[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]

Dear Martin,

Many thanks for this explanation which, of course, is very reasonable ;-)

But - and I may be real slow on this - why is the same seemingly not true for the random effects as well (summary and confint give the same absolute values)?

Cheers, Lorenz


Am 12.09.2014 um 14:51 schrieb "Martin Maechler" <maechler at stat.math.ethz.ch>:

>>>>>>  <lorenz.gygax at agroscope.admin.ch>
>>>>>>    on Fri, 12 Sep 2014 11:20:42 +0000 writes:
> 
>> [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?
> 
> Yes, the conf.ints are for the sigmas as their name suggest, and
> sigmas are standard deviations aka  sqrt(<variances>).
> 
> You're welcome 
> und herzlichen eidgenössischen Gruss,
> Martin