[R-sig-ME] Question on estimating intraclass correlation (and significance and confidence intervals) with binomial data using mixed model and/or GEE

[Muldoon, Ariel]

Tom Wenseleers <Tom.Wenseleers at ...> writes:


> Also a couple of remaining questions:
> 1) Is there any way / any model / other approach (eg using a GEE?) 
> that would allow for negative intraclass correlations? (right now ICCs 
> are always positive, but in rare cases one might expect negative 
> intraclass correlations)

> Don't know.  In principle, one way to do it is to allow compound symmetric structures rather than using grouping >variables at a level of individual latent effects (i.e. if this were a LMM fitted via nlme::lme you would use pdCompSymm >to structure the random effects).

I've been working through Stroup's new GLMM book, and he shows an example of using a marginal model with compound symmetry structure to allow for a negative covariance that gives equivalent results to allowing for a negative variance in the conditional model.  That's for a Gaussian example, though.  Switching to a marginal model for a non-Gaussian case is a lot more complex and would take a lot of thought (for me) to make sure I wanted the marginal estimates.  I definitely don't know if it makes sense to use the covariance matrix for a binomial marginal model for ICC or not.
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