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st: Additive R2 in FE --> BE CSTS models?


From   Robert dungmeister <mahutga4@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Additive R2 in FE --> BE CSTS models?
Date   Sat, 29 Sep 2007 14:38:07 -0700 (PDT)

Hello all.

I have what may be an obvious question.  Setting
asside issues of bias and consistency, let's pretend
that we simply want to provide the best in sample fit
to a set of cross sectional time series data--i.e. we
want to account for both the within and between case
variation.

One approach would be to estimate two models: one with
the fixed effects (fe) estimator and one with the
between effects (be) estimator.  This would give you
estimates of "Bfe" and "Bbe", which in some sense are
additive (again, leaving asside issues of bias and
consistency) estimates of some hypothetical model (Bx
= BfeX + BbeX) because the group means are orthogonal
to the mean deviated observations on both sides.

However, if you wanted to generate some kind of pseudo
R2 of this hypothetical model that combines the fe and
be estimates of B, is there an obvious way to
decompose the variance explained in each model so as
to add them together to get anything like a measure of
the total variance (i.e. that between and within
cases) explained?   

Thanks for your thoughts.

Best,

Roberto



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