Global tests of geographical weighted regressions

Four 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)

Arguments

go, x, object

a gwr object returned by gwr()
…

arguments passed through (unused)
approx

default FALSE, if TRUE, use only (n - tr(S)) instead of (n - 2*tr(S) - tr(S'S)) as the GWR degrees of freedom

Details

The papers in the references give the background for the analyses of variance presented.

Value

BFC99.GWR.test, BFC02.gwr.test, LMZ.F1GWR.test and LMZ.F2GWR.test return "htest" objects, LMZ.F3GWR.test a matrix of test results.

References

Fotheringham, A.S., Brunsdon, C., and Charlton, M.E., 2002, Geographically Weighted Regression, Chichester: Wiley; http://gwr.nuim.ie/

See also

gwr

Examples

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
col.d <- gwr.sel(CRIME ~ INC + HOVAL, data=columbus,
  coords=cbind(columbus$X, columbus$Y), gweight=gwr.bisquare)
#> Bandwidth: 12.65221 CV score: 8180.619 
#> Bandwidth: 20.45127 CV score: 7552.85 
#> Bandwidth: 25.27136 CV score: 7508.227 
#> Bandwidth: 23.68132 CV score: 7519.864 
#> Bandwidth: 28.25033 CV score: 7491.85 
#> Bandwidth: 30.09144 CV score: 7486.673 
#> Bandwidth: 31.69353 CV score: 7483.663 
#> Bandwidth: 31.08159 CV score: 7484.706 
#> Bandwidth: 32.21945 CV score: 7482.846 
#> Bandwidth: 32.54449 CV score: 7482.371 
#> Bandwidth: 32.74538 CV score: 7482.088 
#> Bandwidth: 32.86953 CV score: 7481.916 
#> Bandwidth: 32.94626 CV score: 7481.812 
#> Bandwidth: 32.99368 CV score: 7481.748 
#> Bandwidth: 33.02299 CV score: 7481.708 
#> Bandwidth: 33.04111 CV score: 7481.684 
#> Bandwidth: 33.0523 CV score: 7481.669 
#> Bandwidth: 33.05922 CV score: 7481.659 
#> Bandwidth: 33.0635 CV score: 7481.654 
#> Bandwidth: 33.06614 CV score: 7481.65 
#> Bandwidth: 33.06777 CV score: 7481.648 
#> Bandwidth: 33.06878 CV score: 7481.647 
#> Bandwidth: 33.06941 CV score: 7481.646 
#> Bandwidth: 33.06979 CV score: 7481.645 
#> Bandwidth: 33.07003 CV score: 7481.645 
#> Bandwidth: 33.07018 CV score: 7481.645 
#> Bandwidth: 33.07027 CV score: 7481.645 
#> Bandwidth: 33.07032 CV score: 7481.645 
#> Bandwidth: 33.07037 CV score: 7481.645 
#> Bandwidth: 33.07037 CV score: 7481.645 
#> Warning: Bandwidth converged to upper bound:33.0704149683672
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)
#> 
#> 	Brunsdon, Fotheringham & Charlton (1999) ANOVA
#> 
#> data:  col.bisq
#> F = 1.2954, df1 = 14.042, df2 = 45.445, p-value = 0.2473
#> alternative hypothesis: greater
#> sample estimates:
#> SS GWR improvement   SS GWR residuals 
#>           269.0627          5745.8301 
#>