gbnlpanel - Non-linear panel 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.

gbnlpanel 6.2                                       June 2021                                       GBNLPANEL(1)

       Each row of a block represents a single process realization. Blocks are separated by two white spaces and
       represent    model    variables,    columns   represent   the   time   variable.   Input   is   read   as
       (X1_[r,t],...,Xj_[r,t],...  XN_[r,t]), where r is the row, t the  column  and  j  the  block.  The  model
       assumes that

       FUN(X1_[r,t],...,XN_[t,t]) - c_r = e_{r,t}

       with e i.i.d and 'c' arow specific element, which can be fixed (fixed effect) or a normal random variable
       (random effect).

       gbnlpanel 'x1-a*x2-c,a=0,c=0' < data.dat
              linear panel regression with one independent variable

       gbnlpanel - Non-linear panel regression

-M     type of model (default 0)

       0      fixed effects

       1      random effects

       -O     type of output  (default 0)

       0      parameters

       1      parameters and errors

       2      <variables> and panel statistics

       3      parameters and variance matrix

       -V     variance matrix estimation (default 0)

       0      < J^{-1} >, computed via fully-reduced log-likelihood

       1      < H^{-1} >, computed via fully-reduced log-likelihood

       2      < H^{-1} J H^{-1} >, computed via fully-reduced log-likelihood

       3      < J^{-1} >, computed via non-reduced log-likelihood

       4      < H^{-1} >,  computed via non-reduced log-likelihood

       5      < H^{-1} J H^{-1} >, computed via non-reduced log-likelihood

       -v     verbosity level (default 0)

       0      just results

       1      comment headers

       2      summary statistics

       3      covariance matrix

       4      minimization steps

       5      model definition

       -e     minimization tolerance (default 1e-6)

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

       -h     this help

       -A     comma  separated  MLL  optimization  options:  step,tol,iter,eps,msize,algo.  Use empty fields for
              default.  (default 0.1,0.01,500,1e-6,1e-6,0)

       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 (not recommended), 4 simplex, 5 Broyden-Fletcher-Goldfarb-Shanno-2

       Report bugs to <gbutils@googlegroups.com>

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

gbnlpanel [options] <FUN>