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

[Ista Zahn]

Thanks for all the responses, it helps. Professor Turner -- I realize
my diagram showing students nested withing exam subject is misleading
-- my question was "why is it less misleading to diagram exam subject
as being nesting within students?". Your response, in conjunction with
Professor Bates' response helped clear that up for me (i.e., it
doesn't really make sense to describe nesting either way: it's
crossed!).

Also, I recognize (as you both pointed out) that the example is
somewhat trivial and with only two levels of exam subject there are
much simpler ways to look at it. I wanted to keep the example as
simple as possible in order to focus on the nested/crossed issue.

It's confusing when people use the "hammer and nail" approach,
especially as with the case I quoted the authors take care to
distinguish between crossed and nested structures in other contexts. I
had assumed that because they paid a lot of attention to this in a
previous discussion they would be careful with their examples, but I
think now they were just being a bit sloppy.

Thanks again for helping me understand.

-Ista

On Tue, Oct 6, 2009 at 4:16 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
> In re-reading my posting I see that I have used the word "subject" in
> two different ways, perhaps causing some confusion.  In the early
> going my use of subject is to distinguish math from English.  In the
> later going I slip into using subject as the observational unit, which
> earlier I was calling student.  Sorry for the confusion.
>
> On Tue, Oct 6, 2009 at 3:11 PM, Douglas Bates <bates at stat.wisc.edu> wrote:
>> 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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>>>>
>>>
>>> _______________________________________________
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>>>
>>
>



-- 
Ista Zahn
Graduate student
University of Rochester
Department of Clinical and Social Psychology
http://yourpsyche.org