[R-sig-ME] lmer vs glmmPQL

[Fabian Scheipl]

Ben Bolker said:
>
> My take would be to pick lmer over glmmPQL every time, provided
> it can handle your problem -- in general it should be more accurate.

That's what I wanted to demonstrate to my students last week, so I did
a small simulation study with a logit-model with random intercepts:

logit(P(y_ij=1)) =  x_ij + b_i;
b_i ~N(0,1);
 x_ij ~U[-1,1];
 i=1,..,m;
 j=1,...,n_i

The pdfs with the results are attached (m subjects, ni obs/subject,
RPQL is PQL with iterated REML fits on the working observations
instead of ML, nAGQ=11 for AGQ).
The results surprised me :
- For the estimated standard deviation of the random intercepts, PQL
actually has (much) lower rmse for small and medium-sized data sets
and bias is about the same for LA, AGQ and PQL for small datasets.
- There were no relevant differences in rmse or bias for the estimates
of the fixed effects.

Differences for poisson data should be even smaller, since their
likelihood is more normal-ish.
glmer may still be preferrable since its much faster and more stable
than glmmPQL, but accuracy for smaller datasets may be better for PQL.

Best,
Fabian
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