[R] GLMMPQL spatial autocorrelation

Wed May 30 12:12:41 CEST 2012

Dear Alex,

I'm cc'ing this to the mixed models list which is more appropriate for the question. Please send all follow up posts only to that list.

First a few more general remarks.
- You are using the data argument of glmmPQL. So there is no need to attach() the data.frame. I recommend avoid to use attach(). You will get into troubles with it, sooner or later...
- The correlation structures of the nlme package (which is used by glmmPQL), work on the residuals WITHIN the groups at the deepest levels of the random effects. So in your case only within individual sites. I guess that you are more interested in spatial correlation among sites than within sites.
- Adding a random intercept per site is equivalent of adding a compound symmetry correlation structure along site.
- which kind of residuals did you look at? You need the normalised one to see the effect of the correlation structure.

Then there is a more theoretical remark. Does a correlation structure on the residuals makes sense when using a binomial or poisson model? Compare is the formula notation of a (gaussian) linear (mixed) model with that of a generalised linear (mixed) model. You'll see that the lmm formula contains an epsilon term where the generalised version does not. This makes sense when you look at the distributions. The Gaussian distribution is defined by two parameters: mu (= combined effect of fixed and random effect) and sigma (the standard deviation of the epsilons). The binomial disitribution is only defined by one parameter: mu (= combined effect of fixed and random effect). It's variance depends on mu.
The correlation structures of nlme work on the epsilons, changing there joint distribution from i.i.d. (thus non correlated)  to the specified correlation structure. So how will that work on a generalised model where you have no epsilons?
Another reasoning is that a correlation struction in a gaussian models affects the variance (sigma) but not the mean (mu). But in binomial case those parameters are linked. So if the correlation structure has an effect on the variance then it must have an effect on the mean. And thus it will be conflicting with the fixed and random effects.

What IMHO would make sense for a generalised model are correlated random effects. E.g. the BLUPs of nearby sites have a stronger correlation than BLUPs of distant sites. Those kind of correlation structure are currently not available in neither nlme nor lme4.

Best regards,

Thierry

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
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-----Oorspronkelijk bericht-----
Van: r-help-bounces op r-project.org [mailto:r-help-bounces op r-project.org] Namens Alexroyan
Verzonden: dinsdag 29 mei 2012 15:06
Aan: r-help op r-project.org
Onderwerp: [R] GLMMPQL spatial autocorrelation

Dear all,

I am experiencing problems using the glmmPQL function in the MASS package (Venables & Ripley 2002) to model binomial data with spatial autocorrelation.

My question  - is the presence of birds affected by various hydrological parameters?

Presence/absence data were collected from 83 sites and coupled against hydrological data from the same site. The bird survey sampling effort varied at each site so I want to include this as a random effect (fAVGNTS). I have also conducted a join count test which suggests that there is some spatial autocorrelation. Consequently I have used the following code:

library(MASS)
attach(Birds)
Birds$x <- Birds$LONGITUDE
Birds$y <- Birds$LATITUDE
M <- glmmPQL(PRESENCE~ HYDROVAR1 + HYDROVAR2, random=  ~ 1|fAVGNTS, correlation =  corExp(form = ~ x + y), family = binomial(link = "logit"), data = Birds)

The model seems to run fine. However, when I compare the results of this model and the residual spread against the same model but without the correlation function, there is absolutely no difference at all.

I am somewhat confused by this as both Dormann et al. 2007 and Bivand et al.
2008 have suggested the use of the glmmPQL function to model binomial data with spatial autocorrelation and random effects.

Therefore I am wondering if anyone knows why this has occurred and secondly I am wondering if the correlation function does indeed work outside of gls?

Many thanks in advance for your help.

Best regards

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