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

[lorenz.gygax at agroscope.admin.ch]

Dear all,

based on Bens suggestion (and it has come up again in another post) I made a first try in using bootMer and boot.ci.

> [... 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 ...)

I first defined a function that calculates the quotient of the within-subject variance (given by the variable 'ID' in my typical models) relative to the summed within-subject variance (subject is on the highest nesting level in the nested random effects that I currently use):

withinVar.fn <- function (mer.obj, subj= 'ID') {
    vars <- as.data.frame (VarCorr (mer.obj))
    vars [vars [, 'grp'] == subj, 'vcov'] / sum (vars [vars [, 'grp'] != subj, 'vcov'])
}

Then you can run the bootstrap and calculate the confidence interval:

HHbT.boot <- bootMer (HHbT.fin.lmer, withinVar.fn, nsim= 1000, parallel= 'multicore', ncpus= 2)
boot.ci (HHbT.boot, type= 'perc')

I was a bit worried about the distribution of my variable of interest being a quotient and also tried log-ing the division. At least in this example, the distribution seems even worse with the transformation and the results of the percentile confidence interval using the non-transformed quotient seems to give quite reasonable results.

Any hints to where I may have been (too) naïve in my approach are appreciated.

Many thanks again. Regards, Lorenz