[R-sig-eco] Binomial GLMM or GAMM with random intercept and temporal correlation

[eric.stolen]

Sam;
We had a similar situation with a GLMM with temporal autocorrelation in the
binary response variable Reyier et al. 2014). Because we wanted to use model
selection based on AIC, we could not use the quasi-likelihood estimates from
glmmPQL. Instead we used an approach called "State dependence" by Hammel et
al. (2012). Basically, we included the state of the response in the previous
time period as a predictor, and also tried lagged versions (the lagged
response order 2, 3, 4, 5, 6). We compared the estimates of the effect of
the lagged variables with those from models fit with glmmPQL, and found that
the methods agreed fairly well.

For the case with uneven intervals, have you thought about how the organism
preceives time? For instance, if samples occurred between events or stages
in an animals life it may not matter that intervals are uneven. Another idea
is perhaps you can model in a Bayesian framework with unobserved states in
the intervals that were not sampled.
Eric Stolen

Hamel, S., N. G. Yoccoz, and J. M. Gaillard. 2012. Statistical evaluation of
parameters estimating autocorrelation and individual heterogeneity in
longitudinal studies. Methods in Ecology and Evolution 3:731-742.

Reyier, E. A., B. R. Franks, D. D. Chapman, D. M. Scheidt, E. D. Stolen, and
S. H. Gruber. 2014. Regional-scale migrations and habitat use of juvenile
lemon sharks (Negaprion brevirostris) in the US South Atlantic. PLoS ONE
9:e88470.
http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0088470#pone-0088{Hamel, 


SamiC wrote
> Dear ecology mailing list,
> 
> I am trying to model some binomial data (0/1) as a function of sex (0/1)
> and DistanceToFeature (continuous km’s) with an interaction between the
> two.  My data is nested and I therefore want to include a random intercept
> for InidividualID and within that I want to include an AR1 correlation
> structure as the data is serially/temporally auto-correlated.  I
> understand any correlation structure should be nested within the random
> effect.
> 
> So far I have tried running the model using glmmPQL as 
> 
> glmmPQL(Y ~ DistanceToFeature * Sex + (1|InidividualID),
> correlation=corAR1(form=~1|IndividualID/ContinuousBout),
> family=’binomial’, data=’birds’) 
> 
> (note – ContinuousBout is an ID for where there are time gaps in the
> data).
> 
> However, although this runs, am I right in understanding that I should not
> use PQL estimation with binomial data as it gives biased results?  Does
> anyone know of a way I can model this?
> 
> I understand that this is also the case if I wish to use GAMM (as later I
> will be modelling a non-linear explanatory as well)?  
> 
> Additionally I will also be running a similar set up but where the data
> are not equally spaced in time (and therefore an AR1 structure would not
> apply). Can anyone give a recommendation of a modelling framework for this
> also.
> 
> Any help would be much appreciated.
> 
> Thank you
> 
> Sam





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