[R-sig-ME] why would using p-values of GLMM for distr other than Gaussian be correct?

[Joshua Wiley]

Hi Pablo,

I think it depends on the assumptions.  In theory with the right
degrees of freedom, you could fit linear mixed effects models on a
smaller sample reasonably.

There are no degrees of freedom typically for glms, and GLMMs follow
suit.  Things like logistic regression rely on large sample
theory---you have a big enough sample degrees of freedom are
effectively infinite---the parameters are normally distributed and a z
test is fine.  The same would hold for linear mixed models.  If you
had say, 50000 observations from 1000 groups, p values assuming z =
b/se ~ Gaussian is pretty sensible.

Cheers,

Joshua



On Mon, Sep 23, 2013 at 3:09 PM, Pablo Inchausti
<pablo.inchausti.f at gmail.com> wrote:
> Hello,
> I am teaching a graduate course on statistics for ecologists, one of whose
> topics is GLMM.  I explain to the students the issue (somewhat recurrent in
> this list) of why p values of fixed effects are not provided in lmer due to
> the dispute/uncertainty on how to count degrees of freedom for random
> effects. DBates, among others, have answered queries in this regard several
> times. In this case, I explain how to use mcmcsamp to obtain p-values and
> Conf Intervals for the fixed effects using Bayesian approaches when
> family=Gaussian.
>
> When one uses lmer for dist other than Gaussian the p-values of fixed
> effects are actually printed. My question is WHY would these p-values for
> family != Gaussian  be correct and adequate. I have searched for an answer
> in the mailings of this list, but could not find one. Nor in my own library
> and in many web searches. Is it because the function mcmcsamp currently
> only accepts dist=Gaussian? To my mind, the p-values of fixed effects would
> be subject to the same issues and "problems" regardless of the prob
> distribution used in the analysis, because these issues arise from having a
> mixed model.
>
> Also, mcmcsamp only seems to accept a random effects structure having
> random slopes and intercepts that are independent by construction. This
> forces the user to fit a different (and often less adequate) model in order
> to use the function mcmcsamp to obtain the p-values and conf Intervals of
> fixed effects.
>
> Advance apologies if this is a double posting and if these questions are on
> the silly/pointless realm.
>
> I would appreciate any help/suggestions on these two questions.
>
> Regards,
>
> Pablo Inchausti
>
>         [[alternative HTML version deleted]]
>
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-- 
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://joshuawiley.com/
Senior Analyst - Elkhart Group Ltd.
http://elkhartgroup.com