# [R] how lambda is computed in smoot.spline given _df_

Wolski wolski at molgen.mpg.de
Mon Nov 8 10:39:26 CET 2004

```Hi,

I posted some days ago a question concerning the computation of lambda in the smooth.spline function (which I repreat at the bottom of the mail) given _df_ .
Unfortunately the documentation is not clear to me. Maybee someone can help to answer in my view the basic question:

If the penalized log likelihood is L = (y - f)' W (y - f) + lambda c' Sigma c

how the _lambda_ in the above equation is computed if _df_ is given and _spar_ not?

And, Is there a way to define lambda directly?

Yours.
/E

Hi,

I am usign the smooth.spline function.

I am not sure how the _df_ (degrees of freedom) parameter,
if set, influences _lambda_ in eq:

L = (y - f)' W (y - f) + lambda c' Sigma c

Is _df_  substituting tr(Sigma), if defined, in the equation: r = tr(X' W X) / tr(Sigma)
which is used to compute: lambda = r * 256^(3*spar - 1)?

And how _spar_ is set if not defined?

/E

```