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

Murray Jorgensen maj at waikato.ac.nz
Wed Apr 6 23:59:36 CEST 2011

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

   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!


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

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