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Re: st: Deriving Bayes estimates from xtmelogit


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Deriving Bayes estimates from xtmelogit
Date   Thu, 09 Sep 2010 11:11:34 -0500

Jamie Fagg <j.fagg@qmul.ac.uk> asks:

> I am trying to derive Bayes estimates from a 3-level logistic regression
> model in Stata version 10.1.

> The model has the following structure, where psychometric items are nested
> in individuals, nested in geographic areas.

> Level 1: psychometric items
> Level 2: individuals
> Level 3: geographic areas

> I read in Rabe-Hesketh and Skrondal (Multilevel and Longitudinal modelling
> using Stata, 2008, p.162) that "Empirical Bayes predictions of the random
> intercepts ... can be obtained" from xtmixed using -predict- with the
> reffects option

> I couldn't find any analogous advice in the section about multilevel
> logistic regression models so I ran the model and ran the predict eb,
> reffects (see code below).

> Is this the correct way to derive Bayes predictions from xtmelogit?

Yes this would be correct, with the one caveat that what you obtain are
empirical Bayes _modal_ predictions, rather than empirical Bayes mean
predictions.  In a logistic regression setting, the posterior distribution of
the random effects is no longer symmetric, and thus the posterior modes and
the posterior means, while very similar for most data, are not strictly equal.

Posterior mean predictions after multilevel logistic regression are not
available in current official Stata, but you could obtain these by
alternatively fitting your model using -gllamm-; see -ssc describe gllamm- for
details.

--Bobby
rgutierrez@stata.com
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