glmmADMB: Generalized Linear Mixed Models using AD Model Builder

Dear R-users,

because lme(r) & glmmpql, which are based on Penalized Quasi Likelihood, 
are not very robust with Bernoulli responses, I wanted to test glmmADMB. 
I run the following simulation study:

500 samples are drawn with the model specification:
y = (intercept*f1+pred2*f2+pred3*f3)+(intercept*ri+pred2*rs)
     where pred2 and pred3 are predictors distributed N(0,1)
     f1..f3 are fixed effects, f1=-1, f2=1.5, f3=0.5
     ri is random intercept with associated variance var_ri=0.2
     rs is random slope with associated variance var_rs=0.4
     the covariance between ri and rs "covr"=0.1

1500 units/dataset, class size=30

convergence:
~~~~~~~~~~~~
No crashes.
5/500 Datasets had on exit a gradient of the log-likelihood > 0.001 
though. Removing the datasets with questionable convergence doesn't seem 
to effect the simulation analysis.

bias:
~~~~~~
f1=-1.00531376
f2= 1.49891060
f3= 0.50211520
ri= 0.20075947
covr=0.09886267
rs= 0.38948382

Only the random slope "rs" is somewhat low, but i don't think it is of 
significance

coverage alpha=.95: (using asymmetric confidence intervals)
~~~~~~~~~~~~~~~~~~~~~~~~
f1=0.950
f2=0.950
f3=0.966
ri=0.974
covr=0.970
rs=0.970

While some coverages are somewhat high, confidence intervals based on 
asymptotic theory will not have exactly the nominal coverage level, but 
with simulations (parametric bootstrap) that can be corrected for.

I can highly recommend this excellent package to anyone fitting these 
kinds of models, and want to thank Hans Skaug & Dave Fournier for their 
hard work!

Roel de Jong.

glmmADMB: Generalized Linear Mixed Models using AD Model Builder

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