Not sure it applies exactly to the cases discussed so far here, but there is
analytical and simulation evidence against using BLUP-based residuals of
mixed models for bootstrapping. See:Morris, J.S. (2002). The BLUPs are not
"best" when it comes to bootstrapping.
Statistics & Probability Letters 56, 425-450.

A PDF is available on his website.

Reinhold

On Jan 8, 2008 11:21 PM, Ben Bolker <bolker@ufl.edu> wrote:

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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@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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