[R-sig-ME] Help understanding residual variance

[Ista Zahn]

Thanks Josh, the comparison with SAS and Stata is very useful. I'll
see what my consultant has to say about this example.

Best,
Ista

On Thu, Mar 29, 2012 at 11:29 AM, Joshua Wiley <jwiley.psych at gmail.com> wrote:
> Hi Ista,
>
> To me the onis is on the statistician consultant to explain *why* you
> cannot have both random intercepts and slopes.  Does the consultant
> have papers to reference or proofs?
>
> In any case, this is hardly exclusive to 'R doing something strange'.
> SAS and Stata happily join the gang.  See the attached file for code
> and output from all three using a minidataset simulated in R.
>
> I suppose one could bicker over whether a random intercept and slope
> is a good idea, but possible it certainly is.  You might suggest that
> it is poor fare to voice strong opinions about matters which one does
> not understand.
>
> Cheers,
>
> Josh
>
> On Thu, Mar 29, 2012 at 3:29 AM, Ista Zahn <istazahn at gmail.com> wrote:
>> 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
>>>>
>>>> _______________________________________________
>>>> R-sig-mixed-models at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>> _______________________________________________
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>
>
>
> --
> Joshua Wiley
> Ph.D. Student, Health Psychology
> Programmer Analyst II, Statistical Consulting Group
> University of California, Los Angeles
> https://joshuawiley.com/