Dear all,
I am currently trying to find out if there is a way to calculate a pseudo R2
value from the output of SAR error models or spatial GLS models. I have seen
this presented in publications, and the program SAM (Spatial analysis in
macroecology) produces this value... but I need to implement the calculation of
this pseudo R2 in a piece of R code I am writing. The authors of SAM say they
calculate their pseudo R2 using Nagelkerke's 1991 furmulation, which I also
have seen used in various other places; so I have tried to use it with R output
from functions errorsarlm and gls in R, but the results do not make sense.
Here is what I am doing:
For SAR error model:
my.lm<-lm(Y~X1+X2+X3, data=DATA)
coords<-as.matrix(cbind(DATA$x,DATA$y))
nb.5<-dnearneigh(coords,0,5)
nb.5.w<-nb2listw(nb.5, glist=NULL, style="W", zero.policy=TRUE)
my.sar.error<- errorsarlm(my.lm, listw=nb.5.w, na.action="na.omit")
lL.B <- logLik(my.sar.error)
lL.0 <- updata(my.sar.error, ~1)
yN<-nrow(DATA)
Nagelkerke<-(1-exp((lL.B-lL.0)*(-2/yN)))/(1-exp((lL.0)*(2/yN)))
Nagelkerke[1]
For the GLS it looks almost identical:
exp.correl.structure<-corExp(form=~x+y)
my.gls<-gls(Y~X1+X2+X3, data=DATA, correlation=exp.correl.structure,
method="ML"))
lL.B <- logLik(my.gls)
lL.0 <- updata(my.gls, ~1)
yN<-nrow(DATA)
Nagelkerke<-(1-exp((lL.B-lL.0)*(-2/yN)))/(1-exp((lL.0)*(2/yN)))
Nagelkerke[1]
>From running these analyses, I obtain that the pseudo R2 is of almost 0.997,
>while the ols R2 is of only 0.59. I know this two numbers are not really
>comparable (I do not expect them to be the same), but also the pseudo R2
>produced by SAM is of around 0.55. So I am not sure what is wrong. I think the
>pseudo R2 I am obtaining is for the model after accountiong for all the
>spatial autocorrelation, rather than only from what can be predicted by the
>explanatory variables in the model. If any one knows of a way to do this, or
>has any ideas of approaches to take or resources to visit, I would appreciate
>the input.
Thanks in advance,
Sebastian
J. Sebastián Tello
Department of Biological Sciences
285 Life Sciences Building
Louisiana State University
Baton Rouge, LA, 70803
(225) 578-4284 (office and lab.)
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