[R-sig-ME] spatial autocorrelation as random effect with count data

[Sima Usvyatsov]

Hello,

I am working on a spatially autocorrelated dataset with a negative binomial
(count) response variable. I have been using the glmmPQL approach (MASS),
but I seem to have a hard time fitting the fixed effects. I came across the
mention that one could build the spatial autocorrelation into a random
effect (https://stat.ethz.ch/pipermail/r-sig-mixed-models/2011q1/015364.html).


I've done some searching but could not find a straightforward example of
this practice. I have 20 sampling locations (sampled repeatedly to a 4,000
point dataset) and I know that there is spatial autocorrelation between
them (by looking at autocorrelation plots of a naive model). The 20 grid
points are clustered into 4 strata, and I am interested in the strata
effects (so would like to keep the strata as fixed).

How would I go about expressing the spatial autocorrelation in this setup?
In the future I'd like to explore GAMs for this application, but for now
I'm stuck with a GLM approach... I would love to be able to use glmer()
with a random effect that expresses spatial autocorrelation.

Here's a fake dataset.

library(MASS)

df <- data.frame(Loc = as.factor(rep(1:20, each = 5)), Lat = rep(rnorm(20,
30, 0.1), each = 5), Lon = rep(rnorm(20, -75, 1), each = 5), x =
rnegbin(100, 1, 1), Stratum = rep(1:5, each = 20))

Thank you so much!

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