Running OLS
MODEL<-PctBach ~ PctRural+PctEld+PctFB+PctPov+PctBlack
MOD.OLS<-lm(MODEL, data=gSRDF@data)
summary(MOD.OLS)
##
## Call:
## lm(formula = MODEL, data = gSRDF@data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.4471 -2.0275 -0.3775 1.6223 18.7245
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 17.24373 1.75329 9.835 < 2e-16 ***
## PctRural -0.07032 0.01358 -5.179 6.93e-07 ***
## PctEld 0.01145 0.12953 0.088 0.929693
## PctFB 1.85247 0.30683 6.037 1.14e-08 ***
## PctPov -0.25524 0.07248 -3.522 0.000566 ***
## PctBlack 0.04911 0.02648 1.854 0.065602 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.714 on 153 degrees of freedom
## Multiple R-squared: 0.5884, Adjusted R-squared: 0.575
## F-statistic: 43.75 on 5 and 153 DF, p-value: < 2.2e-16
Moran’s I for residuals
coords = cbind(Longitud,Latitude)
dist.mat<-as.matrix(dist(coords, method="euclidean"))
dist.mat.inv<-1/dist.mat
diag(dist.mat.inv)<-0
dist.W1<-mat2listw(dist.mat.inv, row.names = data$SR_ID, style="W")
lm.morantest(MOD.OLS, listw = dist.W1)
##
## Global Moran I for regression residuals
##
## data:
## model: lm(formula = MODEL, data = gSRDF@data)
## weights: dist.W1
##
## Moran I statistic standard deviate = 4.4215, p-value = 4.901e-06
## alternative hypothesis: greater
## sample estimates:
## Observed Moran I Expectation Variance
## 1.907755e-02 -9.075049e-03 4.054098e-05
RES<-residuals(MOD.OLS)
colours <- c("dark blue", "blue", "red", "dark red")
MAP.RES<-SpatialPointsDataFrame(data=data.frame(RES), coords=cbind(Longitud,Latitude))
spplot(MAP.RES, cuts=quantile(RES), col.regions=colours, cex=1)
Running GWR
coords<-cbind(gSRDF@data$Longitud,gSRDF@data$Latitude)
bw<-gwr.sel(MODEL, coords = coords, gweight = gwr.Gauss, adapt = TRUE)
## Adaptive q: 0.381966 CV score: 2246.445
## Adaptive q: 0.618034 CV score: 2298.206
## Adaptive q: 0.236068 CV score: 2245.9
## Adaptive q: 0.3057039 CV score: 2233.276
## Adaptive q: 0.3082464 CV score: 2233.181
## Adaptive q: 0.3163436 CV score: 2235.26
## Adaptive q: 0.307651 CV score: 2233.182
## Adaptive q: 0.3079746 CV score: 2233.168
## Adaptive q: 0.3079339 CV score: 2233.17
## Adaptive q: 0.3080266 CV score: 2233.166
## Adaptive q: 0.3081106 CV score: 2233.162
## Adaptive q: 0.3081625 CV score: 2233.16
## Adaptive q: 0.3082032 CV score: 2233.168
## Adaptive q: 0.3081625 CV score: 2233.16
MOD.GWR<-gwr(MODEL, coords = coords, adapt = bw, hatmatrix = TRUE)
MOD.GWR
## Call:
## gwr(formula = MODEL, coords = coords, adapt = bw, hatmatrix = TRUE)
## Kernel function: gwr.Gauss
## Adaptive quantile: 0.3081625 (about 48 of 159 data points)
## Summary of GWR coefficient estimates at data points:
## Min. 1st Qu. Median 3rd Qu. Max.
## X.Intercept. 14.1902994 15.4994133 17.1733971 18.1741029 18.8831188
## PctRural -0.0814128 -0.0732267 -0.0646942 -0.0562377 -0.0519377
## PctEld -0.1969998 -0.0966747 -0.0642309 -0.0285829 0.0171665
## PctFB 0.9407392 1.3594518 2.0628107 2.7363501 3.0864117
## PctPov -0.3070984 -0.2572649 -0.2025800 -0.1247436 -0.0412649
## PctBlack -0.0191289 0.0074139 0.0341490 0.0610207 0.0878578
## Global
## X.Intercept. 17.2437
## PctRural -0.0703
## PctEld 0.0114
## PctFB 1.8525
## PctPov -0.2552
## PctBlack 0.0491
## Number of data points: 159
## Effective number of parameters (residual: 2traceS - traceS'S): 15.98299
## Effective degrees of freedom (residual: 2traceS - traceS'S): 143.017
## Sigma (residual: 2traceS - traceS'S): 3.408584
## Effective number of parameters (model: traceS): 12.16292
## Effective degrees of freedom (model: traceS): 146.8371
## Sigma (model: traceS): 3.363954
## Sigma (ML): 3.232729
## AICc (GWR p. 61, eq 2.33; p. 96, eq. 4.21): 853.2405
## AIC (GWR p. 96, eq. 4.22): 836.5033
## Residual sum of squares: 1661.636
## Quasi-global R2: 0.6759729
MAPA: PctBLACK
georgia_lines<- fortify(georgia, region="Label")
## SpP is invalid
results<-as.data.frame(MOD.GWR$SDF)
data$coefPctBlack<-results$PctBlack
gwr.point1<-ggplot(data, aes(x=Longitud,y=Latitude))+geom_point(aes(colour=data$coefPctBlack ))+scale_colour_gradient2(low = "red", mid = "white", high = "blue", midpoint = 0, space = "rgb", na.value = "grey50", guide = "colourbar", guide_legend(title="Coefs"))
gwr.point1+geom_path(data=georgia_lines,aes(long, lat, group=id), colour="grey")+coord_equal()
MAPA: PctPov
results<-as.data.frame(MOD.GWR$SDF)
data$coefPctPov<-results$PctPov
gwr.point1<-ggplot(data, aes(x=Longitud,y=Latitude))+geom_point(aes(colour=data$coefPctPov ))+scale_colour_gradient2(low = "red", mid = "white", high = "blue", midpoint = 0, space = "rgb", na.value = "grey50", guide = "colourbar", guide_legend(title="Coefs"))
gwr.point1+geom_path(data=georgia_lines,aes(long, lat, group=id), colour="grey")+coord_equal()
MAPA: PctFB
results<-as.data.frame(MOD.GWR$SDF)
data$coefPctFB<-results$PctFB
gwr.point1<-ggplot(data, aes(x=Longitud,y=Latitude))+geom_point(aes(colour=data$coefPctFB ))+scale_colour_gradient2(low = "red", mid = "white", high = "blue", midpoint = 0, space = "rgb", na.value = "grey50", guide = "colourbar", guide_legend(title="Coefs"))
gwr.point1+geom_path(data=georgia_lines,aes(long, lat, group=id), colour="grey")+coord_equal()
MAPA: PctRural
results<-as.data.frame(MOD.GWR$SDF)
data$coefPctRural<-results$PctRural
gwr.point1<-ggplot(data, aes(x=Longitud,y=Latitude))+geom_point(aes(colour=data$coefPctRural ))+scale_colour_gradient2(low = "red", mid = "white", high = "blue", midpoint = 0, space = "rgb", na.value = "grey50", guide = "colourbar", guide_legend(title="Coefs"))
gwr.point1+geom_path(data=georgia_lines,aes(long, lat, group=id), colour="grey")+coord_equal()
