[R] formula for a mixed model ANOVA

[ripley@stats.ox.ac.uk]

I think lack of balance makes mixed-model AOV inappropriate.

As I understand it, Individual is a random effect. You may as well averge
the results for each individual rather than try a mixed-effect analysis
with Error(Individual).  You are not interested (I think) in the
components of variance, and on the individuals' means are in the stratum
with the factors of interest.

You will have a  5x2x2 factorial with unequal replication, that will
complicate model choice and interpretation.

On Mon, 2 Sep 2002, Philippe Grosjean wrote:

> Hi,
>
> I am not very familiar with complex ANOVA, so, I am not sure about the
> formula to use with aov() in this particular case. Could someone help me?
>
> Here is my data. I have an unbalanced plan with 4 factors: "Site", "Sex",
> "Age" and "Individual". "Site" is a 5-level fixed factor; "Sex" is of course
> a 2-levels fixed factor, as is "Age". "Individual" is a nested random
> factor: we sampled 4 to 10 individuals for each combinations Site*Sex*Age.
> 150 replicate measurements were made on each sampled individual ("OTM",
> toxicity test; % of broken DNA for randomly selected cells).
>
> if the formula "OTM ~ (Site*Sex*Age)/Individual" correct?
>
> The purpose of this study is to choose a statistic that best summarizes the
> 150 measurements (mean, median, quantile, % of counts above a certain
> level,...) in order to simplify the analysis to "stat(OTM) ~ Site*Sex*Age"
> (where stat(OTM) is the statitstic applied by individual), in such a way
> that intergroup variance is highest.

Well, AOV does that with mean anyway.  Surely you want the ratio of the
intergroup/intergroup variances to be highest?

-- 
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 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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