(no subject)
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.