I have 27 sites and each site has six samples. This is a classic case where
the data are nested. But the data, show spatial auto-correlation too.

Here, there are the firsts lines of the table:

Site

Samples

X

Y

OD

A

1

573773

8190515

3.65

A

2

573805.7

8190535

3.65

A

3

573830.7

8190554

3.75

A

4

573802.3

8190595

3.7

A

5

573837.4

8190615

3.6

A

6

573855.9

8190573

2.9

B

1

573766

8191513

3.65

B

2

573806.5

8191480

4

B

3

573848.4

8191473

4.5

B

4

573892

8191479

4.75

B

5

573936.4

8191495

4.75

B

6

573993.9

8191594

4.7

Where: 1 at 6 are samples in each site. X and Y are geographics coordinates
and OD are the value of the variable.

How do I remove the effect of space? What is the best option?

I adjusted the model using the *function gls (Generalised least squares)*
 of *package nlme:*

OD2.a<-gls(OD~1, data=table)
M1C.a<-gls(OD~1,correlation=corRatio(form=~X+Y,nugget=TRUE),data=table)
M1E.a<-gls(OD~1,correlation=corExp(form=~X+Y,nugget=TRUE),data=table)
M1S.a<-gls(OD~1,correlation=corSpher(form=~X+Y,nugget=TRUE),data=table)
M1L.a<-gls(OD~1,correlation=corLin(form=~X+Y,nugget=TRUE),data=table)
M1G.a<-gls(OD~1,correlation=corGaus(form=~X+Y,nugget=TRUE),data=table)
AIC(OD2.a, M1C.a, M1E.a, M1S.a, M1L.a, M1G.a)

Despite the M1C.a was the best model, showing the effect of the spatial
auto correlation, but the data are nested.

I want to generate values (residuals) without the effect of the space and
use the values in *Mixed Effects Model:*

OD.model<-lme(OD.new~X1+X2+X3, random=~1| Site, data= table)

This is possible?

Thanks

-- 
Izaias M. Fernandes
Doutorando em Biologia de Água Doce e Pesca Interior
Instituto Nacional de Pesquisas da Amazônia - Brazil

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