[R-sig-ME] Ben's Point about Centering and GLMM (was: Re: Low intercept estimate in a binomial glmm

[Paul Johnson]

On Fri, Apr 5, 2013 at 1:24 AM, John Maindonald
<john.maindonald at anu.edu.au> wrote:
> Surely it is an issue of how you define multi-collinearity.
>
I don't think so. The definition is the same, but multi-collinearity's
effect is different for every point in the X space.  I mean, the
elevation in variance estimates due to multi-collinearity depends on
where you place the y axis. The point estimates that appear in
regression output are different when you center because you move the y
axis about by centering.  But if you fit in one spot, and then project
the answer over to the other spot, the answer you get about slope,
standard error, etc is all the same. In either model.

Centering appeals to many practitioners because it seems to give
parameters with smaller standard errors, but its an illusion.
Uncertainty about predictions is hour-glass shaped in the X space, and
if you go into the middle, you have less uncertainty.

> 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.
>

I think that's a mistake, and have the examples in the rockchalk
vignette to demonstrate it.  If you say "what is the slope when
observed X = x", and "what is the uncertainty of your estimate when X
= x?" all of these models give exactly the same answer.

But back to Ben's point about GLMM.  That's an eye opener.

I'd like to make a working example of the problem that centering
affects estimates (beyond rounding error).  I need to know a test case
that is likely to produce the effect mentioned before I can go any
further.

pj
--
Paul E. Johnson
Professor, Political Science      Assoc. Director
1541 Lilac Lane, Room 504      Center for Research Methods
University of Kansas                 University of Kansas
http://pj.freefaculty.org               http://quant.ku.edu