I'm trying to do a simple (?) analysis of a 1D spatial data set,
allowing for spatial autocorrelation. (Actually, I'm comparing expected
vs. observed for a spatial model of a 1D spatial data set.) I'm using
models like
gls(obs~exp,correlation=corExp(form=~pos),data=data)
or
gls(obs~exp,correlation=corLin(form=~pos),data=data)
This form is supposed to fit a linear model of obs=a*exp+b using an
autocorrelation model based on the position variable "pos".
The problem: I get reasonable answers for the slope & intercept, but the
estimated ranges for the autocorrelation functions are huge and seemingly
unconnected to the pictures I get when I plot acf(resid(M0)) [where M0 is
the OLS fit to the data]. I tried simulating a bunch of "data" with
different data sizes: the disturbing thing is that the range results get
(much) worse, not better, as the number of data points goes up [from n=30,
around the real size, to n=50, to n=100]. When I am able to get
confidence intervals on the range, they often don't make sense either.
On the other hand, the estimates of slope and intercept are reasonable in
reality and in the simulations.
I've skipped the gory details at this point. A more complete write-up
is at http://www.zoo.ufl.edu/bolker/tiwari-new-reg.pdf if anyone wants
more information ...
Should I be concerned about this? Are there any obvious diagnostics of
non-convergence etc.? (Reported AIC values suggest that the models with
autocorrelation *are* preferable, by quite a bit -- I could pursue this
further.) Or should I just not worry about it and move on?
Ben Bolker
--------------------------
simulation code:
library(MASS)
simdata <- function(sd=200,range=2,n=NULL,mmin=0) {
if (is.null(n)) mile <- seq(mmin,17.5,by=0.5) else {
mile <- seq(mmin,17.5,length=n)
}
mean <- 3000-50*(mile-10)^2
v <- sd^2
dist <- abs(outer(mile,mile,"-"))
Sigma <- v*exp(-dist/range)
X <- mvrnorm(1,mu=mean,Sigma=Sigma)
data.frame(mile=mile,X=X,mean=mean)
}
--
620B Bartram Hall bolker at zoo.ufl.edu
Zoology Department, University of Florida http://www.zoo.ufl.edu/bolker
Box 118525 (ph) 352-392-5697
Gainesville, FL 32611-8525 (fax) 352-392-3704
