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Conservative "ANOVA tables" in lmer
2 messages · John Maindonald, Douglas Bates
On 9/10/06, John Maindonald <john.maindonald at anu.edu.au> wrote:
A Wiki entry is an excellent idea. I am happy to try to help. An account of mcmcsamp() might be very useful part of the Wiki. My limited investigations suggest that once the data starts to overwhelm the prior (maybe ~3 df for an effect that is of interest), the posterior distribution that it gives provides a very good approximation to the sampling distribution. I have been meaning to put aside time to try to work out, with the help of a colleague here at ANU, how the Kenward & Roger (Biometrics, 1997) approximation might be implemented in lmer, but it has'nt yet happened and is unlikely to do so for a while.
I think it would be nontrivial to do this for a general case. A literal translation of the formulas in that paper may be suitable for simple cases but not for general cases. Like many papers in this literature this one has the inverse of an n by n matrix (n being the number of observations) embedded in the middle of most of the formulas. Given that some users are seriously considering fitting models for which n is in the millions, forming and manipulating an n by n matrix in such cases is out of the question unless you can exploit special properties of the matrix.
John Maindonald email: john.maindonald at anu.edu.au phone : +61 2 (6125)3473 fax : +61 2(6125)5549 Centre for Mathematics & Its Applications, Room 1194, John Dedman Mathematical Sciences Building (Building 27) Australian National University, Canberra ACT 0200. On 10 Sep 2006, at 8:00 PM, r-help-request at stat.math.ethz.ch wrote:
From: Spencer Graves <spencer.graves at pdf.com>
Date: 10 September 2006 4:54:50 PM
To: Andrew Robinson <A.Robinson at ms.unimelb.edu.au>
Cc: Douglas Bates <bates at stat.wisc.edu>, R-Help <r-
help at stat.math.ethz.ch>
Subject: Re: [R] Conservative "ANOVA tables" in lmer
Hi, Doug, et al.:
I'll volunteer to do the same, which is an extension of much
of what I've been doing for R Help for a while now.
Regarding writing a FAQ, what about a Wiki entry (and maybe
ultimately a vignette)? This thread provides notes around which
such could be built. Another piece might be an example from
Scheff? (1958), which I sent as a reply to an earlier comment on
this thread, (foolishly sent without reducing the "cc" list, which
means it "awaits moderator approval"). Each time a question of
this nature arises, someone checks the Wiki, edits adds something
to it if necessary, then replies to the list with the reference to
the appropriate Wiki entry.
Spencer Graves
Andrew Robinson wrote:
On Thu, Sep 07, 2006 at 07:59:58AM -0500, Douglas Bates wrote:
I would be happy to re-institute p-values for fixed effects in the summary and anova methods for lmer objects using a denominator degrees of freedom based on the trace of the hat matrix or the rank of Z:X if others will volunteer to respond to the "these answers are obviously wrong because they don't agree with <whatever> and the idiot who wrote this software should be thrashed to within an inch of his life" messages. I don't have the patience.
This seems to be more than fair to me. I'll volunteer to help explain why the anova.lmer() output doesn't match SAS, etc. Is it worth putting a caveat in the output and the help files? Is it even worth writing a FAQ about this? Cheers Andrew
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