[R-sig-ME] question about an unbalanced design using lmer

[Henrik Singmann]

Dear Xiyue and Thiery,

While more data points may affect the estimation process in that way 
they do not seem to affect the fixed-effects estimates in that way. To 
be more precise, the fixed effect estimate seems to correspond to the 
unweighted mean (i.e., the mean in which each level of the random effect 
is weighted equally) and not to the weighted mean (in which each data 
point is weighted equally).

I had a similar problem some time ago:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2014q3/022478.html

Thanks to the help of Jake Westfall I was able to get the desired result 
(i.e., a fixed-effect estimate corresponding to the weighted mean), by 
adding group size as fixed effect to my model, see:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2014q3/022481.html

There might be other approaches to achieve this as well (i.e., some 
post-fit weighting), but I am not sure how to implement this (perhaps 
using lsmeans somehow).

I hope this helps,
Henrik


Am 17.10.2016 um 11:09 schrieb Thierry Onkelinx:
> Dear Xiyue,
>
> Don't think in terms of cells but in terms of observations. The model tries
> to minimise the residuals. So combinations with more observations have more
> residuals and thus a stronger impact on the MSE.
>
> Best regards,
>
> ir. Thierry Onkelinx
> Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
> Forest
> team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> Kliniekstraat 25
> 1070 Anderlecht
> Belgium
>
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> 2016-10-12 19:48 GMT+02:00 Xiyue Liao <liaoxiyue2011 at gmail.com>:
>
>> Hi,
>>
>> I'm using lmer in the R package lme4 to do a one-way anova analysis with a
>> fixed effect term and a random effect term. So the fixed effect is about
>> four medical conditions and the random effect is about randomly sampled
>> donors. Now for some combinations of donors and medical conditions, there
>> are more than one measurement, which makes the whole design unbalanced. I
>> think that lmer can handle such a case, and I have run the code without any
>> error message. However, I don't understand how this routine put weight on
>> the cells with more measurements than other cells. Could you give me some
>> hint?
>>
>> Thanks in advance for your help.
>>
>> Sincerely,
>>
>> Xiyue
>>
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>>
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