LMZ.F3GWR.test.RdFour related test statistics for comparing OLS and GWR models based on bapers by Brunsdon, Fotheringham and Charlton (1999) and Leung et al (2000), and a development from the GWR book (2002).
LMZ.F3GWR.test(go)
LMZ.F2GWR.test(x)
LMZ.F1GWR.test(x)
BFC99.gwr.test(x)
BFC02.gwr.test(x, approx=FALSE)
# S3 method for gwr
anova(object, ..., approx=FALSE)a gwr object returned by gwr()
arguments passed through (unused)
default FALSE, if TRUE, use only (n - tr(S)) instead of (n - 2*tr(S) - tr(S'S)) as the GWR degrees of freedom
The papers in the references give the background for the analyses of variance presented.
BFC99.GWR.test, BFC02.gwr.test, LMZ.F1GWR.test and LMZ.F2GWR.test return "htest" objects, LMZ.F3GWR.test a matrix of test results.
Fotheringham, A.S., Brunsdon, C., and Charlton, M.E., 2002, Geographically Weighted Regression, Chichester: Wiley; http://gwr.nuim.ie/
data(columbus, package="spData")
col.bw <- gwr.sel(CRIME ~ INC + HOVAL, data=columbus,
coords=cbind(columbus$X, columbus$Y))
#> Bandwidth: 12.65221 CV score: 7432.209
#> Bandwidth: 20.45127 CV score: 7462.704
#> Bandwidth: 7.83213 CV score: 7323.545
#> Bandwidth: 4.853154 CV score: 7307.57
#> Bandwidth: 5.125504 CV score: 7322.796
#> Bandwidth: 3.012046 CV score: 6461.764
#> Bandwidth: 1.874179 CV score: 6473.378
#> Bandwidth: 2.475485 CV score: 6109.995
#> Bandwidth: 2.447721 CV score: 6098.372
#> Bandwidth: 2.228647 CV score: 6064.1
#> Bandwidth: 2.264538 CV score: 6060.774
#> Bandwidth: 2.280666 CV score: 6060.649
#> Bandwidth: 2.274969 CV score: 6060.601
#> Bandwidth: 2.2751 CV score: 6060.601
#> Bandwidth: 2.27506 CV score: 6060.601
#> Bandwidth: 2.275019 CV score: 6060.601
#> Bandwidth: 2.27506 CV score: 6060.601
col.gauss <- gwr(CRIME ~ INC + HOVAL, data=columbus,
coords=cbind(columbus$X, columbus$Y), bandwidth=col.bw, hatmatrix=TRUE)
BFC99.gwr.test(col.gauss)
#>
#> Brunsdon, Fotheringham & Charlton (1999) ANOVA
#>
#> data: col.gauss
#> F = 2.7786, df1 = 41.724, df2 = 26.867, p-value = 0.003244
#> alternative hypothesis: greater
#> sample estimates:
#> SS GWR improvement SS GWR residuals
#> 4765.792 1249.101
#>
BFC02.gwr.test(col.gauss)
#>
#> Brunsdon, Fotheringham & Charlton (2002, pp. 91-2) ANOVA
#>
#> data: col.gauss
#> F = 4.8154, df1 = 46.000, df2 = 19.384, p-value = 0.0002152
#> alternative hypothesis: greater
#> sample estimates:
#> SS OLS residuals SS GWR residuals
#> 6014.893 1249.101
#>
BFC02.gwr.test(col.gauss, approx=TRUE)
#>
#> Brunsdon, Fotheringham & Charlton (2002, pp. 91-2) ANOVA (approximate
#> degrees of freedom - only tr(S))
#>
#> data: col.gauss
#> F = 4.8154, df1 = 46.000, df2 = 25.072, p-value = 3.876e-05
#> alternative hypothesis: greater
#> sample estimates:
#> SS OLS residuals SS GWR residuals
#> 6014.893 1249.101
#>
anova(col.gauss)
#> Analysis of Variance Table
#> Df Sum Sq Mean Sq F value
#> OLS Residuals 3.000 6014.9
#> GWR Improvement 26.616 4765.8 179.055
#> GWR Residuals 19.384 1249.1 64.441 2.7786
anova(col.gauss, approx=TRUE)
#> Analysis of Variance Table
#> approximate degrees of freedom (only tr(S))
#> Df Sum Sq Mean Sq F value
#> OLS Residuals 3.000 6014.9
#> GWR Improvement 20.928 4765.8 227.72
#> GWR Residuals 25.072 1249.1 49.82 4.5709
if (FALSE) {
col.d <- gwr.sel(CRIME ~ INC + HOVAL, data=columbus,
coords=cbind(columbus$X, columbus$Y), gweight=gwr.bisquare)
col.bisq <- gwr(CRIME ~ INC + HOVAL, data=columbus,
coords=cbind(columbus$X, columbus$Y), bandwidth=col.d,
gweight=gwr.bisquare, hatmatrix=TRUE)
BFC99.gwr.test(col.bisq)
}