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

[Dominick Samperi]

I should add that I personally think the BLUP is a good thing!

Why? Because it provides a beautiful link between two topics
that should be of interest to readers of this list: hypothesis
testing and smoothing spline fitting. For the smoothing spline
connection see Terry Speed's comments that follow Robinson (1991).

Indeed, in a smoothing spline context there is much less confusion
about what is a fixed effect and what is a random effect. The fixed
effects are the coefficients of the finite dimensional kernel of the
smoothing operator, for example.

Of course, the common denominator here is the fact that
a penalized objective (leading to BLUP's) appears in both
subject areas.

Dominick

On Mon, Mar 28, 2011 at 12:21 AM, Dominick Samperi <djsamperi at gmail.com> 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.
>
> 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
>