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

Jarrod Hadfield j.hadfield at ed.ac.uk
Mon Mar 28 10:59:08 CEST 2011

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?



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  
> 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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