logistic_regression_derivatives.m

GNU Octave is a high-level language, primarily intended for numerical computations. It provides a c

## Copyright (C) 1995, 1996, 1997  Kurt Hornik
## 
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## the Free Software Foundation; either version 2, or (at your option)
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## Called by logistic_regression.  Calculates derivates of the
## log-likelihood for ordinal logistic regression model.
  
## Author:  Gordon K. Smyth <[e-mail]>
## Adapted-By:  KH <[e-mail]>
## 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