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:[EMAIL PROTECTED] Sent: Thursday, November 13, 2003 10:50 AM
To: Douglas Bates; [EMAIL PROTECTED]
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?
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