R help - Aug 2012 - spatial auto-correlation structure in nlme

Dear R users,

I'm estimating a mixed effects model in which the spatial correlation is
controlled for by the "corGaus" structure. I'm wondering if there
is a
document or paper that explains how the spatial correlation structure (such
as "corExp" or "corGaus") works.

Let me use the example and data posted on UCLA's R FAQ webpage to explain
my problems. The link for the webpage is:
http://www.ats.ucla.edu/stat/r/faq/spatial_regression.htm

install.packages("nlme")
library(nlme)

spdata <-
read.table("http://www.ats.ucla.edu/stat/R/faq/thick.csv", header
= T, sep = ",")
dummy <- rep(1, 75)
spdata <- cbind(spdata, dummy)

### estimate the null model ###
soil.model <- lme(fixed = thick ~ soil, data = spdata, random = ~ 1 |
dummy, method = "ML")
summary(soil.model)
plot(Variogram(soil.model,form=~north+east))

### updated the model by the spatial correlation structure ####
soil.gaus <- update(soil.model, correlation=corGaus(1,form=~north+east))
summary(soil.gaus)
plot(Variogram(soil.gaus,form=~north+east))

My questions are:

1) Is there a way that I can tell, to what extent the spatial correlation
has been controlled for by the model, besides the improvements of AIC, BIC,
and Loglik?

2) where can I find the formulas for the corExp or corGaus?

Thanks!

Gary

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