[R-sig-ME] Why BLUP may not be a good thing

[Murray Jorgensen]

Hi Doug,

Yes, the methods that the two papers I cite are concerned with are not 
truly maximum likelihood in that they seek to maximize over the 
parameters and the individual random effects simultaneously or in a kind 
of "MM" alternating algorithm. McCulloch places PQL in this class. I 
suppose they might be ML of a sort if one regarded the individual values 
of the random effects as parameters. I knew someone (the late Prof 
Christopher Wallace) who insisted on regarding them as such, but he 
followed his own school of inference "Minimum Message Length" in which 
the bad properties of ML estimation of such extended parameter sets 
seemed to be avoided.

I like your definition of the individual random effects as 'conditional 
modes' which (unless you follow Chris Wallace) seems to be the right way 
to look at them beyond the linear context.

Murray

On 7/04/2011 10:21 a.m., Douglas Bates wrote:
> I think McCulloch may have been referring to algorithms that alternate
> between estimating parameters in a linear mixed model and parameters
> in a generalized linear or nonlinear least squares model.
>
> The definition of the maximum likelihood estimator isn't up for
> debate.  Once you have defined the probability model you have defined
> the mle's for the model's parameters given the observed data.

-- 
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
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