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-d)!*

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.bath.ac.uk/~sw283/

### See Also

`gam`

### Examples

null.space.dimension(2,0)

[Package

*mgcv* version 1.3-23

Index]