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author | Rik <rik@octave.org> |
---|---|
date | Wed, 28 Aug 2013 08:33:02 -0700 |
parents | 72c96de7a403 |
children |
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## 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 ## <http://www.gnu.org/licenses/>. ## -*- 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 <Thomas.Fuereder@ci.tuwien.ac.at> ## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> ## 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