magic.post.proc             package:mgcv             R Documentation

_A_u_x_i_l_l_i_a_r_y _i_n_f_o_r_m_a_t_i_o_n _f_r_o_m _m_a_g_i_c _f_i_t

_D_e_s_c_r_i_p_t_i_o_n:

     Obtains Bayesian parameter covariance matrix, frequentist
     parameter estimator covariance matrix, estimated degrees of 
     freedom for each parameter and leading diagonal of influence/hat
     matrix,  for a penalized regression estimated by 'magic'.

_U_s_a_g_e:

     magic.post.proc(X,object,w)

_A_r_g_u_m_e_n_t_s:

       X: is the model matrix.

  object: is the list returned by 'magic' after fitting the  model with
          model matrix 'X'.

       w: is the weight vector used in fitting, or the weight matrix
          used  in fitting (i.e. supplied to 'magic', if one was.). If
          'w' is a vector then its elements are typically proportional
          to reciprocal variances (but could even be negative).  If 'w'
          is a matrix then  't(w)%*%w' should typically give the
          inverse of the covariance matrix of the response data
          supplied to 'magic'.

_D_e_t_a_i_l_s:

     'object' contains 'rV' (V, say), and  'scale' (s, say) which can
     be  used to obtain the require quantities as follows. The Bayesian
     covariance matrix of  the parameters is VV's. The vector of 
     estimated degrees of freedom for each parameter is the leading
     diagonal of  VV'X'W'WX  where W is either the  weight matrix 'w'
     or the matrix 'diag(w)'. The  hat/influence  matrix is given by 
     WXVV'X'W' .

     The frequentist parameter estimator covariance matrix is 
     VV'X'W'WXVV's:  it is sometimes useful for testing terms for
     equality to zero.

_V_a_l_u_e:

     A list with three items: 

      Vb: the Bayesian covariance matrix of the model parameters.

      Ve: the frequentist covariance matrix for the parameter
          estimators.

     hat: the leading diagonal of the hat (influence) matrix.

     edf: the array giving the estimated degrees of freedom associated 
          with each parameter.

_A_u_t_h_o_r(_s):

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

_S_e_e _A_l_s_o:

     'magic'