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<p><tt>Dear Roger and list members,</tt></p>
<p><tt>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? <br>
</tt></p>
<p><tt>Can you please enlighten me as to what's going on, what I am
doing wrong, or what I should try?</tt></p>
<p><tt>Thanks in advance for you time.</tt></p>
<p><tt>Peter<br>
</tt></p>
<p><tt>The data are here:</tt></p>
<p><tt><a class="moz-txt-link-freetext"
href="https://drive.google.com/file/d/1Z3FIGIAbYvXqGETn0EWLjTOY8MYpZi_S/view?usp=sharing"
moz-do-not-send="true">https://drive.google.com/file/d/1Z3FIGIAbYvXqGETn0EWLjTOY8MYpZi_S/view?usp=sharing</a><br>
</tt></p>
<p><tt>The analysis goes like this:</tt></p>
<tt>library(spatialreg)<br>
library(spdep)<br>
library(tidyverse)<br>
library(car)<br>
library(ncf)<br>
<br>
<br>
data <- read_csv("for_RAR.csv")<br>
set.seed(12345)<br>
x <- data$ses.mntd<br>
y <- log(data$RAR)<br>
ols_for_RAR <- lm(y ~ x)<br>
## qqplot() and shapiro.test() show residuals are nicely
distributed<br>
# x is significant and R-square about 0.2, demonstrated here<br>
car::Anova(ols_for_RAR,type="III")<br>
summary(ols_for_RAR)<br>
<br>
# the following appears to make an acceptable neighbor network<br>
c1<-c(data$LONG)<br>
c2<-c(data$LAT)<br>
cbindForests<-cbind(c1,c2)<br>
# a value of 0.7, below, is sufficient to join all the points.<br>
# qualitatively the results aren't affected, as far as I see by
setting this higher<br>
# However, the number of eigenvectors generated by
SpatialFiltering() varies a lot<br>
nbnear4 <- dnearneigh(cbindForests, 0, 0.7) <br>
plot(nbnear4, cbindForests, col = "red", pch = 20)<br>
<br>
# SAC appears significant at short distances (<10km), which is
what I want to remove<br>
cor_for <- correlog(c1, c2, residuals(ols_for_RAR), increment =
1, resamp = 1000, latlon=TRUE, na.rm = TRUE)<br>
plot(cor_for$correlation[1:20],type="s")<br>
# p-values<br>
print(cor_for$p[which(cor_for$p < 0.05)])<br>
# Moran's I values<br>
cor_for$correlation[which(cor_for$p < 0.05)]<br>
<br>
# Generate optimized spatial eigenvectors using SpatialFiltering()
and use them<br>
# Several vectors are generated depending on values in
dnearneigh()<br>
spfilt_mntd_RAR<- spatialreg::SpatialFiltering(y ~ x,
nb=nbnear4,style = "W", tol=0.0001, ExactEV = TRUE)<br>
new_mod <- lm(y ~ x + fitted(spfilt_mntd_RAR))<br>
car::Anova(new_mod, type="III")<br>
summary(new_mod)<br>
<br>
# Plot Moran's I at distances under 20km<br>
cor_for_1c <- correlog(c1, c2, residuals(new_mod), increment =
1, resamp = 1000, latlon=TRUE, na.rm = TRUE)<br>
plot(cor_for_1c$correlation[1:20],type="s")<br>
<br>
# Extract significant values of Moran's I<br>
cor_for_1c$p[which(cor_for_1c$p < 0.05)]<br>
cor_for_1c$correlation[which(cor_for_1c$p < 0.05)]<br>
<br>
# The result is that Moran's I is significant at additional short
distances</tt><br>
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<p><font face="Arial">_+_+_+_+_+_+_+_+_<br>
</font><font face="Arial"><font style="font-size: 12pt" size="3"><br>
Peter
B. Pearman<br>
Ikerbasque Research Professor</font></font></p>
<p style="margin-bottom: 0.08in"><font face="Arial"><font
style="font-size: 12pt" size="3">Laboratory
for Computational Ecology and Evolution<br>
Depart</font></font><font face="Arial"><font
style="font-size: 12pt" size="3">a</font></font><font
face="Arial"><font style="font-size: 12pt" size="3">mento
de Biolog</font></font><font face="Arial"><font
style="font-size: 12pt" size="3"><span lang="es-ES">í</span></font></font><font
face="Arial"><font style="font-size: 12pt" size="3">a
Vegetal y Ecología<br>
Facultad de Ciencias y Tecnología<br>
Ap.
644<br>
Universidad del País Vasco/</font></font> <font
face="Arial"><font style="font-size: 12pt" size="3">Euskal
Herriko Unibertsitatea</font></font></p>
<p style="margin-bottom: 0in"><font face="Arial"><font
style="font-size: 12pt" size="3">Barrio
Sarriena s/n<br>
48940 Leioa, Bizkaia </font></font>
</p>
<p><font face="Arial"><font style="font-size: 12pt" size="3">SPAIN</font></font></p>
<p><font face="Arial"><font style="font-size: 12pt" size="3">Tel.
</font></font> <font face="Arial"><font style="font-size:
12pt" size="3"><span lang="de-DE">+34
94 601 8030</span></font></font></p>
<p lang="de-DE"><font face="Arial"><font style="font-size: 12pt"
size="3">Fax
+34 94 601 3500</font></font></p>
<p><a href="http://www.ehu.es/peter.pearman"><font face="Arial"><font
style="font-size: 12pt" size="3"><span lang="de-DE">www.ehu.eus/es/web/bgppermp</span></font></font></a></p>
<p> </p>
<p><font face="Arial"><font style="font-size: 12pt" size="3"><span
lang="de-DE">When</span></font></font>
<font face="Arial"><font style="font-size: 12pt" size="3"><span
lang="de-DE">you
believe in things that you don’t understand</span></font></font></p>
<p><font face="Arial"><font style="font-size: 12pt" size="3"><span
lang="de-DE">Then</span></font></font>
<font face="Arial"><font style="font-size: 12pt" size="3"><span
lang="de-DE">you
suffer</span></font></font></p>
<p>
<font face="Arial"><font style="font-size: 12pt" size="3"><span
lang="de-DE">--
Stevie Wonder </span></font></font>
</p>
<p style="margin-bottom: 0in"><br>
</p>
<p style="margin-bottom: 0in"><font face="Arial"><font
style="font-size: 8pt" size="1"><span lang="de-DE">Download
my public encryption key here: <a
href="https://pgp.mit.edu/">https://pgp.mit.edu/</a></span></font></font></p>
<p style="margin-bottom: 0in"><font face="Arial"><font
style="font-size: 8pt" size="1"><span lang="de-DE">and</span></font></font>
<font face="Arial"><font style="font-size: 8pt" size="1"><span
lang="de-DE">please
use it when you send me e-mail.</span></font></font></p>
<p> </p>
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