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Backed out changeset dcf8922b724b
author Mike Miller <mtmiller@octave.org>
date Wed, 20 Apr 2016 11:06:03 -0700
parents dcf8922b724b
children bac0d6f07a3e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 1996-2015 Kurt Hornik
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {} manova (@var{x}, @var{g})
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21 ## Perform a one-way multivariate analysis of variance (MANOVA).
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22 ##
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23 ## The goal is to test whether the p-dimensional population means of data
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24 ## taken from @var{k} different groups are all equal. All data are assumed
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25 ## drawn independently from p-dimensional normal distributions with the same
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26 ## covariance matrix.
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27 ##
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28 ## The data matrix is given by @var{x}. As usual, rows are observations and
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29 ## columns are variables. The vector @var{g} specifies the corresponding
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30 ## group labels (e.g., numbers from 1 to @var{k}).
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31 ##
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32 ## The LR test statistic (@nospell{Wilks' Lambda}) and approximate p-values are
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33 ## computed and displayed.
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34 ## @seealso{anova}
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35 ## @end deftypefn
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36
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37 ## The Hotelling-Lawley and Pillai-Bartlett test statistics are coded.
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38 ## However, they are currently disabled until they can be verified by someone
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39 ## with sufficient understanding of the algorithms. Please feel free to
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40 ## improve this.
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41
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42 ## Author: TF <Thomas.Fuereder@ci.tuwien.ac.at>
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43 ## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at>
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44 ## Description: One-way multivariate analysis of variance (MANOVA)
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45
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46 function manova (x, g)
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47
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48 if (nargin != 2)
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49 print_usage ();
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50 endif
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51
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52 if (isvector (x))
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53 error ("manova: X must not be a vector");
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54 endif
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55
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56 [n, p] = size (x);
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57
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58 if (! isvector (g) || (length (g) != n))
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59 error ("manova: G must be a vector of length rows (X)");
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60 endif
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61
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62 s = sort (g);
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63 i = find (s (2:n) > s(1:(n-1)));
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64 k = length (i) + 1;
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65
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66 if (k == 1)
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67 error ("manova: there should be at least 2 groups");
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68 else
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69 group_label = s ([1, (reshape (i, 1, k - 1) + 1)]);
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70 endif
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71
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72 x -= ones (n, 1) * mean (x);
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73 SST = x' * x;
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75 s = zeros (1, p);
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76 SSB = zeros (p, p);
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77 for i = 1 : k;
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78 v = x (find (g == group_label (i)), :);
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79 s = sum (v);
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80 SSB += s' * s / rows (v);
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81 endfor
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82 n_b = k - 1;
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83
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84 SSW = SST - SSB;
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85 n_w = n - k;
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86
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87 l = real (eig (SSB / SSW));
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88
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89 if (isa (l, "single"))
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90 l(l < eps ("single")) = 0;
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91 else
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92 l(l < eps) = 0;
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93 endif
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94
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95 ## Wilks' Lambda
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96 ## =============
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97
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98 Lambda = prod (1 ./ (1 + l));
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99
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100 delta = n_w + n_b - (p + n_b + 1) / 2;
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101 df_num = p * n_b;
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102 W_pval_1 = 1 - chi2cdf (- delta * log (Lambda), df_num);
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103
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104 if (p < 3)
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105 eta = p;
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106 else
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107 eta = sqrt ((p^2 * n_b^2 - 4) / (p^2 + n_b^2 - 5));
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108 endif
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109
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110 df_den = delta * eta - df_num / 2 + 1;
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111
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112 WT = exp (- log (Lambda) / eta) - 1;
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113 W_pval_2 = 1 - fcdf (WT * df_den / df_num, df_num, df_den);
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114
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115 if (0)
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116
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117 ## Hotelling-Lawley Test
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118 ## =====================
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119
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120 HL = sum (l);
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121
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122 theta = min (p, n_b);
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123 u = (abs (p - n_b) - 1) / 2;
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124 v = (n_w - p - 1) / 2;
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125
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126 df_num = theta * (2 * u + theta + 1);
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127 df_den = 2 * (theta * v + 1);
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128
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129 HL_pval = 1 - fcdf (HL * df_den / df_num, df_num, df_den);
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130
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131 ## Pillai-Bartlett
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132 ## ===============
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133
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134 PB = sum (l ./ (1 + l));
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135
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136 df_den = theta * (2 * v + theta + 1);
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137 PB_pval = 1 - fcdf (PB * df_den / df_num, df_num, df_den);
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138
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139 printf ("\n");
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140 printf ("One-way MANOVA Table:\n");
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141 printf ("\n");
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142 printf ("Test Test Statistic Approximate p\n");
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143 printf ("**************************************************\n");
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144 printf ("Wilks %10.4f %10.9f \n", Lambda, W_pval_1);
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Mike Miller <mtmiller@octave.org>
parents: 21633
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145 printf (" %10.9f \n", W_pval_2);
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Mike Miller <mtmiller@octave.org>
parents: 21633
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146 printf ("Hotelling-Lawley %10.4f %10.9f \n", HL, HL_pval);
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Mike Miller <mtmiller@octave.org>
parents: 21633
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147 printf ("Pillai-Bartlett %10.4f %10.9f \n", PB, PB_pval);
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Mike Miller <mtmiller@octave.org>
parents: 21633
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148 printf ("\n");
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781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
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149
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
parents:
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150 endif
781c930425fd [project @ 1998-10-29 05:23:08 by jwe]
jwe
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151
21634
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Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
152 printf ("\n");
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Mike Miller <mtmiller@octave.org>
parents: 21633
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153 printf ("MANOVA Results:\n");
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Mike Miller <mtmiller@octave.org>
parents: 21633
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154 printf ("\n");
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Mike Miller <mtmiller@octave.org>
parents: 21633
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155 printf ("# of groups: %d\n", k);
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Mike Miller <mtmiller@octave.org>
parents: 21633
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156 printf ("# of samples: %d\n", n);
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Mike Miller <mtmiller@octave.org>
parents: 21633
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157 printf ("# of variables: %d\n", p);
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Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
158 printf ("\n");
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Mike Miller <mtmiller@octave.org>
parents: 21633
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159 printf ("Wilks' Lambda: %5.4f\n", Lambda);
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Mike Miller <mtmiller@octave.org>
parents: 21633
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160 printf ("Approximate p: %10.9f (chisquare approximation)\n", W_pval_1);
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Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
161 printf (" %10.9f (F approximation)\n", W_pval_2);
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Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
162 printf ("\n");
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jwe
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163
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164 endfunction
17338
1c89599167a6 maint: End m-files with 1 blank line.
Rik <rik@octave.org>
parents: 14138
diff changeset
165