[R-sig-Geo] eigenvectors increase spatial autocorrelation in ols regression

[Spencer Graves]

       Have you considered the "corSpher" and "corSpatial" functions in 
the nlme package?


       Spencer Graves


On 2020-07-22 05:09, Peter B. Pearman wrote:
>
> Dear Roger and list members,
>
> I have a ols regression and want to remove spatial autocorrelation 
> (SAC) from the residuals, in order to avoid its potential effects of 
> SAC on the hypothesis tests (and the reviewers/editor).  I have 
> generated spatial eigenvectors with SpatialFiltering(), and added the 
> generated vectors to the regression.  Surprisingly, SAC appears to 
> become more pronounced.  I also tried ME(), but many more vectors are 
> produced and SAC is also not removed.  Isn't including the vectors 
> from SpatialFiltering() supposed to reduce SAC?
>
> Can you please enlighten me as to what's going on, what I am doing 
> wrong, or what I should try?
>
> Thanks in advance for you time.
>
> Peter
>
> The data are here:
>
> https://drive.google.com/file/d/1Z3FIGIAbYvXqGETn0EWLjTOY8MYpZi_S/view?usp=sharing
>
> The analysis goes like this:
>
> library(spatialreg)
> library(spdep)
> library(tidyverse)
> library(car)
> library(ncf)
>
>
> data <- read_csv("for_RAR.csv")
> set.seed(12345)
> x <- data$ses.mntd
> y <- log(data$RAR)
> ols_for_RAR <- lm(y ~ x)
> ## qqplot() and shapiro.test() show residuals are nicely distributed
> # x is significant and R-square about 0.2, demonstrated here
> car::Anova(ols_for_RAR,type="III")
> summary(ols_for_RAR)
>
> # the following appears to make an acceptable neighbor network
> c1<-c(data$LONG)
> c2<-c(data$LAT)
> cbindForests<-cbind(c1,c2)
> # a value of 0.7, below, is sufficient to join all the points.
> # qualitatively the results aren't affected, as far as I see by 
> setting this higher
> # However, the number of eigenvectors generated by SpatialFiltering() 
> varies a lot
> nbnear4 <- dnearneigh(cbindForests, 0, 0.7)
> plot(nbnear4, cbindForests, col = "red", pch = 20)
>
> # SAC appears significant at short distances (<10km), which is what I 
> want to remove
> cor_for <- correlog(c1, c2, residuals(ols_for_RAR), increment = 1, 
> resamp = 1000, latlon=TRUE, na.rm = TRUE)
> plot(cor_for$correlation[1:20],type="s")
> # p-values
> print(cor_for$p[which(cor_for$p < 0.05)])
> # Moran's I values
> cor_for$correlation[which(cor_for$p < 0.05)]
>
> # Generate optimized spatial eigenvectors using SpatialFiltering() and 
> use them
> # Several vectors are generated depending on values in dnearneigh()
> spfilt_mntd_RAR<- spatialreg::SpatialFiltering(y ~ x, nb=nbnear4,style 
> = "W", tol=0.0001, ExactEV = TRUE)
> new_mod <- lm(y ~ x + fitted(spfilt_mntd_RAR))
> car::Anova(new_mod, type="III")
> summary(new_mod)
>
> # Plot Moran's I at distances under 20km
> cor_for_1c <- correlog(c1, c2, residuals(new_mod), increment = 1, 
> resamp = 1000, latlon=TRUE, na.rm = TRUE)
> plot(cor_for_1c$correlation[1:20],type="s")
>
> # Extract significant values of Moran's I
> cor_for_1c$p[which(cor_for_1c$p < 0.05)]
> cor_for_1c$correlation[which(cor_for_1c$p < 0.05)]
>
> # The result is that Moran's I is significant at additional short 
> distances
> -- 
>
> _+_+_+_+_+_+_+_+_
>
> Peter B. Pearman
> Ikerbasque Research Professor
>
> Laboratory for Computational Ecology and Evolution
> Departamento de Biología Vegetal y Ecología
> Facultad de Ciencias y Tecnología
> Ap. 644
> Universidad del País Vasco/ Euskal Herriko Unibertsitatea
>
> Barrio Sarriena s/n
> 48940 Leioa, Bizkaia
>
> SPAIN
>
> Tel. +34 94 601 8030
>
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>
> www.ehu.eus/es/web/bgppermp <http://www.ehu.es/peter.pearman>
>
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>
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