Don and Dennis,
Thanks for your comments, I have some points and futher questions on the
ussue below.
For both Dennis and Don: I think the option of aggregating the information
is a viable one. Yet, I cannot help but think there is some way to do this
taking into account the fact that there is variation within organizations.
I mean, if I have a organizational salary mean of .70 (70%) with a very tiny
s.d. it is different than a mean of .70 with a large s.d. Should be some
way to account for this. In addition, the problems with aggregation are
well documented and I believe in gereneral suggest that aggregated results
overestimate relationships.
Don: I suggested that the problem was not a traditional multilevel problem.
Perhaps I am wrong, but here is where I thought the difference was.
Typically, say in a classroom problem, I want to assess the effect of
classroom characterisitcs (student/teacher ratio, teacher experience, etc.)
which are constant within classrooms on say student performance, which
varies within classroom across individuals. The difference between this and
the problem I presented is that the OUTCOME is a contextual variable. That
is, rather than individual-level varaition, the outcome caries only at the
organizational level. Perhaps this can be modeled with MLMs, but it is
certainly different than the typical problem.
With regard to independence, I am talking about the independence of the
X2's. That is X2-1 is not independent of X2-2 and X2-4 is not independent
of X2-5. This is because these cases come from the same organization. So,
if we simply regressed Y~X2, not accounting for X1 in the model, this causes
problems for ANOVA and regression, the GLM family more generally. The lack
of independence here is exactly the reason for repeated measures and MLM
more generally, no?
Perhaps I am making to much of the issue, but the data structure is one that
I have not encountered before and I found it something of an interesting and
challenging problem, just hoping I might learn something along the way.
Would appreciate any comments on my comments above.
Oh, and just so there is no confusion, the data below I constructed. It
reflects that structure of the data and nature of the relatinoship, but I
generated this data set. In addition, the real thing does include variables
such as tenure, previous experience, etc. that are also used as covariates
at the individual level. Of course, this also means that these would need
be aggregated as well if that approach is taken.
Best
> ID X1 X2 Y
> 1 1 0.70 0.40
> 2 1 0.80 0.40
> 3 1 0.65 0.40
> 4 2 1.20 0.25
> 5 2 1.10 0.25
> 6 3 0.90 0.30
> 7 4 0.50 0.50
> 8 4 0.60 0.50
> 9 4 0.70 0.50
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