Dear all,
This is my first post here--hope this is appropriate.
I'm trying to figure out how to simulate quantities of interest from a
mixed (multilevel) logit model. The logit.mixed documentation makes
this look straightforward, but I'd like to know what's going on "under
the hood".
Accounting for estimation uncertainty for the fixed effects is
straightforward--just the same as a single-level model. But what about
taking into account uncertainty about the random effects? I've
searched around on the Internet (and read the lme4 documentation) and
haven't had any luck figuring out how to do this in R.
(I realize that the random effects at each level are by definition a
distribution with a mean of 0, so I guess in many instances
simulations for quantities of interest can simply leave out the random
effects, because their mean effect is 0. But if we want to simulate
for a particular set of X values in a specific group versus in another
group, the random effect will clearly matter.)
Doug Bates is on record as saying that standard errors don't make
sense for the random effects
(
http://www.stat.columbia.edu/~cook/movabletype/archives/2008/12/uncertainty…
), since each estimate is not likely to follow a symmetrical
distribution. And lme4's mcmcsamp(), as I understand it, is not
operational. Gelman and Hill (2007) suggest using a Bayesian approach
and BUGS--getting a posterior distribution of estimates--but I don't
know BUGS and would rather not have to learn just for this. MLwiN
includes SEs for random effects, but doesn't have a straightforward
facility for estimating quantities of interest.
So my question (if this all makes sense) is how Zelig deals with this
issue. Is it finding some way to take into account estimation
uncertainty for the random effects? Or just treating each random
effect as a given, and only taking into account estimation uncertainty
for the fixed effects?
Any illumination about this point would be much appreciated.
Thanks,
Malcolm Fairbrother
University of Bristol