X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?a=blobdiff_plain;ds=sidebyside;f=octave_packages%2Fm%2Fstatistics%2Ftests%2Fmanova.m;fp=octave_packages%2Fm%2Fstatistics%2Ftests%2Fmanova.m;h=01f75515cb07beffee33f35097657ee26a5c13d5;hb=1c0469ada9531828709108a4882a751d2816994a;hp=0000000000000000000000000000000000000000;hpb=63de9f36673d49121015e3695f2c336ea92bc278;p=CreaPhase.git diff --git a/octave_packages/m/statistics/tests/manova.m b/octave_packages/m/statistics/tests/manova.m new file mode 100644 index 0000000..01f7551 --- /dev/null +++ b/octave_packages/m/statistics/tests/manova.m @@ -0,0 +1,161 @@ +## Copyright (C) 1996-2012 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 +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {} manova (@var{x}, @var{g}) +## Perform a one-way multivariate analysis of variance (MANOVA). The +## goal is to test whether the p-dimensional population means of data +## taken from @var{k} different groups are all equal. All data are +## assumed drawn independently from p-dimensional normal distributions +## with the same covariance matrix. +## +## The data matrix is given by @var{x}. As usual, rows are observations +## and columns are variables. The vector @var{g} specifies the +## corresponding group labels (e.g., numbers from 1 to @var{k}). +## +## The LR test statistic (Wilks' Lambda) and approximate p-values are +## computed and displayed. +## @end deftypefn + +## Three test statistics (Wilks, Hotelling-Lawley, and Pillai-Bartlett) +## and corresponding approximate p-values are calculated and displayed. +## (Currently NOT because the fcdf respectively betai code is too bad.) + +## Author: TF +## Adapted-By: KH +## Description: One-way multivariate analysis of variance (MANOVA) + +function manova (x, g) + + if (nargin != 2) + print_usage (); + endif + + if (isvector (x)) + error ("manova: Y must not be a vector"); + endif + + [n, p] = size (x); + + if (!isvector (g) || (length (g) != n)) + error ("manova: G must be a vector of length rows (Y)"); + endif + + s = sort (g); + i = find (s (2:n) > s(1:(n-1))); + k = length (i) + 1; + + if (k == 1) + error ("manova: there should be at least 2 groups"); + else + group_label = s ([1, (reshape (i, 1, k - 1) + 1)]); + endif + + x = x - ones (n, 1) * mean (x); + SST = x' * x; + + s = zeros (1, p); + SSB = zeros (p, p); + for i = 1 : k; + v = x (find (g == group_label (i)), :); + s = sum (v); + SSB = SSB + s' * s / rows (v); + endfor + n_b = k - 1; + + SSW = SST - SSB; + n_w = n - k; + + l = real (eig (SSB / SSW)); + + if (isa (l, "single")) + l (l < eps ("single")) = 0; + else + l (l < eps) = 0; + endif + + ## Wilks' Lambda + ## ============= + + Lambda = prod (1 ./ (1 + l)); + + delta = n_w + n_b - (p + n_b + 1) / 2; + df_num = p * n_b; + W_pval_1 = 1 - chi2cdf (- delta * log (Lambda), df_num); + + if (p < 3) + eta = p; + else + eta = sqrt ((p^2 * n_b^2 - 4) / (p^2 + n_b^2 - 5)); + endif + + df_den = delta * eta - df_num / 2 + 1; + + WT = exp (- log (Lambda) / eta) - 1; + W_pval_2 = 1 - fcdf (WT * df_den / df_num, df_num, df_den); + + if (0) + + ## Hotelling-Lawley Test + ## ===================== + + HL = sum (l); + + theta = min (p, n_b); + u = (abs (p - n_b) - 1) / 2; + v = (n_w - p - 1) / 2; + + df_num = theta * (2 * u + theta + 1); + df_den = 2 * (theta * v + 1); + + HL_pval = 1 - fcdf (HL * df_den / df_num, df_num, df_den); + + ## Pillai-Bartlett + ## =============== + + PB = sum (l ./ (1 + l)); + + df_den = theta * (2 * v + theta + 1); + PB_pval = 1 - fcdf (PB * df_den / df_num, df_num, df_den); + + printf ("\n"); + printf ("One-way MANOVA Table:\n"); + printf ("\n"); + printf ("Test Test Statistic Approximate p\n"); + printf ("**************************************************\n"); + printf ("Wilks %10.4f %10.9f \n", Lambda, W_pval_1); + printf (" %10.9f \n", W_pval_2); + printf ("Hotelling-Lawley %10.4f %10.9f \n", HL, HL_pval); + printf ("Pillai-Bartlett %10.4f %10.9f \n", PB, PB_pval); + printf ("\n"); + + endif + + printf ("\n"); + printf ("MANOVA Results:\n"); + printf ("\n"); + printf ("# of groups: %d\n", k); + printf ("# of samples: %d\n", n); + printf ("# of variables: %d\n", p); + printf ("\n"); + printf ("Wilks' Lambda: %5.4f\n", Lambda); + printf ("Approximate p: %10.9f (chisquare approximation)\n", W_pval_1); + printf (" %10.9f (F approximation)\n", W_pval_2); + printf ("\n"); + +endfunction