null.space.dimension          package:mgcv          R Documentation

_T_h_e _b_a_s_i_s _o_f _t_h_e _s_p_a_c_e _o_f _u_n-_p_e_n_a_l_i_z_e_d _f_u_n_c_t_i_o_n_s _f_o_r _a _T_P_R_S

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

     null.space.dimension(d,m)

_A_r_g_u_m_e_n_t_s:

       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.

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

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

_A_u_t_h_o_r(_s):

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

_R_e_f_e_r_e_n_c_e_s:

     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/>

_S_e_e _A_l_s_o:

     'gam'

_E_x_a_m_p_l_e_s:

     null.space.dimension(2,0)

