# [R] conf int mixed effects

Joerg Schaber Joerg.Schaber at uv.es
Thu Nov 13 17:33:16 CET 2003

```OK, I am convinced that CI for random effects might not really be
meaningful.
By the way, the article I mentioned does indeed only cover the 2-way
model (one fixed effect, one random effect), I think.

But talking about CI of the variance components. How do I extract those?
In the summary function something like

<snip>
Random effects:
Formula: ~1 | s
(Intercept) Residual
StdDev:    2.633981 8.583093
<snip>

is displayed which are the square roots of the variance components, I
suppose. However, I did not manage to access them directly (at least the
intercept part, the residual part is accessible via the 'sigma'
parameter of the summary function).

greetings,

joerg

Liaw, Andy wrote:

>I'm by no mean expert in this, but... Are you referring to confidence
>intervals for variance components, instead of random effects?
>
>As Prof. Bates said, computing CI on random effects is a bit strange
>philosophically, because random effects are sort of estimates of random
>quantities, unlike fixed effects, which are estimates of some "population
>constants".  The definition of CI is that with certain probability, when the
>data generation and model fitting is repeated infinite number of times, the
>computed CI will "cover" the "true population constant".  There's no "true
>population constant" for random effects, but there is for a variance
>component.
>
>HTH,
>Andy
>
>
>
>>-----Original Message-----
>>From: Joerg Schaber [mailto:Joerg.Schaber at uv.es]
>>Sent: Thursday, November 13, 2003 10:50 AM
>>To: Douglas Bates; r-help at stat.math.ethz.ch
>>Subject: Re: [R] conf int mixed effects
>>
>>
>>  I naively thought when I can give estimates of the random effects I
>>should also be able to calculate confidence levels of these estimates
>>(that's what statistics is about, isn't it?)
>>For example, similar to the fixed case, I can calculate a
>>variance-covariance matrix (C) for the random effects (e.g. following
>>Hemmerle and Hartley,TECHNOMETRICS 15 (4): 819-831 1973) and
>>using the
>>t-value for the given confidence level and degrees of freedom
>>(t), I can
>>estimate confidence intervals for random effect i (r[i]) as something
>>like r[i] +- t*sqrt(C[i][i]).
>>What does the statistician say?
>>
>>
>>
>>

```