MEtaProspModInf           package:missreg           R Documentation

_P_r_o_s_p_e_c_t_i_v_e _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 first part of the profile loglikelihood
     regarding to the model of interest  using the discrete partition
     version.

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

     MEtaProspModInf(theta,nderivs=2,y,x,wts=1,modelfn,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, ranged from 0
          (loglikelihood only) to 2 (information matrix).

       y: The response of interest, can be either a vector or matrix.

       x: A 3-dimensional array (R*C*M) specifying the covariates
          values,  with R the number of observations, C the length of
          'theta' and M the number  of linear predictors used.

     wts: An optional vector of weights ('n_i') to be used in the
          fitting process. The default is 1.

 modelfn: A class of sub-functions called by 'MEtaProspModInf' to
          calculate the values  and their derivatives with respect to
          the linear predictor ('eta''s) of X for the model of 
          interest 'f(Y|X; theta)'.

 off.set: The offset provided in a matrix form (R*M) with R the number
          of  observations and M the number of linear predictors used.

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

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

     This sub-function is used to implement prospective regression
     models with a fixed number of M linear predictors. It calculates
     the value and its derivatives for the first part of  the profile
     loglikelihood in the form of 'l*(theta,Q)' within each s-stratum 

      'sum_{A(s)}{n_i^(s)*log{f(y_i^{(s)}|x_i^{(s)};theta)}} ', 

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

       'eta_{im} = o_{im}+x_{i(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 curent 'theta' values when
          'nderivs>=1';  'NULL' otherwise.

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

_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:

     'ML2Inf'

