gam.fit                 package:mgcv                 R Documentation

_G_A_M _P-_I_R_L_S _e_s_t_i_m_a_t_i_o_n _w_i_t_h _G_C_V/_U_B_R_E _s_m_o_o_t_h_n_e_s_s _e_s_t_i_m_a_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     This is an internal function of package 'mgcv'. It is a
     modification of the function 'glm.fit', designed to be called from
     'gam'. The major modification is that rather than solving a
     weighted least squares problem at each IRLS step,  a weighted,
     penalized least squares problem is solved at each IRLS step with
     smoothing parameters associated with each penalty chosen by GCV or
     UBRE, using routine 'magic'.  For further information on usage see
     code for 'gam'. Some regularization of the  IRLS weights is also
     permitted as a way of addressing identifiability related problems
     (see  'gam.control'). Negative binomial parameter estimation is
     supported.

     The basic idea of estimating smoothing parameters at each step of
     the P-IRLS is due to Gu (1992), and is termed `performance
     iteration' or `performance oriented iteration'.

_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:

     Gu (1992) Cross-validating non-Gaussian data. J. Comput. Graph.
     Statist. 1:169-179

     Gu and Wahba (1991) Minimizing GCV/GML scores with multiple
     smoothing parameters via the Newton method. SIAM J. Sci. Statist.
     Comput. 12:383-398

     Wood, S.N. (2000)  Modelling and Smoothing Parameter Estimation
     with Multiple  Quadratic Penalties. J.R.Statist.Soc.B
     62(2):413-428

     Wood, S.N. (2004) Stable and efficient multiple smoothing
     parameter estimation for generalized additive models. J. Amer.
     Statist. Ass. 99:637-686

_S_e_e _A_l_s_o:

     'gam.fit3',  'gam', 'mgcv', 'magic'

