## Copyright (C) 1995, 1996, 1997  Kurt Hornik
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2, or (at your option)
## any later version.
##
## 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.
##
## You should have received a copy of the GNU General Public License
## along with this file.  If not, write to the Free Software Foundation,
## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

## Called by logistic_regression.  Calculates derivates of the
## log-likelihood for ordinal logistic regression model.

## Author:  Gordon K. Smyth <gks@maths.uq.oz.au>
## Adapted-By:  KH <Kurt.Hornik@ci.tuwien.ac.at>
## Description:  Derivates of log-likelihood in logistic regression

function [dl, d2l] ...
      = logistic_regression_derivatives (x, z, z1, g, g1, p)

  ## first derivative
  v = g .* (1 - g) ./ p; v1 = g1 .* (1 - g1) ./ p;
  dlogp = [(dmult (v, z) - dmult (v1, z1)), (dmult (v - v1, x))];
  dl = sum (dlogp)';

  ## second derivative
  w = v .* (1 - 2 * g); w1 = v1 .* (1 - 2 * g1);
  d2l = [z, x]' * dmult (w, [z, x]) - [z1, x]' * dmult (w1, [z1, x]) ...
      - dlogp' * dlogp;

endfunction