Re: Interpretation of Components for Splines

# Re: Interpretation of Components for Splines

```On Fri, 30 Apr 1999, Peter M. Saama wrote:

> >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 large the
> >fit tends to interpolation. The additional variance component, ie
> >dev(time), allows for the presence of group effects, and can only be
> >fitted if there is replication at each (or most) time point. This is in
> >line with the usual one-way random effects analysis where you would fit
> >y~ mu !r group
> >in asreml to get correct analysis ie estimating both an error and between
> >groups variance.
> >
> >The usual roughness penalty that is described in most smoothing texts is
> >actually lambda = 1/gamma(spl).
>
> Thank you for your remarks. As you know, it is customary to specify
> heritability as a function of the genetic and total variability. In
> formulating linear functions of the variance components, should the
> components for spl(time) and dev(time) be considered a part of the total
> variability or should one include them in the genetic variation?
yes well this opens up another issue.

The text book formula for h^2 is hard to apply for more general
situations. I prefer to calculate h^2 from prediction error variances
(pev) of BLUPS.
Roughly,

pev = sigma^2_g * ( 1 - h^2)

pev can be calc'd form the .vrb file from the asreml job. I have
functions to do this. it's actually better to use the average pairwise
variance. The above takes account of the other sources of variation, such
as spatial/temporal/ etc

cheers

> > Peter /
> >...........................................................................
> ....
> >      Brian Cullis                       Tel: 02 6938 1855
> >      NSW Agriculture                    Fax: 02 6938 1809
> >      Wagga Agricultural Institute     email: brian.cullis@agric.nsw.gov.au
> >      Pine Gully Rd
> >      WAGGA WAGGA  NSW 2650
>
> --
> Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml
>

...............................................................................
Brian Cullis                       Tel: 02 6938 1855
NSW Agriculture                    Fax: 02 6938 1809
Wagga Agricultural Institute     email: brian.cullis@agric.nsw.gov.au
Pine Gully Rd
WAGGA WAGGA  NSW 2650

```