Computing heritability
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Computing heritability

  I have been combing through the recent ASREML listserver email archive
with plenty of confusion in terms of my understanding how does one simply
compute the variance of y and the variance of u (e.g. any terms that
involve genetics or animal) on a day by day basis when one has repeated
measures on animals in a pedigreed (i.e. animal model) ASREML analysis.
I've been trying to think through such a derivation on a random
coefficients model basis.  Given the 'mixed model' structure of spline models:

   y = X beta + Z u + e

I might be inclined to write the variance-covariance of y as:

    Z var(u) Z' + var(e)

and the variance-covariance of u as:

    Z var(u) Z'

and use that to determine the heritability on a day by day basis.  Also,
since the spline(day) term is really not a 'random effect' per se (i.e. it
is a term that is constant across all animals and measures deviation from
linear trend...isn't it?), I would not include this in the determination of
the variance of y.

There are undoubtedly several things wrong with my loose cannon thinking
here and so my question is... what are they?  I read in a previous email: 

" I could change the spl(time) component without changing the fit of the

and then in another email:

 "The component for spl(time) is a variance component, but it controls the
amount of smoothing. If this component (actually the ratio gamma) tends to
zero, the spline fit tends to a straight line, as it gets larger the fit
tends to interpolation"

These responses appear to conflict with each other (?)
Also, what is the meaning of the "overall heritability" that is given in
the .pvs file when genetic, environmental variances are potentially
heterogeneous over days and the random effects 'design matrix' is not
necessarily 0's and 1's?

I look forward to your comments...


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