spatial autocorrelation as random effect with count data
I was introduced today (by Roger Bivand) to the glmmTMB package that looks very exciting. As a co-author, I was wondering why you didn't suggest it - is there a reason it's a no-go in my situation? From a super quick read, and a very naive thinking, is this not equivalent to the gpmmPQL setup below? mod1 <- glmmTMB(Count ~ Stratum + SiteInStratum + ...other predictors + # random variable (1 | RoundStart) + # autocorrelation exp(site.Easting + site.Northing | RoundStart), family = nbinom2, # or nbinom1 - I guess decide based on residuals? correlation = corExp(form=~site.Easting + site.Northing + RoundStart) where RoundStart is the time of starting sampling along the repeated, set, 20-point sampling grid, easting and northing are the 20 points' coords, Stratum is the allocation of the 20 sampling points to 5 strata and SiteInStratum is the 1:4 allocation within stratum. This is my current setup: mod1 <- glmmPQL(Count ~ Stratum + SiteInStratum + ...other predictors, random = ~ 1 |RoundStart, family = quasipoisson, correlation = corExp(form=~site.Easting + site.Northing + RoundStart) I have INLA and GAMs on my to-do list for this year - sounds like really helpful ways to go about things, I just haven't gotten there yet... Thank you so much!
On Wed, Jan 10, 2018 at 5:34 PM, Ben Bolker <bbolker at gmail.com> wrote:
PS: depending on how badly you wanted this, it would be possible to what Doug Bates said (impose spatial dependence on the random effects for the 20 spatial points) via the modular machinery of glmer, but it would take some effort and knowledge ... On Wed, Jan 10, 2018 at 3:59 PM, Sima Usvyatsov <ghiaco at gmail.com> wrote:
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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