[R] Why aov() with Error() gives three strata?

[peter dalgaard]

At any rate: 

Error(SUBJECT/IV)

specifies two random effects: SUBJECT and SUBJECT:IV. This is most easily understood if you conceptually arrange your data in a SUBJECT x IV table: One effect is a set of random errors added to each row, the other is a set of effects added to each cell. 

If you have more than one observation within each cell, then you need a third set of errors to account for differences within cells and this is labeled "Within" variation. With one observation per cell, this stratum disappears (as far as I recall, haven't checked). 

Actually, this oversimplifies a little: What actually happens is that data gets split into 

1: row means
2: differences between cells within rows
3: differences between observations within cells

and if the stratum variances are decreasing, then this can be interpreted using random effects as above, with variances of each component proportional to the successive differences. (All assuming that you have a balanced data layout, otherwise aov() is just the wrong tool.)

-pd

> On 28 Dec 2017, at 19:36 , Jorge Fernando Saraiva de Menezes <jorgefernandosaraiva at gmail.com> wrote:
> 
> Bert, thanks for the reply but I feel that my question is less about
> statistics and more about R interface. Specifically, because the output of
> R seems different than other programs (systat, for example, gives a between
> and a within table instead of a three level one).
> 
> I am familiar with the connection between mixed models and repeated
> measures,and how mixed models are essentially replacing the aov models due
> to their greater flexibility. But I feel that despite understanding a
> little of the logic behind the mixed models that aov error terms seem
> completely different to me than lmer randoms.
> 
> I will post in those support lists you pass to me, if nothing comes from
> here. However I had little luck in the stats exchange when I tried there.
> 
> About a local expert, I am once more in a corner. there are many people in
> my department who excel in statistics. But I none use R, drastically
> reducing their ability to explain to me the output of aov.
> 
> Em 28 de dez de 2017 20:04, "Bert Gunter" <bgunter.4567 at gmail.com> escreveu:
> 
>> Jorge:
>> 
>> FYI, *generally speaking,* queries that are mostly statistical in
>> nature, such as yours, are off topic here -- this list is about R
>> programming help, not statistical help. Having said that, you still
>> may get a useful response here -- the r-help/statistics intersection
>> *is* nonempty. However, if not, 2.5 suggestions:
>> 
>> 1. Try posting to r-sig-mixed-models instead. Repeated measures are a
>> type of mixed/multilevel model and you may receive some useful
>> suggestions there, including alternative R approaches to fitting such
>> model (e.g. using lme() or lmer() ).
>> 
>> 2. Alternatively, try posting to a statistics site like
>> stats.stackexchange.com.
>> 
>> 2.5. Or, if you can, the best idea might be to sit down with a local
>> statistics expert.
>> 
>> Cheers,
>> Bert
>> 
>> 
>> 
>> Bert Gunter
>> 
>> "The trouble with having an open mind is that people keep coming along
>> and sticking things into it."
>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>> 
>> 
>> On Thu, Dec 28, 2017 at 7:52 AM, Jorge Fernando Saraiva de Menezes
>> <jorgefernandosaraiva at gmail.com> wrote:
>>> Dear list users,
>>> 
>>> I am trying to learn Repeated measures ANOVA using the aov() interface,
>> but
>>> I'm struggling to understand its output.
>>> 
>>> According to tutorials on the web, formula for a repeated measures design
>>> is:
>>> 
>>> aov(Y ~ IV+ Error(SUBJECT/IV) )
>>> 
>>> This formula does work but it returns three strata (Error:SUBJECT, Error:
>>> SUBJECT:IV, Error: Within), when I would expect two strata (Within and
>>> Between subjects). I've seems some tutorials  show the exactly same
>> setup,
>>> but returning only the two first strata.
>>> 
>>> Is it possible to have two or three strata depending on the data?
>>> If there is always three strata, how this would fit the interpretation of
>>> between vs within effects?
>>> 
>>> Below a reproducible example that gives three strata:
>>> 
>>> data(beavers)
>>> data=data.frame(id =
>>> rep(c("beaver1","beaver2"),c(nrow(beaver1),nrow(beaver2))),
>> rbind(beaver1,beaver2))
>>> data$activ=factor(data$activ)
>>> #balance dataset to have 6 samples for every combination of beaver and
>>> activity.
>>> balanced = split(data,interaction(data$id,data$activ))
>>> sizes = sapply(balanced,nrow)
>>> selected = lapply(sizes,sample.int,6)
>>> balanced = mapply(function(x,y) {x[y,]}, balanced,selected,SIMPLIFY=F)
>>> balanced = do.call(rbind,balanced)
>>> aov(temp~activ+Error(id/activ),data=balanced)
>>> 
>>> Thanks,
>>> Jorge
>>> 
>>>        [[alternative HTML version deleted]]
>>> 
>>> ______________________________________________
>>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/
>> posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>> 
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com