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

[Ryan King]

You might also be interested in the HGLM literature on this topic:
they do exactly the "bad" thing and jointly maximize random effects
and variance components.

You can look at the procedure as corresponding to the laplace
approximation to the marginal likelihood, which works well when there
is lots of information per-random effect.  The most incisive
discussion I read on the topic happens in the replies to

1.Lee, Y. Conditional and Marginal Models: Another View. Statist. Sci.
19, 219-238 (2004).
and
1.Lee, Y. Likelihood Inference for Models with Unobservables: Another
View. Statist. Sci. 24, 255-269 (2009).

in particular
1.Meng, X.L. Decoding the h-likelihood. Statistical Science 24, 280–293 (2009).

Also neat is a technical report by Lee where he extends the procedure
to include lasso-like variable selection.

1.Lee, Y. & Oh, H. RANDOM-EFFECT MODELS FOR VARIABLE SELECTION. (2009).
http://statistics.stanford.edu/~ckirby/techreports/GEN/2009/2009-04.pdf

Ryan King
Dept Health Studies
University of Chicago

On Wed, Apr 6, 2011 at 6:26 PM,
<r-sig-mixed-models-request at r-project.org> wrote:

> Date: Thu, 07 Apr 2011 09:59:36 +1200
> From: Murray Jorgensen <maj at waikato.ac.nz>
> To: R Mixed Models <r-sig-mixed-models at r-project.org>
> Subject: [R-sig-ME] Why BLUP may not be a good thing
> Message-ID: <4D9CE248.6060306 at waikato.ac.nz>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
>
> I could be wrong-headed but it seems to me that in a GLMM context BLUP
> falls into a class of procedures that has been found to have bad
> properties in a missing-data (EM) context. See
>
> @ARTICLE{lr83,
>   author  = {Little, R. J. A. and Rubin, D. B.},
>   title   = {On jointly estimating parameters and
> missing data by maximizing the complete data likelihood},
>   journal = {Amer. Statist.},
>   volume  = {37},
>   number  = {},
>   pages   = {218-220},
>   year    = {1983}
> }
>
> whose abstract follows:
>
> One approach to handling incomplete data occasionally encountered in the
> literature is to treat the missing data as parameters and to maximize
> the complete-data likelihood over the missing data and parameters. This
> article points out that although this approach can be useful in
> particular problems, it is not a generally reliable approach to the
> analysis of incomplete data. In particular, it does not share the
> optimal properties of maximum likelihood estimation, except under the
> trivial asymptotics in which the proportion of missing data goes to zero
> as the sample size increases.
>
> In the GLMM context we have the article
>
> Maximum Likelihood Algorithms for Generalized Linear Mixed Models
> Charles E. McCulloch Journal of the American Statistical Association,
> Vol. 92, No. 437 (Mar., 1997), pp. 162-170
>
> McCulloch calls BLUP-like algorithms "joint maximization" methods and
> finds that they have poor properties, as we might expect from the
> Little-Rubin article.
>
> It may be that BLUP is one of those things that looses good properties
> when shifted from a linear to non-linear context.
>
> On the other hand it's also possible that I have completely
> misunderstood what people mean by BLUP in a GLMM context, in which case
> I'd like to be helped out of my confusion!
>
> Murray
>
>
> --
> 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
> Phone  +64 7 838 4773 wk    Home +64 7 825 0441   Mobile 021 0200 8350
>
>