Hi Joshua,
Thanks for your response.
I tend to agree (intuitively) with you that when one has 50,000
observations and 1,000 groups for the variable modelled as random effect,
assuming a normal distribution for Wald test =coef/Se(coef) of the fixed
effects without bothering about degrees of freedom is reasonable. However,
the overwhelming majority of analyses deals with tens or at most a hundred
observations and with random effects defined by a factor with a small (but
generally greater than 5) number of categories. It is in this (often
encountered) context that the discussion of how to count the degrees of
freedom for the random effects seems to be critical. This tally of the
degrees of freedom lies between two extremes: as one (because only the
variance of the normally distributed random effect is estimated) or as the
number of categories minus one of the variable modelled as random effect.
In many (most?) cases, the assumption regarding the counting of the degrees
of freedom does make a difference for evaluating the significance of the
fixed effects.
The significance tests of the fixed effects requires having the degrees of
freedom of the model, which is why the library lme4 does not provide the
p-values when family=Gaussian but it does provide them whenever family !=
Gaussian, which was the question I posed in my mail. Other programs (SAS,
Statistica) take a position/assumption about the degrees of freedom of the
random effects that is at the very least debatable. DBates and others
recommend using Bayesian methods to estimate the p-vales and the Conf
Intervals, but the commonly available R functions only work for GLMM with
family =Gaussian and with independent random slopes and intercepts.
I hope that this mail helps clarify the questions I posed.
Cheers
Pablo


On 23 September 2013 18:50, Joshua Wiley <jwiley.psych@gmail.com> wrote:

> 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@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]]
> >
> > _______________________________________________
> > R-sig-mixed-models@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>
>
> --
> Joshua Wiley
> Ph.D. Student, Health Psychology
> University of California, Los Angeles
> http://joshuawiley.com/
> Senior Analyst - Elkhart Group Ltd.
> http://elkhartgroup.com
>

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