fix.family.link             package:mgcv             R Documentation

_M_o_d_i_f_y _f_a_m_i_l_i_e_s _f_o_r _u_s_e _i_n _G_A_M _f_i_t_t_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     Generalized Additive Model fitting by `outer' iteration, requires
     extra derivatives of the variance and link functions to be  added
     to family objects. The functions add what is needed.

_U_s_a_g_e:

     fix.family.link(fam)
     fix.family.var(fam)
     fix.family.ls(fam)

_A_r_g_u_m_e_n_t_s:

     fam: A 'family'.

_D_e_t_a_i_l_s:

     Outer iteration GAM estimation requires derivatives of the GCV,
     UBRE/gAIC, GACV, REML or ML score, which are obtained by finding
     the derivatives of the model coefficients w.r.t. the log smoothing
     parameters, using the implicit function theorem.  The expressions
     for the derivatives require the second and third derivatives of
     the link  w.r.t. the mean (and the 4th derivatives if Fisher
     scoring is not used). Also required are the first and second
     derivatives of the variance function w.r.t. the mean (plus the
     third  derivative if Fisher scoring is not used). Finally REML or
     ML estimation of smoothing parameters requires the log saturated
     likelihood and its first two derivatives w.r.t. the scale
     parameter. These functions add functions evaluating these
     quantities to a family. 

     If the family already has functions 'dvar', 'd2var', 'd3var',
     'd2link', 'd3link', 'd4link' and for RE/ML 'ls', then these
     functions simply  return the family unmodified: this allows
     non-standard links to be used with 'gam' when using outer
     iteration (performance iteration operates with unmodified
     families). Note that if you only need Fisher scoring then 
     'd4link' and 'd3var' can be dummy, as they are ignored. similalry
     'ls' is only needed for  RE/ML.

     The 'dvar' function is a function of a mean vector, 'mu', and
     returns a vector of corresponding first derivatives of the family
     variance function. The 'd2link' function is also a function of a
     vector of mean values, 'mu': it returns a vector of second
     derivatives of the link, evaluated at 'mu'. Higher derivatives are
     defined similarly.

     If modifying your own family, note that you can often get away
     with supplying only a 'dvar' and 'd2var', function if your family
     only requires links that occur in one of the standard families.

_V_a_l_u_e:

     A family object with extra component functions 'dvar', 'd2var',
     'd2link', 'd3link', 'd4link' and 'ls'.

_A_u_t_h_o_r(_s):

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

_S_e_e _A_l_s_o:

     'gam.fit3'