llmnp                 package:bayesm                 R Documentation

_E_v_a_l_u_a_t_e _L_o_g _L_i_k_e_l_i_h_o_o_d _f_o_r _M_u_l_t_i_n_o_m_i_a_l _P_r_o_b_i_t _M_o_d_e_l

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

     'llmnp' evaluates the log-likelihood for the multinomial probit
     model.

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

     llmnp(beta, Sigma, X, y, r)

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

    beta: k x 1 vector of coefficients 

   Sigma: (p-1) x (p-1) Covariance matrix of errors 

       X: X is n*(p-1) x k array. X is from differenced system. 

       y: y is vector of n indicators of multinomial response (1, ...,
          p). 

       r: number of draws used in GHK 

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

     X is (p-1)*n x k matrix.  Use 'createX' with 'DIFF=TRUE' to create
     X. 

     Model for each obs:  w = Xbeta + e.   e ~ N(0,Sigma). 

     censoring mechanism: 

     if y=j (j<p),  w_j > max(w_{-j}) and w_j >0    
      if y=p,  w < 0                   

     To use GHK, we must transform so that these are rectangular
     regions e.g.  if y=1,  w_1 > 0 and w_1 - w_{-1} > 0. 

     Define A_j such that if j=1,...,p-1, A_jw = A_jmu + A_je > 0 is
     equivalent to y=j. Thus, if y=j, we have A_je > -A_jmu.  Lower
     truncation is -A_jmu and cov = A_jSigmat(A_j).   For j=p, e < -
     mu.

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

     value of log-likelihood (sum of log prob of observed multinomial
     outcomes).

_W_a_r_n_i_n_g:

     This routine is a utility routine that does *not* check the input
     arguments for proper dimensions and type.

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

     Peter Rossi, Graduate School of Business, University of Chicago,
     Peter.Rossi@ChicagoGsb.edu.

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

     For further discussion, see _Bayesian Statistics and Marketing_ by
     Rossi, Allenby and McCulloch, Chapters 2 and 4. 
      <URL:
     http://gsbwww.uchicago.edu/fac/peter.rossi/research/bsm.html>

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

     'createX', 'rmnpGibbs'

_E_x_a_m_p_l_e_s:

     ##
     ## Not run: ll=llmnp(beta,Sigma,X,y,r)

