[RsigME] testing fixed effects in binomial lmer...again?
Ben Bolker
bolker at ufl.edu
Tue Jan 8 23:21:31 CET 2008
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David Duffy wrote:
 On Tue, 8 Jan 2008, Dimitris Rizopoulos wrote:
>> On Jan 8, 2008 5:38 AM, Achaz von Hardenberg <fauna at pngp.it> wrote:
>>
>>> However, I am not sure about what I should do to test for the
>>> significance of fixed effects in the binomial case
> What about Bootstrap (parametric or not)? Would it be useful in this
> case?
>

 The only problem is specifying a bootstrap mechanism that respects the
 structure of the random effects. So for time series data, your bootstrap
 samples have to remain AR1 or whatever (ie you don't want gaps
appearing that
 aren't in the observed data), and for genetic type data (the kind I have),
 that pseudosample people are appropriately related to one another.
Resampling
 clusters works for that kind of data, though I think you need many
clusters.
 There are several papers in the area of genetic linkage analysis that
have
 validated bootstrapping for a test that a variance component is zero.

 But for testing simple hypotheses about particular fixed effects,
 a permutation/randomization test should work, I think.

 David Duffy.
~ My favorite solution (which worked in nlme, I think, but might
take some time to get for lme4 ...) would to be able to generate
posterior simulations from the reduced model, then use these to
generate a null distribution for F statistics (or whatever) for
the model comparison. This seems as though it would actually be
a relatively straightforward extension of mcmcsamp, once it exists 
although arguably once you have mcmcsamp you wouldn't need it
any more ...
~ Ben Bolker
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