# gwr.montecarlo: Monte Carlo (randomisation) test for significance of GWR... In GWmodel: Geographically-Weighted Models

## Description

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

## Usage

 ```1 2``` ```gwr.montecarlo(formula, data = list(),nsims=99, kernel="bisquare",adaptive=F, bw, p=2, theta=0, longlat=F,dMat) ```

## Arguments

 `formula` Regression model formula of a formula object `data` a Spatial*DataFrame, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp `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` bandwidth used in the weighting function, possibly calculated by `bw.gwr` `p` the power of the Minkowski distance, default is 2, i.e. the Euclidean distance `theta` an angle in radians to rotate the coordinate system, default is 0 `longlat` if TRUE, great circle distances will be calculated `dMat` a pre-specified distance matrix, it can be calculated by the function `gw.dist`

## Value

 `pmat` A vector containing p-values for all the GWR parameters

## Note

The function “montecarlo.gwr” (in the early versions of GWmodel) has been renamed as “gwr.montecarlo”, while the old name is still kept valid.

## Author(s)

Binbin Lu [email protected]

## 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

Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.

Charlton, M, Fotheringham, S, and Brunsdon, C (2007), GWR3.0.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```## Not run: data(LondonHP) DM<-gw.dist(dp.locat=coordinates(londonhp)) bw<-bw.gwr(PURCHASE~FLOORSZ,data=londonhp,dMat=DM, kernel="gaussian") #See any difference in the next two commands and why? res.mont1<-gwr.montecarlo(PURCHASE~PROF+FLOORSZ, data = londonhp,dMat=DM, nsim=99, kernel="gaussian", adaptive=FALSE, bw=3000) res.mont2<-gwr.montecarlo(PURCHASE~PROF+FLOORSZ, data = londonhp,dMat=DM, nsim=99, kernel="gaussian", adaptive=FALSE, bw=300000000000) ## End(Not run) ```

### Example output

```Loading required package: maptools
Checking rgeos availability: TRUE
Welcome to GWmodel version 2.0-4.
Note: This verision has been re-built with RcppArmadillo to improve its performance.
Fixed bandwidth: 28008.52 CV score: 901202470969
Fixed bandwidth: 17313.68 CV score: 842907727581
Fixed bandwidth: 10703.9 CV score: 736181883398
Fixed bandwidth: 6618.837 CV score: 607130814353
Fixed bandwidth: 4094.128 CV score: 529769270141
Fixed bandwidth: 2533.772 CV score: 496244493691
Fixed bandwidth: 1569.419 CV score: 558268461315
Fixed bandwidth: 3129.775 CV score: 504912379213
Fixed bandwidth: 2165.422 CV score: 500148436808
Fixed bandwidth: 2761.425 CV score: 498237171785
Fixed bandwidth: 2393.075 CV score: 496399101924
Fixed bandwidth: 2620.728 CV score: 496732595196
Fixed bandwidth: 2480.03 CV score: 496150911653
Fixed bandwidth: 2446.816 CV score: 496183570335
Fixed bandwidth: 2500.558 CV score: 496166149711
Fixed bandwidth: 2467.344 CV score: 496154814854
Fixed bandwidth: 2487.871 CV score: 496153635785
Fixed bandwidth: 2475.184 CV score: 496151178429
Fixed bandwidth: 2483.025 CV score: 496151494463
Fixed bandwidth: 2478.179 CV score: 496150836405
Fixed bandwidth: 2477.035 CV score: 496150899230
Fixed bandwidth: 2478.886 CV score: 496150839373
Fixed bandwidth: 2477.742 CV score: 496150850527
Fixed bandwidth: 2478.449 CV score: 496150833774
Fixed bandwidth: 2478.616 CV score: 496150834475
Fixed bandwidth: 2478.346 CV score: 496150834229
Fixed bandwidth: 2478.513 CV score: 496150833832
Fixed bandwidth: 2478.41 CV score: 496150833868
Fixed bandwidth: 2478.474 CV score: 496150833765
Fixed bandwidth: 2478.489 CV score: 496150833779
Fixed bandwidth: 2478.465 CV score: 496150833764
Fixed bandwidth: 2478.459 CV score: 496150833766
Fixed bandwidth: 2478.468 CV score: 496150833764
Fixed bandwidth: 2478.47 CV score: 496150833764
Fixed bandwidth: 2478.467 CV score: 496150833764
Fixed bandwidth: 2478.466 CV score: 496150833764
Fixed bandwidth: 2478.467 CV score: 496150833764
Fixed bandwidth: 2478.468 CV score: 496150833764
Fixed bandwidth: 2478.467 CV score: 496150833764
Fixed bandwidth: 2478.467 CV score: 496150833764
Fixed bandwidth: 2478.467 CV score: 496150833764
Fixed bandwidth: 2478.467 CV score: 496150833764
Fixed bandwidth: 2478.467 CV score: 496150833764

Tests based on the Monte Carlo significance test

p-value
(Intercept)    0.47
PROF           0.15
FLOORSZ        0.03

Tests based on the Monte Carlo significance test

p-value
(Intercept)    0.44
PROF           0.49
FLOORSZ        0.45
```

GWmodel documentation built on Feb. 15, 2019, 5:06 p.m.