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

[Douglas Bates]

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) 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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