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Re: st: xtmelogit vs. gllamm


From   rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp LP)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: xtmelogit vs. gllamm
Date   Thu, 26 Jul 2007 10:26:19 -0500

Klaus Haberkern <haberkern@soziologie.unizh.ch> asks:

> concerning STATA 10. Is it possible 1) to run
> Multilevel-logistic-Regressions with 4 (or more) levels, 2) if so, does it
> reduce computing time substantially (compared to gllamm), e.g. minutes or
> hours instead of days or weeks?

Yes, you can use -xtmelogit- on models with 4 or more levels.  

Speed comparisons of -xtmelogit- with -gllamm- are very problem specific, but
I can offer some general guidelines.  In general you will find -xtmelogit- to
be significantly faster than -gllamm- in situations where

1.  Top-level (largest) panels are large, say, 20 or more observations
    per largest panel.

and/or

2.  The total dimension of the random effects at all levels is large, say 
    4 or greater.  For example, if you have a three-level model with a 
    random intercept and one random slope at each level, the total
    random-effects dimension is 3*2 = 6.

Computations become slower as the random-effects dimension described in 2.
increases.  This is the curse of dimensionality due to having to estimate
high-dimensional integrals via Guassian quadrature.  The quadrature
calculations in -xtmelogit- tend to scale better than those in -gllamm- as
this dimension increases.  As such, in complex models computation times that
are 25 to 30 times faster (if not more) when using -xtmelogit- are not
uncommon.

-xtmelogit- also allows for estimation via a Laplacian approximation.  While
not as accurate as Guassian quadrature, the Laplacian approximation has the
advantage of not suffering from the curse of dimensionality.  Computation
times with Laplace tend to only increase quadratically (as opposed to
exponentially) with model complexity.  While the final answer is not as
accurate as that obtained with quadrature, we have found the Laplacian
approximation to be quite reasonable in many problems.

--Bobby
rgutierrez@stata.com
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