## Copyright (C) 1995, 1996, 1997 Kurt Hornik
##
## This file is part of Octave.
##
## Octave 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.
##
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## 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 Octave; see the file COPYING. If not, write to the Free
## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301, USA.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{dl}, @var{d2l}] =} logistic_regression_derivatives (@var{x}, @var{z}, @var{z1}, @var{g}, @var{g1}, @var{p})
## Called by logistic_regression. Calculates derivates of the
## log-likelihood for ordinal logistic regression model.
## @end deftypefn
## Author: Gordon K. Smyth
## Adapted-By: KH
## 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