[R-sig-ME] Is BLUP a good thing?

[Dominick Samperi]

After reading the recent publications on the dangers of applying BLUP to
natural populations (Hadfield et al 2010, Morrissey et al 2010) I was
left wondering why it works at all. The latter paper claims that BLUP
has a long and successful history when applied to animal breeding,
but no examples showing its effectiveness were presented.

The paper Hadfield et al 2010 makes the interesting point that
BLUP's are often used to estimate effects that are not explicitly
accounted for in the model. I think this zeros in precisely on the
problem. If the effect is not accounted for in the model, then
the model is being used metaphorically, making
a scientific analysis of cause/effect relationships very difficult
and open to differing interpretations.

Some recent books on mixed models do not say a word about
BLUP, perhaps to avoid any discussion of the difficulties.

So, twenty years after Robinson (1991) has a consensus
formed on the question of whether or not BLUP is indeed a good thing?

Doug Bates makes the useful point that it really should
be called the Bayesian posterior mode, at least in the case of
a Gaussian prior, but even this insight does not really address
the question of how BLUP can be used effectively.

It seems to me the "predicting" (or "estimating") a random effect
that is *assumed* to have a zero mean is a little like
estimating the intercept in a linear model for
which the intercept has been excluded. Similarly, how does one
estimate a random effect when the assumed noise is spherical?
Furthermore, note that the formula for the random effect BLUP
predicts exactly zero as the G-matrix goes to zero, something
that Gianola refers to as "paradoxical".

I understand how an analysis of variance can help to determine
what factors are more important than others, but extracting
information from "white noise" is bound to leave much room
for differing interpretations. This is not to say that the conclusions
are necessarily wrong or ineffective, but they may not be effective
for the traditional reasons (p-values, etc.), and consensus may
play as large a role as science/statistics.

Being a non-expert I hope that these comments are not considered
to be too basic or off-topic.

Thanks,
Dominick