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

[Dominick Samperi]

Thanks for the feedback. Here are the full citations:

1. J.D. Hadfield, A.J. Wilson, D. Garant, B.C. Sheldon, L.E.B. Kruk (2010),
    "The Misuse of BLUP in Ecology and Evolution",
    The American Naturalist, 175(1), 116-125
2. M.B. Morrissey, L.E.B. Kruk, A.J. Wilson (2010),
    "The danger of applying the breeder's equation in observational studies
    of natural populations",
    J. of Evolutionary Biology, 23(11), 2277-2288
3. G.K. Robinson (1991),
    "That BLUP is a good thing: The estimation of random effects",
    Statistical Sciendes, 6(1), 15-51
4. D. Gianola (2003),
    "Inferences about breeding values",
    Chapter 17 in The Handbook of Statistical Genetics, p.531,
    quote: "Paradoxically, in the limit, it is no longer possible to predict
    breeding values uniquely as a degeneracy in rank occurs."

On Mon, Mar 28, 2011 at 4:59 AM, Jarrod Hadfield <j.hadfield at ed.ac.uk> wrote:
> 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
>>
>>>
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>>
>>
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>
>
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> Scotland, with registration number SC005336.
>
>