Re: Interpretation of Components for Splines
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Re: Interpretation of Components for Splines

> 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 /
> --
> Asreml mailinglist archive:

Arthur Gilmour PhD          
Senior Research Scientist (Biometrics)                 fax: <61> 2 6391 3899
NSW Agriculture                                             <61> 2 6391 3922
Orange Agricultural Institute               telephone work: <61> 2 6391 3815
Forest Rd, ORANGE, 2800, AUSTRALIA                    home: <61> 2 6362 0046

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