[R-sig-ME] Design question about repeated measures as nested vs crossed structures

[Rolf Turner]

On 7/10/2009, at 8:35 AM, Ista Zahn wrote:

> Sorry for the off-topic post, I've been struggling to understand
> something and don't know where else to turn. I don't understand the
> distinction between nested and cross classified, and I'd really
> appreciate if someone can take a moment to set me straight. The
> example below illustrates my confusion.
>
> I often read/hear multivariate measures data described as nested, but
> this doesn't make sense to me. Here is a typical explanation from
> http://www.cmm.bris.ac.uk/lemma/mod/lesson/view.php?id=255:
>
> "Sometimes we may wish to model more than one response. For example,
> we may wish to consider jointly English and mathematics exam scores
> for students because the two responses are likely to be related. We
> can regard this as a multilevel structure with subjects (English and
> maths) nested within students as shown in Figure 4.5. ..." (the figure
> is here: http://www.cmm.bris.ac.uk/lemma/file.php/13/images-C4/ 
> image007.gif).
>
> To my mind this sounds cross-classified, because each observation is a
> particular combination of person and exam subject. It seems to make
> just as much sense to describe these data as participant nested within
> exam subject, as I've diagrammed here:
> http://ista.scp.rochester.edu/snapshot1.png.
>
> Please, if anyone can clear this up for me I'd really appreciate it.

Dunno if I can clear this up for you.  Unfortunately I usually feel as
confused as you are feeling.  But for what it's worth, my opinion is  
that
the paragraph in quote marks given above is a load of dingos' kidneys  
and
those who wrote it haven't a clue.

Specifically you are *correct* in saying that the design is  
*crossed*. You
have an observation on each student-(exam subject) combination.

Your diagram showing student nested within exam subject is misleading.
Presumably ``St1'' under E is the same student as ``St1'' under M, etc.
You only get nesting if the set of students taking English exams is
different from the set of students taking Maths exams.

Of course you could have partial overlap, in which case you'd get what
I think is called ``partial nesting'', but that's a whole other can of
worms.

Of course the structure described --- with just the two factors
``student'' and ``exam subject'' is so simple that discussing it in
terms of crossing and nesting is overkill.  If the students doing
the maths exam and the students doing the english exam are the same
students you have a ``paired design'' which would usually (rightly
or wrongly) be analyzed via a paired t-test (or possibly the
non-parametric equivalent).  If the students constitute two different
sets of students then you'd have a ``two independent samples'' setting,
and analyze via a two-sample t-test or the non-parametric equivalent.

[In either case the only (possibly) concern would be to make inferences
about the difference between the population mean maths exam score and
the population mean english exam score.  Which is kind of silly anyhow
since you'd be comparing apples and oranges; but that's another story.]

I hope this clarifies more than it obscures.

	cheers,

		Rolf Turner

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