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1 ## Copyright (C) 1996, 1997 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 {Function File} {} manova (@var{y}, @var{g}) |
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21 ## Perform a one-way multivariate analysis of variance (MANOVA). The |
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22 ## goal is to test whether the p-dimensional population means of data |
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23 ## taken from @var{k} different groups are all equal. All data are |
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24 ## assumed drawn independently from p-dimensional normal distributions |
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25 ## with the same covariance matrix. |
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26 ## |
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27 ## The data matrix is given by @var{y}. As usual, rows are observations |
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28 ## and columns are variables. The vector @var{g} specifies the |
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29 ## corresponding group labels (e.g., numbers from 1 to @var{k}). |
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30 ## |
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31 ## The LR test statistic (Wilks' Lambda) and approximate p-values are |
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32 ## computed and displayed. |
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33 ## @end deftypefn |
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34 |
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35 ## Three test statistics (Wilks, Hotelling-Lawley, and Pillai-Bartlett) |
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36 ## and corresponding approximate p-values are calculated and displayed. |
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37 ## (Currently NOT because the f_cdf respectively betai code is too bad.) |
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38 |
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39 ## Author: TF <Thomas.Fuereder@ci.tuwien.ac.at> |
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40 ## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at> |
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41 ## Description: One-way multivariate analysis of variance (MANOVA) |
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42 |
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43 function manova (Y, g) |
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44 |
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45 if (nargin != 2) |
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46 print_usage (); |
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47 endif |
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48 |
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49 if (isvector (Y)) |
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50 error ("manova: Y must not be a vector"); |
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51 endif |
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52 |
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53 [n, p] = size (Y); |
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54 |
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55 if (!isvector (g) || (length (g) != n)) |
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56 error ("manova: g must be a vector of length rows (Y)"); |
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57 endif |
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58 |
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59 s = sort (g); |
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60 i = find (s (2:n) > s(1:(n-1))); |
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61 k = length (i) + 1; |
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62 |
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63 if (k == 1) |
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64 error ("manova: there should be at least 2 groups"); |
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65 else |
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66 group_label = s ([1, (reshape (i, 1, k - 1) + 1)]); |
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67 endif |
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68 |
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69 Y = Y - ones (n, 1) * mean (Y); |
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70 SST = Y' * Y; |
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71 |
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72 s = zeros (1, p); |
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73 SSB = zeros (p, p); |
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74 for i = 1 : k; |
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75 v = Y (find (g == group_label (i)), :); |
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76 s = sum (v); |
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77 SSB = SSB + s' * s / rows (v); |
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78 endfor |
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79 n_b = k - 1; |
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80 |
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81 SSW = SST - SSB; |
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82 n_w = n - k; |
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83 |
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84 l = real (eig (SSB / SSW)); |
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85 l (l < eps) = 0; |
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86 |
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87 ## Wilks' Lambda |
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88 ## ============= |
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89 |
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90 Lambda = prod (1 ./ (1 + l)); |
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91 |
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92 delta = n_w + n_b - (p + n_b + 1) / 2 |
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93 df_num = p * n_b |
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94 W_pval_1 = 1 - chisquare_cdf (- delta * log (Lambda), df_num); |
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95 |
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96 if (p < 3) |
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97 eta = p; |
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98 else |
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99 eta = sqrt ((p^2 * n_b^2 - 4) / (p^2 + n_b^2 - 5)) |
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100 endif |
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101 |
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102 df_den = delta * eta - df_num / 2 + 1 |
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103 |
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104 WT = exp (- log (Lambda) / eta) - 1 |
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105 W_pval_2 = 1 - f_cdf (WT * df_den / df_num, df_num, df_den); |
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106 |
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107 if (0) |
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108 |
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109 ## Hotelling-Lawley Test |
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110 ## ===================== |
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111 |
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112 HL = sum (l); |
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113 |
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114 theta = min (p, n_b); |
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115 u = (abs (p - n_b) - 1) / 2; |
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116 v = (n_w - p - 1) / 2; |
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117 |
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118 df_num = theta * (2 * u + theta + 1); |
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119 df_den = 2 * (theta * v + 1); |
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120 |
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121 HL_pval = 1 - f_cdf (HL * df_den / df_num, df_num, df_den); |
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122 |
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123 ## Pillai-Bartlett |
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124 ## =============== |
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125 |
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126 PB = sum (l ./ (1 + l)); |
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127 |
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128 df_den = theta * (2 * v + theta + 1); |
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129 PB_pval = 1 - f_cdf (PB * df_den / df_num, df_num, df_den); |
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130 |
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131 printf ("\n"); |
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132 printf ("One-way MANOVA Table:\n"); |
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133 printf ("\n"); |
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134 printf ("Test Test Statistic Approximate p\n"); |
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135 printf ("**************************************************\n"); |
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136 printf ("Wilks %10.4f %10.9f \n", Lambda, W_pval_1); |
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137 printf (" %10.9f \n", W_pval_2); |
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138 printf ("Hotelling-Lawley %10.4f %10.9f \n", HL, HL_pval); |
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139 printf ("Pillai-Bartlett %10.4f %10.9f \n", PB, PB_pval); |
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140 printf ("\n"); |
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141 |
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142 endif |
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143 |
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144 printf ("\n"); |
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145 printf ("MANOVA Results:\n"); |
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146 printf ("\n"); |
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147 printf ("# of groups: %d\n", k); |
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148 printf ("# of samples: %d\n", n); |
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149 printf ("# of variables: %d\n", p); |
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150 printf ("\n"); |
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151 printf ("Wilks' Lambda: %5.4f\n", Lambda); |
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152 printf ("Approximate p: %10.9f (chisquare approximation)\n", W_pval_1); |
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153 printf (" %10.9f (F approximation)\n", W_pval_2); |
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154 printf ("\n"); |
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155 |
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156 endfunction |
