15 Mar
2007
15 Mar
'07
2:09 a.m.
Thanks for the quick response.
I gather that whatever program you're using to
run the multilevel model
specifies explicitly what coefficiet is varying in which way. You can
approximate this pretty closely by using the right combination of
covariates in regression or Amelia. e.g., if E(Y)=a+b*X, and you want b
to vary by T[ime], you can say b=c+dT, and substitute this eqn into the
first, giving E(Y)=a+(c+dT)X = a + cX +d(T*X), so if you just put into
Amelia X and T*X, you'd be set. You can extend this pretty far of course.
This makes perfect sense. (Actually, right now my choice of MLM
package is R's lmer4, which requires this exact specification. If a
Level 1 coefficient varries by a level 2 variable, it is modeled as an
interaction.)
But what I am really concerned with is the case when there is a residual
(random effect) across the level 2 untis associated with B. (In
English, B is allowed to wary across, lets say, across countries). To
use the above notation b=c+dT+r where r is normally distributed random
variation with a mean of 0. This would mean that Y=a+(c+dT)X+r+e (where
e is the level 1 residual term.)
What I am concerned with is the omission of r from the imputation model.
(What I really need to do is simulate up some examples and test bias
that way, but I figured I'd ask first. :)
Thanks
L
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