null.space.dimension {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

http://www.maths.bris.ac.uk/~sw15190/

### See Also

`tprs`

### Examples

    require(mgcv)
    null.space.dimension(2,0)

[Package mgcv version 1.8-12 Index]