Hi, I have a linear mixed-effects model object and want to extract the 95% confidence intervals for the fixed and random effects, respectively. I found the function intervals() for confidence intervals for the fixed effects but no corresponding function for the random effects. Does it exist or do I have to calculate the confidence intervals for the random effects myself? Greetings, joerg
Joerg Schaber <Joerg.Schaber at uv.es> writes:> I have a linear mixed-effects model object and want to extract the 95% > confidence intervals for the fixed and random effects, respectively. I > found the function intervals() for confidence intervals for the fixed > effects but no corresponding function for the random effects. Does it > exist or do I have to calculate the confidence intervals for the > random effects myself?You have to calculate them yourself, partly because it is not clear what such an interval should be. Technically, the random effects are not parameters and defining a "confidence interval" on a random variable that is part of the model is, at the very least, awkward.
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?
>>
>>
>>
>>
I am very curious about this. If a particular growth model is specified to
reflect repeated observations on individual i in unit j, such as:
y_{tij} = [B_{00} + B_{01}*(TIME)]+[u_{00}+u_{01}*(TIME)+ e_{tij}]
where Bs are the fixed effects and the u's are the random effects.
The growth of individual i is then computed as:
B_{01} + u_{01}
Is it appropriate to compute a confidence interval around this growth rate? I
so, how might this be accomplished? Based on Doug's comments below, it would
seem that only a CI can be formulated for the fixed portion of the model.
I would appreciate any clarification.
HCD
------
Harold C. Doran
Director of Research and Evaluation
New American Schools
675 N. Washington Street, Suite 220
Alexandria, Virginia 22314
703.647.1628
-----Original Message-----
From: Douglas Bates [mailto:bates at stat.wisc.edu]
Sent: Thursday, November 13, 2003 10:11 AM
To: Joerg Schaber
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] conf int mixed effects
Joerg Schaber <Joerg.Schaber at uv.es> writes:
> I have a linear mixed-effects model object and want to extract the 95%
> confidence intervals for the fixed and random effects, respectively. I
> found the function intervals() for confidence intervals for the fixed
> effects but no corresponding function for the random effects. Does it
> exist or do I have to calculate the confidence intervals for the
> random effects myself?
You have to calculate them yourself, partly because it is not clear
what such an interval should be. Technically, the random effects are
not parameters and defining a "confidence interval" on a random
variable that is part of the model is, at the very least, awkward.
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