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## 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
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