Is BLUP a good thing?

Hi again,

Sorry, I made a mistake. The random effects would not come out at zero if
A=I, they would come out as a proportion of y in the absence of other
fixed-random effects. I'm not sure what Gianola refers to as paradoxical,
could you provide a reference?

Cheers,

Jarrod



On 28 Mar 2011, at 09:47, Jarrod Hadfield wrote:

Hi,

On 28 Mar 2011, at 05:21, Dominick Samperi wrote:

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.

Look at the photos in Hill & Kirkpatrick (2010) Annu. Rev. Ecol. Evol.
Syst ?41:1-19. Those chickens bear testimony to the power of BLUP.

see also http://aipl.arsusda.gov/eval/summary/trend.cfm

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.

This was not a criticism of BLUP, but a criticism of its misuse. ?If I
fitted a repeated-measure mixed model, extracted the BLUP for each
individual, and then did a t-test to see if males and females differed,
people would rightly question my approach. Of course, people weren't doing
things as blatantly silly as this, but they were doing things which were
similar and would have the same sorts of consequences.

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?

It is a good thing, but it should not be used as a short cut for
formulating the appropriate statistical model.

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.

See the interesting paper by Blasco (2001) J. of Anim. Sci. 79 8
2023-2046. on the relationship between BLUP and Bayesian posterior modes
amongst other things.

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 can't find the Gianola paper you refer to. You have to be a bit careful
?here because animal breeders often use G to mean kronecker(V_{a},A) where
V_{a} is a trait x trait matrix of genetic (co)variances and A is the
additive genetic relationship matrix. In evolutionary biology G often refers
to ?V_{a}. ?If V_{a}= 0 then I think it is a good thing that the BLUPs go to
zero. What I think Gianola meant (I am guessing) is that if A goes to an
identity matrix then the BLUP all come out at zero. This is in some ways
paradoxical, and it is so because BLUP are biased predictions of specific
random effects - again I would read the Blasco paper.

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.

Inferences about random effects in a mixed model are usually framed in
terms of estimates of (co)variances rather than BLUPs. ?Depending on
definition this is generally "effective".

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

Thanks,
Dominick

Cheers,

Jarrod

--
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.

--
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.