lmer and p-values (variable selection)
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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