[R-sig-ME] Variance components questions

Douglas Bates bates at stat.wisc.edu
Tue Feb 22 16:29:52 CET 2011

On Mon, Feb 21, 2011 at 5:00 PM, Karim Lounes <kclounes at gmail.com> wrote:
> Hi All,
> I am a biochemist with limited background in statistics, so please forgive
> the naivety of my question.
> I am interested in estimating the precision of a measurement system and the
> variance components of three factors.
> This is how the experiment was designed: 5 samples, each considered a level
> were measured. Each sample was measured twice a day (run) for 10 days (days)
> by two different operators (operator). Each measurement was replicated 3
> times. The factor (days) is not continuous as the goal was to generalize the
> estimation of the precision of the measurement system for all days.
> I have read a number of posts on this list and also read Mr. bates online
> book of lem4.
> >From what I understood the model would be a crossed design and I  run the
> following analysis:
> Measurement ~ samples + (1|days) +  (1|run) +(1|operator)

Yes, I would think so, but I agree with Thierry that there may be more
appropriate models.

> Is this model appropriate? and is there a way to gauge the precision of the
> the estimates of the variance components by a confidence interval?

There are ways using profiling but they are only available in the
development version of the package called lme4a.  On Linux or Windows
systems it can be installed as

install.packages("lme4a", repos="http://r-forge.r-project.org")

then re-fit the model, say as fm, and profile it with

pr <- profile(fm)

A plot of the change in the profiled deviance for each of the variance
components (expressed as standard deviations) is available as


This shows the end points of confidence intervals with 50%, 80%, 90%,
95% and 99% confidence levels, if they can be determined.  The end
points can be retrieved as


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