Mercurial > hg > octave-nkf
annotate scripts/statistics/models/logistic_regression.m @ 17338:1c89599167a6
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| author | Rik <rik@octave.org> |
|---|---|
| date | Wed, 28 Aug 2013 08:33:02 -0700 |
| parents | 72c96de7a403 |
| children | d63878346099 |
| rev | line source |
|---|---|
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1 ## Copyright (C) 1995-2012 Kurt Hornik |
| 3426 | 2 ## |
| 3922 | 3 ## This file is part of Octave. |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 3426 | 9 ## |
| 3922 | 10 ## Octave is distributed in the hope that it will be useful, but |
| 3191 | 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 3426 | 13 ## General Public License for more details. |
| 14 ## | |
| 3191 | 15 ## You should have received a copy of the GNU General Public License |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 3191 | 18 |
| 3454 | 19 ## -*- texinfo -*- |
| 6754 | 20 ## @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}) |
| 3454 | 21 ## Perform ordinal logistic regression. |
| 3191 | 22 ## |
| 3454 | 23 ## Suppose @var{y} takes values in @var{k} ordered categories, and let |
| 24 ## @code{gamma_i (@var{x})} be the cumulative probability that @var{y} | |
| 25 ## falls in one of the first @var{i} categories given the covariate | |
| 26 ## @var{x}. Then | |
| 27 ## | |
| 28 ## @example | |
| 29 ## [theta, beta] = logistic_regression (y, x) | |
| 30 ## @end example | |
| 31 ## | |
| 32 ## @noindent | |
| 3191 | 33 ## fits the model |
| 3454 | 34 ## |
| 35 ## @example | |
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36 ## logit (gamma_i (x)) = theta_i - beta' * x, i = 1 @dots{} k-1 |
| 3454 | 37 ## @end example |
| 3191 | 38 ## |
| 3454 | 39 ## The number of ordinal categories, @var{k}, is taken to be the number |
| 40 ## of distinct values of @code{round (@var{y})}. If @var{k} equals 2, | |
| 41 ## @var{y} is binary and the model is ordinary logistic regression. The | |
| 42 ## matrix @var{x} is assumed to have full column rank. | |
| 43 ## | |
| 44 ## Given @var{y} only, @code{theta = logistic_regression (y)} | |
| 3191 | 45 ## fits the model with baseline logit odds only. |
| 46 ## | |
| 47 ## The full form is | |
| 3454 | 48 ## |
| 49 ## @example | |
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50 ## @group |
| 3454 | 51 ## [theta, beta, dev, dl, d2l, gamma] |
| 52 ## = logistic_regression (y, x, print, theta, beta) | |
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53 ## @end group |
| 3454 | 54 ## @end example |
| 55 ## | |
| 56 ## @noindent | |
| 57 ## in which all output arguments and all input arguments except @var{y} | |
| 58 ## are optional. | |
| 3191 | 59 ## |
| 6754 | 60 ## Setting @var{print} to 1 requests summary information about the fitted |
| 3454 | 61 ## model to be displayed. Setting @var{print} to 2 requests information |
| 62 ## about convergence at each iteration. Other values request no | |
| 63 ## information to be displayed. The input arguments @var{theta} and | |
| 64 ## @var{beta} give initial estimates for @var{theta} and @var{beta}. | |
| 65 ## | |
| 66 ## The returned value @var{dev} holds minus twice the log-likelihood. | |
| 3191 | 67 ## |
| 3454 | 68 ## The returned values @var{dl} and @var{d2l} are the vector of first |
| 69 ## and the matrix of second derivatives of the log-likelihood with | |
| 70 ## respect to @var{theta} and @var{beta}. | |
| 3191 | 71 ## |
| 3454 | 72 ## @var{p} holds estimates for the conditional distribution of @var{y} |
| 73 ## given @var{x}. | |
| 74 ## @end deftypefn | |
| 3191 | 75 |
| 3426 | 76 ## Original for MATLAB written by Gordon K Smyth <gks@maths.uq.oz.au>, |
| 3191 | 77 ## U of Queensland, Australia, on Nov 19, 1990. Last revision Aug 3, |
| 78 ## 1992. | |
| 79 | |
| 3456 | 80 ## Author: Gordon K Smyth <gks@maths.uq.oz.au>, |
| 5428 | 81 ## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> |
| 3456 | 82 ## Description: Ordinal logistic regression |
| 3191 | 83 |
| 84 ## Uses the auxiliary functions logistic_regression_derivatives and | |
| 85 ## logistic_regression_likelihood. | |
