Re: st: xtmelogit

["JVerkuilen (Gmail)" <jvverkuilen@gmail.com>]

On Wed, Nov 14, 2012 at 4:51 AM,  <S.Jenkins@lse.ac.uk> wrote:
>
> Advice commonly given on this list is to start with a less complex model
> and then make it more complicated. Be aware that models of the sort that
> you wish to estimate are intrinsically tricky to fit.

I just taught the mixed logistic regression class last night and
showed this very point. These are hard.


Be aware though that the estimation algorithms
> that MLwiN uses to fit -xtmelogit- type models differ from those used by
> Stata, and so estimates may differ especially for random effects
> parameters. Stata uses adaptive quadrature; MLwiN offers marginal and
> penalised quasi-likelihood options (and MCMC). This can matter. In some
> Monte-Carlo work currently in progress, I find that for a 2-level set-up
> (large N of individuals nested within C countries), -xtmelogit- does a
> distinctly better job at fitting the random effects parameters than does
> MLwiN with method PQL2 (smaller bias, better coverage) particularly in
> the 'small C' case. Both do well regarding the 'fixed' parameters. MLwiN
> estimation time is a fraction of Stata's, however.

There are a number of studies on the bias of PQL approaches to GLMM
estimation. PQL works by approximating the marginal likelihood through
a certain Taylor series expansion and then fitting using a sequence of
approximating linear models. This bias is most notable when the
approximating linear models are relatively poor approximations to the
true problem, such as for binary data with rare events. It works
pretty well for other models, such as mixed Poisson, grouped binomial,
or gamma.

PQL also doesn't generate a proper likelihood so you lose likelihood
ratio tests (but can do Wald tests as I recall).

There's been a bit of work using higher order terms in the series
approximation, but adaptive quadrature and MCMC methods seem to have
supplanted PQL for the most part. It is pretty good for getting
starting values for more accurate methods.

Other options: SAS proc glimmix has three options for use,
quasi-likelihood variants, Laplace and Gaussian quadrature. So does
R's lme library.
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