[R-sig-ME] Confidence interval for relative contribution of random effect variance

[lorenz.gygax at agroscope.admin.ch]

Dear Ben,

Many thanks for your input.

[... snip]

> > Now, apart from this aspect, can confint be tweaked to calculate not
> > only the confidence interval of the 'raw' parameters but also for
> > some function of the parameters? If not, do I need to move to an
> > implementation using MCMC methods (MCMCglmm, Bugs-type of
> > approaches, STAN or Laplaces-Demon) to reach my aim or do you have
> > another (simpler) suggestion?
> 
>   You can compute parametric bootstrap confidence intervals of
> any quantity you want by applying boot.ci() to the results of bootMer()
> (bootMer()'s second argument is the summary function, which you
> can define however you like).  This is computationally expensive,
> though (even more expensive than MCMC-type computations).

Ok. The latter may not be such an issue. This sounds doable and I will be looking into it! (And I can report back on my success ...)

>   In principle you might be able to use likelihood profiling
> (which is what the default confint() method uses) to compute
> profile likelihood confidence intervals of arbitrary quantities,
> but you would need to be able to constrain an optimization algorithm
> to the specified values (i.e., you would need to set nonlinear
> equality constraints; there are functions in nloptr and elsewhere
> (many of them called auglag()) that implement an augmented Lagrange
> multiplier algorithm for such constraints, but I haven't tried it
> out to see how it works.

This sound rather daunting and I fear that I am not up to this ...

> The advantage of parametric bootstrap/MCMC approaches is that
> you also get a finite-size-appropriate result; likelihood profiling
> would inherit the asymptotic assumptions of the likelihood ratio test.
> 
> glmmADMB still implements a post-hoc MCMC sampling strategy simpler
> to mcmcsamp (but you would be on your own for making sure the
> chain was well-behaved, etc.)

Ok that would be another avenue.

Many thanks again! Regards, Lorenz