[R-sig-ME] lmer and p-values (variable selection)

[John Maindonald]

On 07/04/2011, at 7:18 AM, Douglas Bates wrote:

> On Mon, Mar 28, 2011 at 5:40 PM, Ben Bolker <bbolker at gmail.com> wrote:
>> On 03/28/2011 06:15 PM, John Maindonald wrote:
>> 
>>> Elimination of a term with a p-value greater than say 0.15 or 0.2 is
>>> however likely to make little differences to estimates of other terms
>>> in the model.  Thus, it may be a reasonable way to proceed.  For
>>> this purpose, an anti-conservative (smaller than it should be)
>>> p-value will usually serve the purpose.
>> 
>> Note that naive likelihood ratio tests of random effects are likely to
>> be conservative (in the simplest case, true p-values are twice the
>> nominal value)

Just to be sure what is being said here, Ben, you meant "(in the simplest case, 
true p-values are <<half>> the nominal value)"?

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.
http://www.maths.anu.edu.au/~johnm


>> because of boundary issues and those of fixed effects are
>> probably anticonservative because of finite-size effects (see PB 2000
>> for examples of both cases.)
> 
> Well B of PB isn't quite so sure anymore.  You can have situations
> where adding a single, simple, random-effects term can introduce
> millions of coefficients into the linear predictor (although the
> estimates of those coefficients will be shrunk towards zero relative
> to estimating fixed-effects for such a term).  If I understand the
> argument behind DIC (Spiegelhalter, Best, Carlin  and van der Linde,
> 2002) http://www.jstor.org/stable/3088806 properly they would count
> the effective number of degrees of freedom according to the trace of
> the hat matrix, which would be somewhere between 1 and the number of
> levels of the factor.  In some ways that makes more sense to me but I
> still do recognize the argument that we made in the 2000 book.  So I
> remain confused - a not unusual state.
> 
>>> 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.
>>> http://www.maths.anu.edu.au/~johnm
>>> 
>> 
>> Ben
>> 
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