# gwer.montecarlo: Monte Carlo (randomisation) Test for Significance of GWER... In gwer: Geographically Weighted Elliptical Regression

## Description

This function implements a Monte Carlo (randomisation) test to test for significant (spatial) variability of a geographically weighted elliptical regression model's parameters or coefficients.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```gwer.montecarlo( formula, family = Normal, data = list(), nsims = 99, kernel = "bisquare", adaptive = F, bw, p = 2, theta = 0, dispersion = NULL, longlat = F, dMat, control = glm.control(epsilon = 1e-04, maxit = 100, trace = F) ) ```

## Arguments

 `formula` regression model formula of a formula `object`. `family` a description of the error distribution to be used in the model (see `family.elliptical` for details of elliptical distribution). `data` an optional data frame, list or environment containing the variables in the model. `nsims` the number of randomisations. `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). `bw` value of the selected bandwidth used in the weighting function (see `bw.gwer` for bandwidth optimization). `p` the power of the Minkowski distance, default is 2 (Euclidean distance). `theta` an angle in radians to rotate the coordinate system, default is 0 `dispersion` an optional fixed value for dispersion parameter. `longlat` if TRUE, great circle distances will be calculated. `dMat` a pre-specified distance matrix, it can be calculated by the function `gw.dist`. `control` a list of parameters for controlling the fitting process. This is passed by `glm.control`.

## Value

A vector containing p-values for all parameters spatial variability tests

## References

Brunsdon C, Fotheringham AS, Charlton ME (1998) Geographically weighted regression - modelling spatial non-stationarity. Journal of the Royal Statistical Society, Series D-The Statistician 47(3):431-443

`bw.gwer`, `elliptical`, `family.elliptical`
 ```1 2 3 4 5 6 7``` ```data(georgia, package = "spgwr") fit.formula <- PctBach ~ TotPop90 + PctRural + PctFB + PctPov gwer.bw.t <- bw.gwer(fit.formula, data = gSRDF, family = Student(4), adapt = TRUE) gwer.fit.t <- gwer(fit.formula, data = gSRDF, family = Student(4), bandwidth = gwer.bw.t, adapt = TRUE, parplot = FALSE, hatmatrix = TRUE, spdisp = TRUE, method = "gwer.fit") gwer.montecarlo(fit.formula, data = gSRDF, family = Student(3), bw = gwer.bw.t, adaptive = TRUE) ```