothesis test.
`dispersion`	either the supplied argument or the estimated dispersion with standard error.
`hat`	hat matrix of the geographically weighted elliptical model.
`lm`	elliptical global regression on the same model formula.
`results`	a list of results values for fitted geographically weighted elliptical model.
`bandwidth`	the bandwidth used in geographical weighting function.
`fitted`	the fitted mean values of the geographically weighted elliptical model.
`hatmatrix`	a logical value indicating if hatmatrix was considered
`gweights`	a matrix with the geographical weighting for all local elliptical models.
`family`	the `family` object used.
`flm`	a matrix with the fitted values for all local elliptical models.
`adapt`	the `adapt` object used.
`gweight`	the `gweights` object used.
`spdisp`	the `spdisp` object used.
`this.call`	the function call used.
`fp.given`	the `fp.given` object used.
`longlat`	the `longlat` object used.

Brunsdon, C., Fotheringham, A. S. and Charlton, M. E. (1996). Geographically weighted regression: a method for exploring spatial nonstationarity. Geographical analysis, 28(4), 281-298. doi: 10.1111/j.1538-4632.1996.tb00936.x

Fang, K. T., Kotz, S. and NG, K. W. (1990, ISBN:9781315897943). Symmetric Multivariate and Related Distributions. London: Chapman and Hall.

bw.gwer, elliptical, family.elliptical

data(georgia, package = "spgwr")
fit.formula <- PctBach ~ TotPop90 + PctRural + PctFB + PctPov
gwer.bw.t <- bw.gwer(fit.formula, data = gSRDF, family = Student(3), adapt = TRUE)
msgwr.fit.t <- gwer.multiscale(fit.formula, family = Student(3), data = gSRDF, 
                               bws0 = rep(gwer.bw.t, 5), hatmatrix = TRUE, 
                               adaptive = TRUE)