null.space.dimension          package:mgcv          R Documentation

The basis of the space of un-penalized functions for a TPRS

Description:

     The thin plate spline penalties give zero penalty to some
     functions. The space of these functions is spanned by a set of
     polynomial terms. 'null.space.dimension' finds the dimension of
     this space, M, given the number of covariates that the smoother is
     a function of, d, and the order of the smoothing penalty, m. If m
     does not satisfy 2m>d then the smallest possible dimension for the
     null space is found given d and the requirement that the smooth
     should be visually smooth.

Usage:

     null.space.dimension(d,m)

Arguments:

       d: is a positive integer - the number of variables of which the
          t.p.s. is a function. 

       m: a non-negative integer giving the order of the penalty
          functional, or signalling that the default order should be
          used.

Details:

     Thin plate splines are only visually smooth if the order of the
     wiggliness penalty, m, satisfies 2m > d+1. If 2m<d+1 then this
     routine finds the smallest m giving visual smoothness for the
     given d, otherwise the supplied m is used. The null space
     dimension is given by:

     M=(m+d-1)!/(d!(m-1)!

     which is the value returned.

Value:

     An integer (array), the null space dimension M.

Author(s):

     Simon N. Wood simon.wood@r-project.org

References:

     Wood, S.N. (2003) Thin plate regression splines. J.R.Statist.Soc.B
     65(1):95-114

     <URL: http://www.maths.bath.ac.uk/~sw283/>

See Also:

     'tprs'

Examples:

     null.space.dimension(2,0)

