Design question about repeated measures as nested vscrossed structures

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