| 86 | |
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87 function [theta, beta, dev, dl, d2l, p] = logistic_regression (y, x, print, theta, beta) |
| 3426 | 88 |
| 3191 | 89 ## check input |
| 3426 | 90 y = round (vec (y)); |
| 91 [my, ny] = size (y); | |
| 3191 | 92 if (nargin < 2) |
| 3426 | 93 x = zeros (my, 0); |
| 3191 | 94 endif; |
| 3238 | 95 [mx, nx] = size (x); |
| 3191 | 96 if (mx != my) |
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97 error ("logistic_regression: X and Y must have the same number of observations"); |
| 3191 | 98 endif |
| 3426 | 99 |
| 3191 | 100 ## initial calculations |
| 101 x = -x; | |
| 102 tol = 1e-6; incr = 10; decr = 2; | |
| 103 ymin = min (y); ymax = max (y); yrange = ymax - ymin; | |
| 104 z = (y * ones (1, yrange)) == ((y * 0 + 1) * (ymin : (ymax - 1))); | |
| 105 z1 = (y * ones (1, yrange)) == ((y * 0 + 1) * ((ymin + 1) : ymax)); | |
| 3426 | 106 z = z(:, any (z)); |
| 107 z1 = z1 (:, any(z1)); | |
| 3238 | 108 [mz, nz] = size (z); |
| 3426 | 109 |
| 3191 | 110 ## starting values |
| 111 if (nargin < 3) | |
| 3426 | 112 print = 0; |
| 3191 | 113 endif; |
| 3426 | 114 if (nargin < 4) |
| 115 beta = zeros (nx, 1); | |
| 3191 | 116 endif; |
| 3426 | 117 if (nargin < 5) |
| 118 g = cumsum (sum (z))' ./ my; | |
| 119 theta = log (g ./ (1 - g)); | |
| 3191 | 120 endif; |
| 121 tb = [theta; beta]; | |
| 122 | |
| 123 ## likelihood and derivatives at starting values | |
| 124 [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); | |
| 125 [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p); | |
| 126 epsilon = std (vec (d2l)) / 1000; | |
| 3426 | 127 |
| 3191 | 128 ## maximize likelihood using Levenberg modified Newton's method |
| 129 iter = 0; | |
| 130 while (abs (dl' * (d2l \ dl) / length (dl)) > tol) | |
| 131 iter = iter + 1; | |
| 132 tbold = tb; | |
| 133 devold = dev; | |
| 134 tb = tbold - d2l \ dl; | |
| 135 [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); | |
| 136 if ((dev - devold) / (dl' * (tb - tbold)) < 0) | |
| 137 epsilon = epsilon / decr; | |
| 138 else | |
| 139 while ((dev - devold) / (dl' * (tb - tbold)) > 0) | |
| 3426 | 140 epsilon = epsilon * incr; |
| 3191 | 141 if (epsilon > 1e+15) |
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142 error ("logistic_regression: epsilon too large"); |
| 3191 | 143 endif |
| 3426 | 144 tb = tbold - (d2l - epsilon * eye (size (d2l))) \ dl; |
| 145 [g, g1, p, dev] = logistic_regression_likelihood (y, x, tb, z, z1); | |
| 3191 | 146 disp ("epsilon"); disp (epsilon); |
| 147 endwhile | |
| 148 endif | |
| 149 [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p); | |
| 150 if (print == 2) | |
| 151 disp ("Iteration"); disp (iter); | |
| 152 disp ("Deviance"); disp (dev); | |
| 153 disp ("First derivative"); disp (dl'); | |
| 154 disp ("Eigenvalues of second derivative"); disp (eig (d2l)'); | |
| 155 endif | |
| 156 endwhile | |
| 157 | |
| 158 ## tidy up output | |
| 159 | |
| 160 theta = tb (1 : nz, 1); | |
| 161 beta = tb ((nz + 1) : (nz + nx), 1); | |
| 162 | |
| 163 if (print >= 1) | |
| 164 printf ("\n"); | |
| 165 printf ("Logistic Regression Results:\n"); | |
| 3426 | 166 printf ("\n"); |
| 3456 | 167 printf ("Number of Iterations: %d\n", iter); |
| 168 printf ("Deviance: %f\n", dev); | |
| 3191 | 169 printf ("Parameter Estimates:\n"); |
| 170 printf (" Theta S.E.\n"); | |
| 3426 | 171 se = sqrt (diag (inv (-d2l))); |
| 3191 | 172 for i = 1 : nz |
| 173 printf (" %8.4f %8.4f\n", tb (i), se (i)); | |
| 174 endfor | |
| 175 if (nx > 0) | |
| 176 printf (" Beta S.E.\n"); | |
| 177 for i = (nz + 1) : (nz + nx) | |
| 3426 | 178 printf (" %8.4f %8.4f\n", tb (i), se (i)); |
| 3191 | 179 endfor |
| 180 endif | |
| 181 endif | |
| 182 | |
| 183 if (nargout == 6) | |
| 184 if (nx > 0) | |
| 185 e = ((x * beta) * ones (1, nz)) + ((y * 0 + 1) * theta'); | |
| 186 else | |
| 187 e = (y * 0 + 1) * theta'; | |
| 188 endif | |
| 3238 | 189 gamma = diff ([(y * 0), (exp (e) ./ (1 + exp (e))), (y * 0 + 1)]')'; |
| 3191 | 190 endif |
| 3426 | 191 |
| 3191 | 192 endfunction |
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193 |