Re: Interpretation of Components for Splines

# Re: Interpretation of Components for Splines

On Fri, 30 Apr 1999, Arthur Gilmour wrote:

> Both terms are variance components.  The spl(time) component is
> dependent on the scaling of the design matrix used which is not uniquely
> defined.  I.e.  I could change the spl(time) component without changing
> the fit of the spline.
huh, this is hard to follow

>
> I expect there is a direct relationship of these components and the
> spline smoothing parameter but it may not be simple in the unequally replicated
> case.   i.e.  in the unreplicated case there is just a spline variance
> and a residual variance.  In your case there is a spline variance,
> a lack-of-fit variance and a residual variance.  Whether the traditional
> smoothing parameter is a  simple function of these quantities I know not.
The presence of dev(time) is to smooth at the right strata. If dev(time)
is not in the model then the fit will be rougher, ie large spl(time)
component, because the variance component is being estimated relative
only to error. It is crucial that this component is included for
replicated data, as discussed in our paper. It is still playing the same
role except now with another error term, which is akin to

r\sigma^2_g + \sigma^2_e

>
> One key to establishing this relationship is that the Z matrix used in ASREML
> is calculated assuming the variate is on the scale  min=1, max=KNOTS
> i.e. time  goes from 1 to 20 in your example [though not necessarily
> equally spaced within the interval]
>
> I'll pass this on to Ari who may know the answer.
> Otherwise, it means working through the algebra.
unnecessary i feel
> > Respectfully,
> >
> > Peter M. Saama /
> > --
> > Asreml mailinglist archive: http://www.chiswick.anprod.csiro.au/lists/asreml
>
>
> <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
> Arthur Gilmour PhD                    mailto:Arthur.Gilmour@agric.nsw.gov.au
> Senior Research Scientist (Biometrics)                 fax: <61> 2 6391 3899
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...............................................................................
Brian Cullis                       Tel: 02 6938 1855
NSW Agriculture                    Fax: 02 6938 1809
Wagga Agricultural Institute     email: brian.cullis@agric.nsw.gov.au
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