[R] multilevel models and sample size

[Prof Brian Ripley]

On Sun, 27 Nov 2005, Berton Gunter wrote:

> "All models are wrong, but some are useful."  --George Box
>
> I do not understand what you mean by "acceptable, nor "levels" nor "units".
> Specifying your model would help clarify things, I think. If by "levels" you
> mean number of different values of a random factor, than 2 levels is
> unlikely to tell you much useful about the variability of that factor. On
> the other hand, 50 values might be. Depends on the model,the data, and the
> scientific objectives, none of which you have stated clearly enough for me
> to understand, anyway.

My guess is that he means this is a tested design with e.g. 52 classes
containing 19-23 pupils each.  (It always helps to state the real 
problem!)

If so, this is quite a large problem for multilevel models.  The classical 
nested designs for measurement errors typically have two replications at 
the lowest level - you get an idea of the variability from the many 
differences between matched pairs.  Of course the homogeneity assumptions 
have to be approximately true.

> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of ronggui
> Sent: Sunday, November 27, 2005 9:34 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] multilevel models and sample size
>
> It is not a pure  R question,but I hope some one can give me advices.
>
> I want to use analysis my data with the multilevel model.The data has 2
> levels---- the second level has 52 units and each second level unit has
> 19-23 units.I think the sample size is quite small,but just now I can't make
> the sample size much bigger.So I want to ask if I use the multilevel model
> to analysis the data set,will it be acceptable?  or  unacceptable because of
> the small sample size?


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595