[R-sig-ME] Seeming discrepancy between summary and confint; was: Confidence interval for relative contribution of random effect variance

[lorenz.gygax at agroscope.admin.ch]

[snip ...]

> > 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).
> 
>    Hmmm.  The output of
> 
> fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy)
> summary(fm1)
> 
> gives
> 
> 
> Random effects:
>  Groups   Name        Variance Std.Dev. Corr
>  Subject  (Intercept) 612.09   24.740
>           Days         35.07    5.922   0.07
>  Residual             654.94   25.592
> Number of obs: 180, groups:  Subject, 18
> 
>   which shows both the variance and the standard deviation (i.e.
> *not* the uncertainty estimate, just the point estimate of the
> variability on both the variance and the standard deviation scales)

Ok. I admit that I was not very clear perhaps. Let me show an example. I am currently on lme4 version 1.1-7 in R 3.0.1 (my employer is just now updating to 3.1.1 but that always takes a while - so if that was an issue of not having the most recent version, I apologise in advance):

In the example which struck me odd, this was my model

HHbT.fin.lmer <- lmer (HHbT ~ valN +
                       (1 | ID/part/val), fNIRS.df, REML= FALSE)

in which the response is a transformed change in blood deoxy-hemoglobin concentration modelled by a fixed effect (three types of conditions, modelled as a linear predictor in which stimuli have been applied repeatedly) and a nested intercept random effect that accounts for the subject-to-subject variation (ID), the part-to-part variation (three different parts in the experiment) and the type of stimulus. (I am using REML= FALSE because I am conducting come model selection for the fixed effects based on information criteria.)

If I do the summary () this is what I get for the random effects part of the output.

Random effects:
 Groups        Name        Variance Std.Dev.
 val:(part:ID) (Intercept) 0.4599   0.6782  
 part:ID       (Intercept) 0.1773   0.4211  
 ID            (Intercept) 0.1278   0.3575  
 Residual                  9.4302   3.0709  
Number of obs: 1833, groups:  val:(part:ID), 214; part:ID, 72; ID, 25:


If I do

confint (HHbT.fin.lmer, method= 'profile')

I get

                  2.5 %     97.5 %
.sig01       0.41713241  0.9210729
.sig02       0.00000000  0.7535615
.sig03       0.00000000  0.6697109
.sigma       2.96898087  3.1786606

Where the above listed variances for the random effects fit nicely into the confidence intervals (.sig0x) but not the value for the residuals / .sigma where the variance from the summary seems to be approximately squared in respect to the confidence interval.

I guess, I am missing out on something, but on what?

Thanks for further advice.

Regards, Lorenz