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

[Douglas Bates]

On Tue, Oct 6, 2009 at 2:47 PM, Doran, Harold <HDoran at air.org> wrote:
> Ista
>
> We have a description of what this means in the paper in the link below.
> See section 1.6 of the paper. Using your example below, whether or not
> the multiple observations are nested would depend on the setting in
> which they were observed. For instance, if all students had two scores
> and both of those scores were observed in one and only one classroom,
> you would have a nested design.
>
> If some students had one of those scores observed with teacher i and
> another observed with teacher i', then your design would be partially
> crossed.
>
> If every student had one observation observed in one class and the
> second observation in a different class, you would have a fully crossed
> design.

I think Ista's point is somewhat different, Harold, and I would agree
with him that it is more appropriate to consider student and subject
as crossed factors, rather than as nested.

The figure in Ista's message indicates that there are two subjects and
scores for students nested within the subjects.  But that is not what
the description says.  We would generally expect that there would be a
student effect in common with the two scores  Some students may do
better in math than in English and vice versa for others but if we
plotted the two scores by student we would expect them to be
correlated.

Some of the discussion of nested versus non-nested has a "when all
that you have is a hammer, everything looks like a nail" nature to it.
 If you can't fit models with crossed or partially crossed random
effects then you look for ways to characterize effects as nested.

It is somewhat ironic that the motivating example, longitudinal
responses on subjects in some social context (e.g. school, classroom,
neighborhood), for hierarchical linear models or multilevel models
almost inevitably ends up with non-nested groupings.  All you need is
for one subject to move from one group to another over the course of
the study and you no longer have subjects nested within schools, say

This example is a bit different in that we may consider math versus
English to be a fixed-effect and model the random effects as a
vector-valued random effect by student.  We don't have to consider one
factor as nested within the other; we can just use random effects at
the student level but have one component for the math and one
component for the English.  That is, the model could be

score ~ subj + (0+subj|student)

>> -----Original Message-----
>> From: r-sig-mixed-models-bounces at r-project.org
>> [mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf
>> Of Ista Zahn
>> Sent: Tuesday, October 06, 2009 3:35 PM
>> To: r-sig-mixed-models at r-project.org
>> Subject: [R-sig-ME] Design question about repeated measures
>> as nested vscrossed structures
>>
>> 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.
>>
>> -Ista
>>
>> --
>> Ista Zahn
>> Graduate student
>> University of Rochester
>> Department of Clinical and Social Psychology http://yourpsyche.org
>>
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