Your answer to (2) is not correct: the fixed effect is equivalent to
introducing dummy variables only for the linear model. For anything
non-linear, the fixed effect is conditioning on this (for the -clogit-
model, you are conditioning on the number of 0's and 1's in each
center), which is some complicated algebra. Again, for anything
nonlinear, the random effect is a messy numerical integration problem
-- and (3) yes, chances are your estimates of whatever has to deal
with the random effect are going to be unwieldy.
If you are willing to deal with economic terminology, have a look at
Wooldridge, Econometric Analysis of Cross-Sectional and Panel Data,
under the rubric of panel models with limited dependent variables, and
references therein. I think he gives a good exposition -- the
econometric analogue is that we want to control, at least explicitly,
for unobserved characteristics of an individual.
--
Stas Kolenikov
http://stas.kolenikov.name
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