>
> Hello:
>
> When we fit spl(t), and dev(day) in ASREML, the .asr file contains output
> that looks like this:
>
> Source Model terms Gamma Component Compnt/StndErr
> spl(time) 18 18 6.65133 4.113614 1.41 P
> dev(time) 20 20 0.603323E-01 0.103056E-02 0.47 P
> ...
>
> In the above table is 4.113614 a smoothing parameter or is it a variance
> component? Furthermore, in the above table, is 0.103056E-02 a parameter
> used in specification of the roughness penalty or is it a variance component?
>
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.
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.
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.
> Respectfully,
>
> Peter M. Saama /
> --
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Arthur Gilmour PhD mailto:Arthur.Gilmour@agric.nsw.gov.au
Senior Research Scientist (Biometrics) fax: <61> 2 6391 3899
NSW Agriculture <61> 2 6391 3922
Orange Agricultural Institute telephone work: <61> 2 6391 3815
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