null.space.dimension {mgcv} | R Documentation |
The thin plate spline penalties give zero penalty to some functions. The space of these functions is spanned by a set of polynomial terms. This routine 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-d)!
which is the value returned.
An integer, the null space dimension M.
Simon N. Wood snw@st-and.ac.uk
Wahba (1990) spline models of observational data. SIAM.
null.space.dimension(2,0)