gbnlprobit - Non linear probit regression

       Written by Giulio Bottazzi

       Copyright  ©  2001-2018  Giulio  Bottazzi  This  program is free software; you can redistribute it and/or
       modify it under the terms of the GNU General Public License (version 2) as published by the Free Software
       Foundation;

       This program is distributed in the hope that it will be useful, but WITHOUT ANY  WARRANTY;  without  even
       the  implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
       License for more details.

gbnlprobit 6.2                                      June 2021                                      GBNLPROBIT(1)

       Non linear probit estimation. Minimize the negative log-likelihood

              sum_{i in N_0} log(1-F(g(X_i))) + sum_{i in N_1} log(F(g(X_i)))

       where  N_0  and  N_1  are  the  sets  of 0 and 1 observations, g is a generic function of the independent
       variables and F is the normal CDF. It is also possible to minimize the score function

       w_0 sum_{i in N_0} theta(F(g(X_i))-t) +

              w_1 sum_{i in N_1} theta(t-F(g(X_i)))

       where theta is the Heaviside function and t a threshold level. Weights w_0 and w_1 scale the contribution
       of the two subpopulations. The first  column  of  data  contains  0/1  entries.  Successive  columns  are
       independent  variables.  The  model  is  specified  by a function g(x1,x2...) where x1,..  stands for the
       first,second .. N-th column independent variables.

   options:-O     type of output (default 0)

       0      parameters

       1      parameters and errors

       2      <variables> and probabilities

       3      parameters and variance matrix

       4      marginal effects

       -V     variance matrix estimation (default 0)

       0      <gradF gradF^t>

       1      < J^{-1} >

       2      < H^{-1} >

       3      < H^{-1} J H^{-1} >

       -z     take zscore (not of 0/1 dummies)

       -F     input fields separators (default " \t")

       -v     verbosity level (default 0)

       0      just results

       1      comment headers

       2      summary statistics

       3      covariance matrix

       4      minimization steps (default 10)

       5      model definition

       -g     set number of point for global optimal threshold identification

       -h     this help

       -t     set threshold value (default 0)

       0      ignore threshold

       (0,1)  user provided threshold

       1      compute optimal only global

       2      compute optimal

       -M     estimation method

       0      maximum likelihood

       1      min. score (w0=w1=1)

       2      min. score (w0=1/N0, w1=1/N1)

       -A     MLL     optimization     options      (default      0.01,0.1,100,1e-6,1e-6,5)      fields      are
              step,tol,iter,eps,msize,algo. Empty fields for default

       step   initial step size of the searching algorithm

       tol    line search tolerance iter: maximum number of iterations

       eps    gradient tolerance : stopping criteria ||gradient||<eps

       algo   optimization  methods:  0  Fletcher-Reeves, 1 Polak-Ribiere, 2 Broyden-Fletcher-Goldfarb-Shanno, 3
              Steepest descent, 4 simplex

       -B     score optimization options (default 0.1,100,1e-6) fields are  step,iter,msize.  Empty  fields  for
              default

       step   initial step size of the searching algorithm

       iter   maximum number of iterations

       msize  max size, stopping criteria simplex dim. <max size optimization method is simplex

       gbnlprobit - Non linear probit regression

       Report bugs to <gbutils@googlegroups.com>

       Package home page <http://cafim.sssup.it/~giulio/software/gbutils/index.html>

gbnlprobit [options] <functiondefinition>