<lorenz.gygax at agroscope.admin.ch>
on Fri, 12 Sep 2014 11:20:42 +0000 writes:
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:
confint (HHbT.fin.lmer, method= 'profile')
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 eidgen?ssischen Gruss,
Martin