[R-sig-ME] R-sig-mixed-models Digest, Vol 69, Issue 18

[Ben Bolker]

Kumiko Fukumura <kumiko.fukumura at ...> writes:

> 
> Hi,
> 
> RE: "Hauck-Donner effect"
> 

> I was wondering if you could possibly clarify whether Hauck-Donner
> effect affects coefficients for interactions only or it also affects
> fixed effects as well. In my experience, it seems to vary: in some
> situations, many zeros in one or more condition appeared to
> influence the estimate for the interaction only, but they also seem
> to influence fixed effects in other situations (though the fixed
> effects estimates were sensible when the interaction was removed
> from the model).  Another question is what we can do under such
> situations - having many zeros also seem to influence the results of
> model comparisons (using "anova" functions) as well as coefficient
> estimates - I noticed that some recommended the use of model
> comparisons to address the problem, but it doesn't seem to help
> much. Removing some conditions is a possibility, but it's a bit
> shame because we cannot take into account the whole data set in our
> analyses.  I'd be very grateful if you could give us any more
> informati!  on that you know about this phenomenon. Thank you very
> much in advance.

very brief thoughts:

  (1) you should be very, very careful interpreting the meaning
of main effects in the presence of interactions containing them.
  (2) it's possible that you're mixing up two different phenomena,
Hauck-Donner effects (which occur when some effects are strong
so that the likelihood surface is far from quadratic) and complete
separation (which occurs when some breakpoint or set of categories
in the data separates a region of all-zero from a region of all-one
[or all-positive] responses, leading to infinite estimates of
some parameters). (I see that my answer didn't distinguish between
these phenomena very clearly either.)

  Hauck-Donner effects are trivially handled by model comparison.

  Complete separation must be dealt with by bias-reducing algorithms
(Firth: see e.g. the logistf package), by adding Bayesian priors
(see e.g. bayesglm in the arm package or blmer in the blme package
[maybe], or use MCMCglmm, or WinBUGS).

  Neither of these is mixed-model specific, and in fact they're
not R-specific either, so you might want to ask further questions
either on R-help or on http://stats.stackexchange.com ...  
 
> Best wishes
> Kumiko
> 
> Kumiko Fukumura
> University of Strathclyde
 
> >You should look up/Google for "Hauck-Donner effect" (you can find a
> discussion in Venables and Ripley's book), which refers to the
> situation >where the approximation used to compute confidence
> intervals on GLM(M)s breaks down for strong effects.  >You should
> use explicit model comparison (?update, ?anova, ?drop1) to test the
> difference between models with and without the intercept term.

> >However, you might want to be careful with the all-zero case, as it
> will lead to an infinite estimate (in theory) of the interaction
> coefficient -- in >practice it will just lead to a very large,
> poorly constrained estimate.  >You could try a Bayesian method, or
> you could just try leaving out that category and make sure that the
> qualitative results of your analysis remain >unchanged ...