[R-sig-Geo] Strange R2 values from spatial durbin model

[Defriez, Emma]

Hi,
 I am hoping someone might be able to help me. I have been fitting spatial models with spdep. The mixed model appears to best describe the spatial autocorrelation in the data and I am now trying to  find the most parsimonious combination of variables. I have noticed that although the AIC and log likelihood values do change the Nagelkerke R2 remains essentially the same for all models, showing the biggest change when a different weight matrix is used. Below is a small summery table for 3 different models and 4 weight matrices. A single variable model with only var1 explains the same amount of variation as the full model which could be reasonable but a completely different single variable model (var6) still explains the same amount of variation which is very strange. 

I realise that R2 is not used to determine the most appropriate model with this kind of modelling but it has raised alarm bells ,does  this suggests that the model is misspecified? I don't know if I have made a mistake in my code somewhere that I cannot see.


weight         formula       					AIC       	            	 R2         		 LogLik
W 	chl~ var1+var2+var3+var4+var5+var6 		-34554.06 	0.8910829 	17292.03
W            			          chl~ var1		 -33882.83 	0.8886748 	16946.41
W       			                          chl~ var6		 -33581.47 	0.8876084 	16795.74
S 	chl~ var1+var2+var3+var4+var5+var6 		-28317.57 	0.8673353 	14174.79
S          			     	        chl~ var1		 -26324.23 	0.8586102 	13168.12
S           				        chl~ var6		-24746.26 	0.8513727 	12379.13
B	chl~ var1+var2+var3+var4+var5+var6 		-24368.85 	0.8496826 	12200.43
B          				        chl~ var1 		-21194.94 	0.8337000 	10603.47
B           				       chl~ var6 		-19051.44 	0.8220316  	9531.72
C 	chl~ var1+var2+var3+var4+var5+var6		 -24314.47 	0.8494238 	12173.24
C              			       chl~ var1 		-20918.91 	0.8322414 	10465.45
C           				       chl~ var6     		-18839.42 	0.8208338  	9425.71


#############################################################
### Example of code for creating models, weight style and ols formula varied
#############################################################

coords<-cbind(longs,lats)
coords<-as.matrix(coords)

#######################
#Define neighbourhood
nn<-dnearneigh(coords,0,150,longlat = TRUE)

#get inverse distances so further points have less influence
dists <- nbdists(nn, coords)
idw <- lapply(dists, function(x) 1/(x^2))

 #Spatial weights
nnW<-nb2listw(nn, glist=idw, style=W,zero.policy=TRUE)

#-------------------------------------------  model ----------------------------------------------------------#
ols<-lm(as.formula(chl~ var1+var2+var3+var4+var5+var6))

hW <- as(as_dgRMatrix_listw(nnW), "CsparseMatrix")
  set.seed(123456)
  htr <- trW(hW, m = 24)

  mod<-lagsarlm(formula=formula(ols),listw=nnW, na.action=na.omit, type="mixed", method='LU',
              tol.solve=1e-16, zero.policy=TRUE, tr=htr)


sessionInfo()
R version 3.0.2 (2013-09-25)
Platform: x86_64-pc-linux-gnu (64-bit)

locale:
 [1] LC_CTYPE=en_GB.UTF-8       LC_NUMERIC=C
 [3] LC_TIME=en_GB.UTF-8        LC_COLLATE=en_GB.UTF-8
 [5] LC_MONETARY=en_GB.UTF-8    LC_MESSAGES=en_GB.UTF-8
 [7] LC_PAPER=en_GB.UTF-8       LC_NAME=C
 [9] LC_ADDRESS=C               LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] boot_1.3-9   spdep_0.5-68 Matrix_1.1-0 sp_1.0-14

loaded via a namespace (and not attached):
[1] coda_0.16-1     deldir_0.1-1    grid_3.0.2      lattice_0.20-24
[5] LearnBayes_2.12 MASS_7.3-29     nlme_3.1-111    splines_3.0.2

Thanks,
Emma

PhD student 
Faculty of Natural Sciences, Department of Life Sciences
Imperial College London