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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | ```
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 |

`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 |

`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 |

`hatmatrix` |
if TRUE, return the hatmatrix as a component of the result. |

`control` |
a list of parameters for controlling the fitting process. For |

`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 |

`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 |

`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 |

`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 |

`flm` |
a matrix with the fitted values for all local elliptical models. |

`adapt` |
the |

`gweight` |
the |

`spdisp` |
the |

`this.call` |
the function call used. |

`fp.given` |
the |

`longlat` |
the |

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`

1 2 3 4 5 6 | ```
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)
``` |

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