Message-ID: <B291F8F571C9494EA3EAF8C8B471333F22E0D70B@WBF-C7001.bk.evdad.admin.ch>
Date: 2014-09-12T11:05:45Z
From: lorenz.gygax at agroscope.admin.ch
Subject: Confidence interval for relative contribution of random effect variance
In-Reply-To: <loom.20140912T001218-369@post.gmane.org>
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