[R-sig-ME] Help understanding residual variance

[Ista Zahn]

Hi Reinhold,

Good question. My consultant didn't seem impressed when I tried to
articulate that explanation, but perhaps I wasn't clear.

Thanks,
Ista
On Thu, Mar 29, 2012 at 1:45 AM, Reinhold Kliegl
<reinhold.kliegl at gmail.com> wrote:
> But why is Greg Snow's response inadequate?
>
> Restating his argument:  In an LMM we are not estimating individual
> random effects (means, slopes) and individual residuals, but variance
> of random effects and variance of residuals. So there can be
> differences between a subject's observed random effect and random
> slope  and conditional modes of the distribution of the random effects
> (i.e., the point of maximum density), given the observed data and
> evaluated at the parameter estimates.
>
> I think your statistician's answer is a good argument that you must
> not treat conditional modes as independent observations in a
> subsequent analyses. For example, we showed with simulations that
> correlations between conditional modes of slopes and intercepts are
> larger than the correlation parameter estimated in the LMM (Kliegl,
> Masson, & Richer, Visual Cognition, 2010).
>
> Reinhold Kliegl
>
> --
> Reinhold Kliegl
> http://read.psych.uni-potsdam.de/pmr2
>
> On Tue, Mar 27, 2012 at 4:18 AM, Ista Zahn <istazahn at gmail.com> wrote:
>> Hi all,
>>
>> I'm trying to understand what the residual variance in this model:
>>
>> tmp <- subset(sleepstudy, Days == 1 | Days == 9)
>> m1 <- lmer(Reaction ~ 1 + Days + (1 + Days | Subject), data = tmp)
>> tmp$fitted1 <- fitted(m1)
>>
>> represents. The way I read this specification, an intercept and a
>> slope is estimated for each subject. Since each subject only has two
>> measurements, I would expect the Reaction scores to be completely
>> accounted for by the slopes and intercepts. Yet they are not: the
>> Residual variance estimate is 440.278.
>>
>> This is probably a stupid question, but I hope you will be kind enough
>> to humor me.
>>
>> Best,
>> Ista
>>
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