[R-sig-ME] Query lme4

[Ben Bolker]

Elizabeth Crone wrote:
>> In most cases of longitudinal data it would be very difficult to
>> distinguish between an autoregressive structure and a model with
>> random effects specification (AGEACTUAL|Individual).

  Hmm.  Is this true if there are sufficient data?  That is, shouldn't
autocorrelated variation within an individual be detectable even if
there is a linear trend within individuals?  (Isn't this what the
corARxx structures in nlme are for?)

> 
> I think this is true if observations are POSTIVELY autocorrelated,
> but the random individual effects should be separable from NEGATIVE
> autocorrelations, right? [This posting caught my eye because I have
> been wishing I could use something like lme4 to fit mixed models to
> data with strong negative autocorrelations, specifically, probability
> of flowering for plants that flower approximately in alternate
> years.]

  You probably have to do this in WinBUGS etc. for the foreseeable
future.  The good news is that it's reasonably easy to write down a
structure that should produce this, i.e. something like

   X[indiv,time] ~ Binomial(p_indiv(t))
   logit(p_indiv(t)) ~ Normal(a+b*p_indiv(t-1)+...,tau)

  where ... could include covariates, random (but persistent)
among-individual variation, etc..  If -1<b<0 then you get population
dynamics with negative autocorrelation.


-- 
Ben Bolker
Associate professor, Biology Dep't, Univ. of Florida
bolker at ufl.edu / people.biology.ufl.edu/bolker
GPG key: people.biology.ufl.edu/bolker/benbolker-publickey.asc