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1 ## Copyright (C) 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This program is free software; you can redistribute it and/or modify |
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4 ## it under the terms of the GNU General Public License as published by |
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5 ## the Free Software Foundation; either version 2, or (at your option) |
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6 ## any later version. |
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7 ## |
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8 ## This program is distributed in the hope that it will be useful, but |
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9 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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10 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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11 ## General Public License for more details. |
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12 ## |
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13 ## You should have received a copy of the GNU General Public License |
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14 ## along with this file. If not, write to the Free Software Foundation, |
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15 ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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16 |
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17 ## usage: manova (Y, g) |
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18 ## |
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19 ## Performs a one-way multivariate analysis of variance (MANOVA). The |
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20 ## goal is to test whether the p-dimensional population means of data |
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21 ## taken from k different groups are all equal. All data are assumed |
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22 ## drawn independently from p-dimensional normal distributions with the |
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23 ## same covariance matrix. |
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24 ## |
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25 ## Y is the data matrix. As usual, rows are observations and columns |
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26 ## are variables. g is the vector of corresponding group labels (e.g., |
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27 ## numbers from 1 to k), so that necessarily, length (g) must be the |
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28 ## same as rows (Y). |
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29 ## |
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30 ## The LR test statistic (Wilks' Lambda) and approximate p-values are |
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31 ## computed and displayed. |
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32 |
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33 ## Three test statistics (Wilks, Hotelling-Lawley, and Pillai-Bartlett) |
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34 ## and corresponding approximate p-values are calculated and displayed. |
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35 ## (Currently NOT because the f_cdf respectively betai code is too bad.) |
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36 |
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37 ## Author: TF <Thomas.Fuereder@ci.tuwien.ac.at> |
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38 ## Adapted-By: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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39 ## Description: One-way multivariate analysis of variance (MANOVA) |
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40 |
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41 function manova (Y, g) |
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42 |
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43 if (nargin != 2) |
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44 usage ("manova (Y, g)"); |
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45 endif |
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46 |
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47 if (is_vector (Y)) |
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48 error ("manova: Y must not be a vector"); |
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49 endif |
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50 |
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51 [n, p] = size (Y); |
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52 |
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53 if (!is_vector (g) || (length (g) != n)) |
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54 error ("manova: g must be a vector of length rows (Y)"); |
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55 endif |
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56 |
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57 s = sort (g); |
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58 i = find (s (2:n) > s(1:(n-1))); |
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59 k = length (i) + 1; |
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60 |
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61 if (k == 1) |
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62 error ("manova: there should be at least 2 groups"); |
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63 else |
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64 group_label = s ([1, (reshape (i, 1, k - 1) + 1)]); |
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65 endif |
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66 |
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67 Y = Y - ones (n, 1) * mean (Y); |
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68 SST = Y' * Y; |
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69 |
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70 s = zeros (1, p); |
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71 SSB = zeros (p, p); |
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72 for i = 1 : k; |
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73 v = Y (find (g == group_label (i)), :); |
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74 s = sum (v); |
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75 SSB = SSB + s' * s / rows (v); |
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76 endfor |
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77 n_b = k - 1; |
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78 |
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79 SSW = SST - SSB; |
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80 n_w = n - k; |
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81 |
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82 l = real (eig (SSB / SSW)); |
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83 l (l < eps) = 0; |
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84 |
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85 ## Wilks' Lambda |
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86 ## ============= |
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87 |
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88 Lambda = prod (1 ./ (1 + l)); |
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89 |
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90 delta = n_w + n_b - (p + n_b + 1) / 2 |
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91 df_num = p * n_b |
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92 W_pval_1 = 1 - chisquare_cdf (- delta * log (Lambda), df_num); |
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93 |
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94 if (p < 3) |
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95 eta = p; |
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96 else |
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97 eta = sqrt ((p^2 * n_b^2 - 4) / (p^2 + n_b^2 - 5)) |
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98 endif |
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99 |
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100 df_den = delta * eta - df_num / 2 + 1 |
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101 |
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102 WT = exp (- log (Lambda) / eta) - 1 |
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103 W_pval_2 = 1 - f_cdf (WT * df_den / df_num, df_num, df_den); |
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104 |
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105 if (0) |
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106 |
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107 ## Hotelling-Lawley Test |
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108 ## ===================== |
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109 |
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110 HL = sum (l); |
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111 |
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112 theta = min (p, n_b); |
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113 u = (abs (p - n_b) - 1) / 2; |
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114 v = (n_w - p - 1) / 2; |
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115 |
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116 df_num = theta * (2 * u + theta + 1); |
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117 df_den = 2 * (theta * v + 1); |
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118 |
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119 HL_pval = 1 - f_cdf (HL * df_den / df_num, df_num, df_den); |
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120 |
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121 ## Pillai-Bartlett |
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122 ## =============== |
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123 |
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124 PB = sum (l ./ (1 + l)); |
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125 |
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126 df_den = theta * (2 * v + theta + 1); |
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127 PB_pval = 1 - f_cdf (PB * df_den / df_num, df_num, df_den); |
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128 |
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129 printf ("\n"); |
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130 printf ("One-way MANOVA Table:\n"); |
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131 printf ("\n"); |
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132 printf ("Test Test Statistic Approximate p\n"); |
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133 printf ("**************************************************\n"); |
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134 printf ("Wilks %10.4f %10.9f \n", Lambda, W_pval_1); |
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135 printf (" %10.9f \n", W_pval_2); |
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136 printf ("Hotelling-Lawley %10.4f %10.9f \n", HL, HL_pval); |
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137 printf ("Pillai-Bartlett %10.4f %10.9f \n", PB, PB_pval); |
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138 printf ("\n"); |
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139 |
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140 endif |
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141 |
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142 printf ("\n"); |
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143 printf ("MANOVA Results:\n"); |
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144 printf ("\n"); |
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145 printf ("# of groups: %d\n", k); |
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146 printf ("# of samples: %d\n", n); |
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147 printf ("# of variables: %d\n", p); |
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148 printf ("\n"); |
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149 printf ("Wilks' Lambda: %5.4f\n", Lambda); |
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150 printf ("Approximate p: %10.9f (chisquare approximation)\n", W_pval_1); |
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151 printf (" %10.9f (F approximation)\n", W_pval_2); |
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152 printf ("\n"); |
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153 |
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154 endfunction |
