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author | Rik <rik@octave.org> |
---|---|
date | Wed, 28 Aug 2013 08:33:02 -0700 |
parents | 72c96de7a403 |
children | d63878346099 |
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## Copyright (C) 1995-2012 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 3 of the License, or (at ## your option) any later version. ## ## Octave 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 Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{theta}, @var{beta}, @var{dev}, @var{dl}, @var{d2l}, @var{p}] =} logistic_regression (@var{y}, @var{x}, @var{print}, @var{theta}, @var{beta}) ## Perform ordinal logistic regression. ## ## Suppose @var{y} takes values in @var{k} ordered categories, and let ## @code{gamma_i (@var{x})} be the cumulative probability that @var{y} ## falls in one of the first @var{i} categories given the covariate ## @var{x}. Then ## ## @example ## [theta, beta] = logistic_regression (y, x) ## @end example ## ## @noindent ## fits the model ## ## @example ## logit (gamma_i (x)) = theta_i - beta' * x, i = 1 @dots{} k-1 ## @end example ## ## The number of ordinal categories, @var{k}, is taken to be the number ## of distinct values of @code{round (@var{y})}. If @var{k} equals 2, ## @var{y} is binary and the model is ordinary logistic regression. The ## matrix @var{x} is assumed to have full column rank. ## ## Given @var{y} only, @code{theta = logistic_regression (y)} ## fits the model with baseline logit odds only. ## ## The full form is ## ## @example ## @group ## [theta, beta, dev, dl, d2l, gamma] ## = logistic_regression (y, x, print, theta, beta) ## @end group ## @end example ## ## @noindent ## in which all output arguments and all input arguments except @var{y} ## are optional. ## ## Setting @var{print} to 1 requests summary information about the fitted ## model to be displayed. Setting @var{print} to 2 requests information ## about convergence at each iteration. Other values request no ## information to be displayed. The input arguments @var{theta} and ## @var{beta} give initial estimates for @var{theta} and @var{beta}. ## ## The returned value @var{dev} holds minus twice the log-likelihood. ## ## The returned values @var{dl} and @var{d2l} are the vector of first ## and the matrix of second derivatives of the log-likelihood with ## respect to @var{theta} and @var{beta}. ## ## @var{p} holds estimates for the conditional distribution of @var{y} ## given @var{x}. ## @end deftypefn ## Original for MATLAB written by Gordon K Smyth <gks@maths.uq.oz.au>, ## U of Queensland, Australia, on Nov 19, 1990. Last revision Aug 3, ## 1992. ## Author: Gordon K Smyth <gks@maths.uq.oz.au>, ## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> ## Description: Ordinal logistic regression ## Uses the auxiliary functions logistic_regression_derivatives and ## logistic_regression_likelihood. function [theta, beta, dev, dl, d2l, p] = logistic_regression (y, x, print, theta, beta) ## check input y = round (vec (y)); [my, ny] = size (y); if (nargin < 2) x = zeros (my, 0); endif; [mx, nx] = size (x); if (mx != my) error ("logistic_regression: X and Y must have the same number of observations"); endif ## initial calculations x = -x; tol = 1e-6; incr = 10; decr = 2; ymin = min (y); ymax = max (y); yrange = ymax - ymin; z = (y * ones (1, yrange)) == ((y * 0 + 1) * (ymin : (ymax - 1))); z1 = (y * ones (1, yrange)) == ((y * 0 + 1) * ((ymin + 1) : ymax)); z = z(:, any (z)); z1 = z1 (:, any(z1)); [mz, nz] = size (z); ## starting values if (nargin < 3) print = 0; endif; if (nargin < 4) beta = zeros (nx, 1); endif; if (nargin < 5) g = cumsum (sum (z))' ./ my; theta = log (g ./ (1 - g)); endif; tb = [theta; beta]; ## likelihood and derivatives at starting values [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p); epsilon = std (vec (d2l)) / 1000; ## maximize likelihood using Levenberg modified Newton's method iter = 0; while (abs (dl' * (d2l \ dl) / length (dl)) > tol) iter = iter + 1; tbold = tb; devold = dev; tb = tbold - d2l \ dl; [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); if ((dev - devold) / (dl' * (tb - tbold)) < 0) epsilon = epsilon / decr; else while ((dev - devold) / (dl' * (tb - tbold)) > 0) epsilon = epsilon * incr; if (epsilon > 1e+15) error ("logistic_regression: epsilon too large"); endif tb = tbold - (d2l - epsilon * eye (size (d2l))) \ dl; [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); disp ("epsilon"); disp (epsilon); endwhile endif [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p); if (print == 2) disp ("Iteration"); disp (iter); disp ("Deviance"); disp (dev); disp ("First derivative"); disp (dl'); disp ("Eigenvalues of second derivative"); disp (eig (d2l)'); endif endwhile ## tidy up output theta = tb (1 : nz, 1); beta = tb ((nz + 1) : (nz + nx), 1); if (print >= 1) printf ("\n"); printf ("Logistic Regression Results:\n"); printf ("\n"); printf ("Number of Iterations: %d\n", iter); printf ("Deviance: %f\n", dev); printf ("Parameter Estimates:\n"); printf (" Theta S.E.\n"); se = sqrt (diag (inv (-d2l))); for i = 1 : nz printf (" %8.4f %8.4f\n", tb (i), se (i)); endfor if (nx > 0) printf (" Beta S.E.\n"); for i = (nz + 1) : (nz + nx) printf (" %8.4f %8.4f\n", tb (i), se (i)); endfor endif endif if (nargout == 6) if (nx > 0) e = ((x * beta) * ones (1, nz)) + ((y * 0 + 1) * theta'); else e = (y * 0 + 1) * theta'; endif gamma = diff ([(y * 0), (exp (e) ./ (1 + exp (e))), (y * 0 + 1)]')'; endif endfunction