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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 2, or (at your option) |
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8 ## 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, write to the Free |
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA |
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18 ## 02111-1307, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} manova (@var{y}, @var{g}) |
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22 ## Perform a one-way multivariate analysis of variance (MANOVA). The |
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23 ## 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 |
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25 ## assumed drawn independently from p-dimensional normal distributions |
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26 ## with the same covariance matrix. |
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27 ## |
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28 ## The data matrix is given by @var{y}. As usual, rows are observations |
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29 ## and columns are variables. The vector @var{g} specifies the |
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30 ## corresponding group labels (e.g., numbers from 1 to @var{k}). |
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31 ## |
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32 ## The LR test statistic (Wilks' Lambda) and approximate p-values are |
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33 ## computed and displayed. |
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34 ## @end deftypefn |
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35 |
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36 ## Three test statistics (Wilks, Hotelling-Lawley, and Pillai-Bartlett) |
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37 ## and corresponding approximate p-values are calculated and displayed. |
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38 ## (Currently NOT because the f_cdf respectively betai code is too bad.) |
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39 |
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40 ## Author: TF <Thomas.Fuereder@ci.tuwien.ac.at> |
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41 ## Adapted-By: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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42 ## Description: One-way multivariate analysis of variance (MANOVA) |
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43 |
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44 function manova (Y, g) |
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45 |
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46 if (nargin != 2) |
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47 usage ("manova (Y, g)"); |
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48 endif |
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49 |
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50 if (is_vector (Y)) |
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51 error ("manova: Y must not be a vector"); |
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52 endif |
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53 |
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54 [n, p] = size (Y); |
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55 |
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56 if (!is_vector (g) || (length (g) != n)) |
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57 error ("manova: g must be a vector of length rows (Y)"); |
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58 endif |
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59 |
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60 s = sort (g); |
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61 i = find (s (2:n) > s(1:(n-1))); |
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62 k = length (i) + 1; |
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63 |
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64 if (k == 1) |
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65 error ("manova: there should be at least 2 groups"); |
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66 else |
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67 group_label = s ([1, (reshape (i, 1, k - 1) + 1)]); |
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68 endif |
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69 |
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70 Y = Y - ones (n, 1) * mean (Y); |
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71 SST = Y' * Y; |
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72 |
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73 s = zeros (1, p); |
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74 SSB = zeros (p, p); |
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75 for i = 1 : k; |
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76 v = Y (find (g == group_label (i)), :); |
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77 s = sum (v); |
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78 SSB = SSB + s' * s / rows (v); |
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79 endfor |
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80 n_b = k - 1; |
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81 |
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82 SSW = SST - SSB; |
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83 n_w = n - k; |
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84 |
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85 l = real (eig (SSB / SSW)); |
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86 l (l < eps) = 0; |
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87 |
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88 ## Wilks' Lambda |
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89 ## ============= |
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90 |
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91 Lambda = prod (1 ./ (1 + l)); |
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92 |
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93 delta = n_w + n_b - (p + n_b + 1) / 2 |
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94 df_num = p * n_b |
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95 W_pval_1 = 1 - chisquare_cdf (- delta * log (Lambda), df_num); |
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96 |
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97 if (p < 3) |
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98 eta = p; |
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99 else |
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100 eta = sqrt ((p^2 * n_b^2 - 4) / (p^2 + n_b^2 - 5)) |
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101 endif |
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102 |
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103 df_den = delta * eta - df_num / 2 + 1 |
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104 |
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105 WT = exp (- log (Lambda) / eta) - 1 |
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106 W_pval_2 = 1 - f_cdf (WT * df_den / df_num, df_num, df_den); |
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107 |
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108 if (0) |
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109 |
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110 ## Hotelling-Lawley Test |
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111 ## ===================== |
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112 |
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113 HL = sum (l); |
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114 |
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115 theta = min (p, n_b); |
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116 u = (abs (p - n_b) - 1) / 2; |
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117 v = (n_w - p - 1) / 2; |
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118 |
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119 df_num = theta * (2 * u + theta + 1); |
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120 df_den = 2 * (theta * v + 1); |
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121 |
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122 HL_pval = 1 - f_cdf (HL * df_den / df_num, df_num, df_den); |
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123 |
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124 ## Pillai-Bartlett |
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125 ## =============== |
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126 |
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127 PB = sum (l ./ (1 + l)); |
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128 |
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129 df_den = theta * (2 * v + theta + 1); |
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130 PB_pval = 1 - f_cdf (PB * df_den / df_num, df_num, df_den); |
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131 |
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132 printf ("\n"); |
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133 printf ("One-way MANOVA Table:\n"); |
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134 printf ("\n"); |
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135 printf ("Test Test Statistic Approximate p\n"); |
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136 printf ("**************************************************\n"); |
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137 printf ("Wilks %10.4f %10.9f \n", Lambda, W_pval_1); |
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138 printf (" %10.9f \n", W_pval_2); |
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139 printf ("Hotelling-Lawley %10.4f %10.9f \n", HL, HL_pval); |
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140 printf ("Pillai-Bartlett %10.4f %10.9f \n", PB, PB_pval); |
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141 printf ("\n"); |
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142 |
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143 endif |
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144 |
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145 printf ("\n"); |
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146 printf ("MANOVA Results:\n"); |
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147 printf ("\n"); |
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148 printf ("# of groups: %d\n", k); |
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149 printf ("# of samples: %d\n", n); |
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150 printf ("# of variables: %d\n", p); |
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151 printf ("\n"); |
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152 printf ("Wilks' Lambda: %5.4f\n", Lambda); |
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153 printf ("Approximate p: %10.9f (chisquare approximation)\n", W_pval_1); |
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154 printf (" %10.9f (F approximation)\n", W_pval_2); |
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155 printf ("\n"); |
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156 |
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157 endfunction |
