eigenvectors increase spatial autocorrelation in ols regression
On Wed, 22 Jul 2020, 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?
You are using point support (your forests are at points not areas, so that
the observations are not contiguous). The advice to consider this as a
mixed model problem may be relevant. It is certainly the case that
ncf::correlog() should not be used for regression residuals.
Further, your data are in a band 1.5-4.3E, 43.0-43.4N, so using 0.7
degrees in dnearneigh() was a risky choice, and squashes the data. If you
coerce to an sf object and apply an appropriate CRS, you get many fewer
neighbours on average.
library(sf)
data <- st_as_sf(data, coords=c("LONG", "LAT"))
(nbnear4 <- dnearneigh(data, 0, 0.7))
st_crs(data) <- 4326
(nbnear4a <- dnearneigh(data, 0, 27))
# or project to a relevant planar UTM 31N spec.
data_utm31 <- st_transform(data, st_crs(32631))
(nbd <- dnearneigh(data_utm31, 0, 27))
and so on. SpatialFiltering() and ME() test against global residual
autocorrelation in finding candidate eigenvectors, and running
lm.morantest() on the fitted model shows that there is no global
autocorrelation as intended (because positive and negative local
autocorrelation cancels out). I think that the underlying problems are
mixing approaches that are not asking the same questions, and in too
little care in choosing the weights.
Hope this clarifies,
Roger
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 Biolog?a Vegetal y Ecolog?a Facultad de Ciencias y Tecnolog?a Ap. 644 Universidad del Pa?s Vasco/ Euskal Herriko Unibertsitatea Barrio Sarriena s/n 48940 Leioa, Bizkaia SPAIN Tel. ?+34 94 601 8030 Fax? +34 94 601 3500 www.ehu.eus/es/web/bgppermp ? When you believe in things that you don?t understand Then you suffer ??????????????????????? -- Stevie Wonder Download my public encryption key here: https://pgp.mit.edu/ and please use it when you send me e-mail. ?
Roger Bivand Department of Economics, Norwegian School of Economics, Helleveien 30, N-5045 Bergen, Norway. voice: +47 55 95 93 55; e-mail: Roger.Bivand at nhh.no https://orcid.org/0000-0003-2392-6140 https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en