[R] gam function in the mgcv library

[Simon Wood]

On Monday 25 June 2007 13:26, Bill Wheeler wrote:
> I would like to fit a logistic regression using a smothing spline, where
> the spline is a piecewise cubic polynomial. Is the knots option used to
> define the subintervals for each piece of the cubic spline? 
- if you use something like 
gam(y~s(x,bs="cr",k=5),family=binomial,knots=list(x=c(0,.1,.3,.4,.8))
then yes, k is the number of knots and the `knots' list specifies where they 
occur. If you use the default `bs="tp"' then the spline basis functions are 
not really `knot' based, being instead an ordered set of eigenfunctions, that 
are optimal in a defined sense (see Wood, 2003, JRSSB).

> If yes and 
> there are k knots, then why does the coefficients field in the returned
> object from gam only list k coefficients? Shouldn't there be 4k -4
> coefficients?

A k knot natural cubic spline only has k free coefficients, so that is all 
that mgcv:gam reports. If you are thinking about sections of cubic, then the 
other 3 coefficients of each section are determined by the spline  continuity 
conditions + the conditions of having zero second derivative at the end 
knots. Exact details of the `mgcv' "cr" basis are given in section 4.1.2 of 
my 2006  book (see ?gam), but all you really need to know is that it's a 
natural cubic spline basis parameterized in terms of function heights at the 
knots (although there  is a gam identifiability constraint absorbed into the 
parameterization which muddies this neat interpretability a little). 

best,
Simon


> Sincerely,
>
> Bill
>
>
> ---------------------------------
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html and provide commented, minimal,
> self-contained, reproducible code.

-- 
> Simon Wood, Mathematical Sciences, University of Bath, Bath, BA2 7AY UK
> +44 1225 386603  www.maths.bath.ac.uk/~sw283