The basis of the space of un-penalized functions for a TPRS
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.
null.space.dimension(d,m)
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. |
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.
An integer (array), the null space dimension M.
Simon N. Wood simon.wood@r-project.org
Wood, S.N. (2003) Thin plate regression splines. J.R.Statist.Soc.B 65(1):95-114
require(mgcv) null.space.dimension(2,0)
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