Low intercept estimate in a binomial glmm
Well, yes, not necessarily of scant consequence when general optimisation algorithms are used! Also, note that type III sums of squares are defined with respect to a specific parameterisation. Do not use them unless in the rare event that one can make a good case for a particular choice of parameterisation! Random effects are defined with respect to a particular parameterisation. 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
On 06/04/2013, at 11:49 AM, Ben Bolker <bbolker at gmail.com> wrote:
John Maindonald <john.maindonald at ...> writes:
Surely it is an issue of how you define multi-collinearity. Centering is a simple re-parameterisation that, like any other re-parameterisation, makes no difference to the predicted values and their standard errors (well, it will make some small difference to the numerical computational error, but with modern software that should be of scant consequence). Re-parameterisation may however give parameters that are much more interpretable, with much reduced correlations and standard errors That is the primary reason, if there is one, for doing it.
... but unfortunately centering often *can* make a difference in GLMM fitting with lme4. It would be nice eventually to do *internal* orthogonalization of the fixed-effects design matrix (or at least allow a switch for it), to make hand-centering/ scaling/orthogonalization unnecessary, but for the time being there really are cases where centering matters. Ben Bolker
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