[R-sig-ME] (no subject)

[Douglas Bates]

On Fri, Jan 23, 2009 at 11:01 AM, Nicholas Lewin-Koh <nikko at hailmail.net> wrote:
> Wow!
> Now I have to go back and reread Bates and Watts. Thank you  Doug, for
> that very insightful commentary.

> Would Bruce Lindsay's work on the geometry of mixtures be applicable in
> the mixed model setting?

I can't say because I am not familiar with that work.

> Maybe my understanding is a bit shaky (not the
> first time nor the last)
> but aren't the mixed effects, in the case of fixed effects comparisons,
> nuisance parameters?

It depends.  From the analytic point of view, yes they are.  From the
geometric point of view they are another set of coefficients in a
linear predictor so they use up dimensions.  However, their estimates
are not ordinary least squares estimates they are penalized least
squares estimates so they don't really correspond to full dimensions.

> So at least in the case of the likelihood ratio, provided that the
> assumed family (link included)
> the likelihood ratio is in essence a sort of odds ratio between the two
> models.

I haven't really thought of things in that way so I'm not sure what to
say about it.

> Whether or not
> a p-value is valid or even necessary is a different question, and comes
> down to how well
> the distribution can be approximated.

A p-value is a useful metric, when we can calculate it reliably.
However, I don't think we should regard it as the sole purpose of
statistical inference.