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

[lorenz.gygax at agroscope.admin.ch]

Dear all,

earlier this year, I started to look into how I could estimate the relative contribution of the between-subjects variability relative to several levels of (summed) within-subject variabilities in the context of mixed models. Because I am using nlme and lme4 since quite a while that is where I started to look. In the end, I would like to have not only a point estimate but also a measure of precision, that is, either a confidence or credible interval.

When I started to look into this, I came across a two-year old suggestion by Ben Bolker that relied on mcmcsamp (http://stats.stackexchange.com/questions/30797/posterior-simulations-of-the-variances-with-the-mcmcsamp-function) which I liked because the Markov-chain would allow me to calculate the measure of interest for each simulation step and accordingly calculate e.g. an HPD-interval of the ratio of between- versus the (summed) within-subject variability.

Now, doing some more research in the R-archives, help files and vignettes, I realize that I have been off the sig-mixed-models list for too long (due to work load and yes, I will try to be better in future ;-) and that mcmcsamp is no longer supported/developed. On the other hand the function confint () now exists. Many thanks to the developers!

A side-line: Using the confint function on one of my models and comparing the confidence intervals with the point-estimates from the summary of the same model, it seems that confint reports confidence intervals for the estimated standard deviations of the random effects as well as of the error-variability whereas summary reports the standard deviations for the random effects but the variance for the residuals. Is this correct? I seem to remember some such discussion but could not find any note online that would have verified this fact. Page 31 in "Fitting linear mixed-effects models using lme4" discusses this part of the summary output but seems to be using the terms standard deviation and variance somewhat interchangeably (or, more likely, I failed to read it correctly).

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?

Many thanks and regards, Lorenz
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Lorenz Gygax, PD Dr. sc. nat., Scientist
Federal Food Safety and Veterinary Office FFSVO
Centre for Proper Housing of Ruminants and Pigs
Tänikon, CH-8356 Ettenhausen, Switzerland