MEtaStratModInf           package:missreg           R Documentation

_S_t_r_a_t_a _M_o_d_e_l _I_n_f_o_r_m_a_t_i_o_n _f_u_n_c_t_i_o_n _f_o_r _m_o_d_e_l_s _w_i_t_h _M _l_i_n_e_a_r _p_r_e_d_i_c_t_o_r_s.

_D_e_s_c_r_i_p_t_i_o_n:

     A sub-function called by 'ML2Inf' to supply values and its
     derivatives for the third part of the profile loglikelihood
     regarding to the 'h'-distribution at the first phase using the
     discrete partition version.

_U_s_a_g_e:

     MEtaStratModInf(theta, nderivs=2, x, Bcounts, ptildes, stratfn, 
                     off.set=0, ...)

_A_r_g_u_m_e_n_t_s:

   theta: Vector of the parameter values. 

 nderivs: Number of derivatives to be calculated; see
          'MEtaProspModInf'. 

       x: See 'MEtaProspModInf'.

 Bcounts: An optional vector of weights ('m_j') to be used in the
          fitting process. 

 ptildes: A vector of length K (total number of distinct 'h'-values
          observed)  providing values for 'p_k' within each
          's'-stratum.

 stratfn: A class of sub-functions called by 'MEtaStratModInf' to
          calcualte the values and their derivatives with respect to
          the linear predictor ('eta's') of X for   'pr(h_k|x_j;theta)'
          and 'sum_k{p_k*pr(h_k|x_j;theta)}' within each s-stratum.

 off.set: See 'MEtaProspModInf'.

     ...: Further arguments passed to or from related functions.

_D_e_t_a_i_l_s:

     This sub-function is used jointly with 'MEtaProspModInf' for
     regression models with a  fixed number of M linear predictors. It
     calculates the values and their derivatives for the third part of
     the profile loglikelihood in the form of 'l*(theta,Q)' within each
     s-stratum 

       'sum_j{m_j^(s)*log{sum_k{p_k^(s)*pr(h_k^(s)|x_j^(s);theta)}}}' 

      with respect to 'theta' through the M linear predictors
     (m=1,...,M),

       'eta_{jm}=o_{jm}+x_{j(m)}^T*theta ' 

      See "Description of the 'missreg' Library" for all details.

_V_a_l_u_e:

     A list with the following components 

   loglk: Log-likelihood obtained from the current 'theta' values.

   score: Score vector obtained from the current 'theta' values when
          'nderivs>=1';  'NULL' otherwise.

     inf: Observed information matrix obtained from the current 'theta'
          values when 'nderivs=2'; 'NULL' otherwise.

   Qstar: A matrix (J*K) providing values for 'pr(h_k|x_j;theta)'
          within each s-stratum.

  dQstar: A 3-dimensional array (J*K*C) providing the first derivative
          of 
            'pr(h_k|x_j;theta)' w.r.t. 'theta_c' (c=1,...,C).

SptQstar: A vector of length J providing values for 
          'sum_k{p_k*pr(h_k|x_j;theta)}'.

dSptQstar: A matrix (J*C) providing the first derivative of 
           'sum_k{p_k*pr(h_k|x_j;theta)}' w.r.t. 'theta_c' (c=1,...,C).

_A_u_t_h_o_r(_s):

     Chris Wild, Yannan Jiang

_R_e_f_e_r_e_n_c_e_s:

     Description of the 'missreg' Library, Wild and Jiang, 2007.

_S_e_e _A_l_s_o:

     'MEtaProspModInf'; 'ML2Inf'

