Compare Covariance Matrices using Flury's Hierarchy of Tests (V0.95) Analysis of file: vole.dat *** Test for Equality Among the Matrices *** Criterion for Equality: 3981.70147 Number of parameters (Equality): 6 Likelihood ratio test chi-square for H0-equality versus: Proportionality: 0.690 (df = 3, p = 0.8756) Common PC : 38.398 (df = 9, p = 0.0000) CPC(1) : 46.846 (df = 12, p = 0.0000) Unrelated : 53.868 (df = 18, p = 0.0000) Eigenvalues of Best Pooled Covariance Matrix: Vector 1 Vector 2 Vector 3 3.59558 6.2515 197.88541 Eigenvectors for Best Pooled Covariance Matrix: Vector 1 Vector 2 Vector 3 Length 0.557 0.4873 -0.67253 Width -0.74743 -0.05891 -0.66172 Height 0.36207 -0.87125 -0.33141 Best Pooled Covariance Matrix: Length Width Height Length 92.10173 86.38764 42.1761 Width 86.38764 88.67975 42.74439 Height 42.1761 42.74439 26.95101 *** Test for Proportionality Among the Matrices *** Criterion for Proportionality: 3981.01153 Number of parameters (Proportionality): 9 Likelihood ratio test chi-square for H0-proportionality versus: Common PC : 37.708 (df = 6, p = 0.0000) CPC(1) : 46.156 (df = 9, p = 0.0000) Unrelated : 53.178 (df = 15, p = 0.0000) Eigenvalues for Proportional Matrix: Vector 1 Vector 2 Vector 3 3.72342 6.45073 203.10815 Eigenvectors for Proportional Matrix: Vector 1 Vector 2 Vector 3 Length 0.55994 0.48381 -0.67261 Width -0.74762 -0.05486 -0.66185 Height 0.35711 -0.87345 -0.33099 Proportionality constant for CalMales: 1.000000 Maximum likelihood estimate of CalMales (proportionality): Length Width Height Length 94.56304 88.68695 43.23516 Width 88.68695 91.07212 43.80881 Height 43.23516 43.80881 27.64713 Proportionality constant for CalFemales: 0.950894 Maximum likelihood estimate of CalFemales (proportionality): Length Width Height Length 89.91944 84.3319 41.11206 Width 84.3319 86.59994 41.65754 Height 41.11206 41.65754 26.28949 Proportionality constant for OchMales: 0.921994 Maximum likelihood estimate of OchMales (proportionality): Length Width Height Length 87.18656 81.76883 39.86255 Width 81.76883 83.96795 40.39146 Height 39.86255 40.39146 25.49049 Proportionality constant for OchFemales: 0.990611 Maximum likelihood estimate of OchFemales (proportionality): Length Width Height Length 93.67523 87.8543 42.82924 Width 87.8543 90.21708 43.39751 Height 42.82924 43.39751 27.38756 *** Test for Common Principal Components Among the Matrices *** Criterion for CPC: 3943.30386 Number of parameters (CPC): 15 Likelihood ratio test chi-square for H0-CPC versus: CPC(1) : 8.449 (df = 3, p = 0.0376) Unrelated : 15.471 (df = 9, p = 0.0788) Eigenvalues for CPC Matrices: CalMales: Vector 1 Vector 2 Vector 3 244.26251 7.21405 2.52344 CalFemales: Vector 1 Vector 2 Vector 3 188.3879 6.46483 3.42727 OchMales: Vector 1 Vector 2 Vector 3 133.56387 6.00904 4.42709 OchFemales: Vector 1 Vector 2 Vector 3 183.86713 3.90762 5.42525 Eigenvectors for CPC Matrix: Vector 1 Vector 2 Vector 3 Length 0.67313 -0.50601 -0.5393 Width 0.66163 0.08629 0.74485 Height 0.33037 0.8582 -0.39288 Maximum likelihood estimate of CalMales (CPC): Length Width Height Length 113.25669 107.45663 51.72109 Width 107.45663 108.38095 53.1872 Height 51.72109 53.1872 32.36235 Maximum likelihood estimate of CalFemales (CPC): Length Width Height Length 88.01089 82.24184 39.81253 Width 82.24184 84.4174 40.65404 Height 39.81253 40.65404 25.8517 Maximum likelihood estimate of OchMales (CPC): Length Width Height Length 63.34416 57.44356 28.03051 Width 57.44356 60.96919 28.34415 Height 28.03051 28.34415 19.68665 Maximum likelihood estimate of OchFemales (CPC): Length Width Height Length 85.88886 79.53752 40.34103 Width 79.53752 83.52785 38.89183 Height 40.34103 38.89183 23.78329 *** Test for Common Principal Components Among Matrices *** *** Test for 1-Common Principal Component *** Criterion for CPC(1): 3934.85525 Number of parameters [CPC(1)]: 18 Likelihood ratio test chi-square for H0-CPC(1) versus: Unrelated : 7.022 (df = 6, p = 0.3188) Eigenvalues for CPC(1) Matrices: CalMales: Vector 1 Vector 2 Vector 3 244.26267 7.21672 2.52061 CalFemales: Vector 1 Vector 2 Vector 3 188.37654 6.49032 3.41313 OchMales: Vector 1 Vector 2 Vector 3 133.5409 6.92141 3.5377 OchFemales: Vector 1 Vector 2 Vector 3 183.89023 3.81945 5.49032 Eigenvectors of CalMales [CPC(1)]: Vector 1 Vector 2 Vector 3 Length 0.67553 -0.51866 -0.52407 Width 0.65829 0.10409 0.74553 Height 0.33212 0.84862 -0.41175 Eigenvectors of CalFemales [CPC(1)]: Vector 1 Vector 2 Vector 3 Length 0.67553 -0.55273 -0.488 Width 0.65829 0.15399 0.73684 Height 0.33212 0.81901 -0.46789 Eigenvectors of OchMales [CPC(1)]: Vector 1 Vector 2 Vector 3 Length 0.67553 -0.15397 -0.72107 Width 0.65829 -0.31456 0.68389 Height 0.33212 0.93667 0.11114 Eigenvectors of OchFemales [CPC(1)]: Vector 1 Vector 2 Vector 3 Length 0.67553 -0.36929 -0.63818 Width 0.65829 -0.0878 0.74762 Height 0.33212 0.92516 -0.18379 Maximum likelihood estimate of CalMales [CPC(1)]: Length Width Height Length 114.1016 107.24884 52.1702 Width 107.24884 107.3304 53.26786 Height 52.1702 53.26786 32.56799 Maximum likelihood estimate of CalFemales [CPC(1)]: Length Width Height Length 88.76031 81.99107 40.10532 Width 81.99107 83.63999 40.82739 Height 40.10532 40.82739 25.8797 Maximum likelihood estimate of OchMales [CPC(1)]: Length Width Height Length 62.94419 57.97615 28.67947 Width 57.97615 60.20939 27.42614 Height 28.67947 27.42614 20.84642 Maximum likelihood estimate of OchFemales [CPC(1)]: Length Width Height Length 86.67431 79.28004 40.5966 Width 79.28004 82.78703 39.14 Height 40.5966 39.14 23.73866 *** Principal Component Analysis of Each Matrix Separately *** Eigenstructure of CalMales: Eigenvalues: Vector 1 Vector 2 Vector 3 2.51972 7.19001 244.29028 Eigenvectors: Vector 1 Vector 2 Vector 3 Length 0.52591 0.52525 -0.66898 Width -0.74437 -0.09632 -0.66079 Height 0.41151 -0.84548 -0.34032 Eigenstructure of CalFemales: Eigenvalues: Vector 1 Vector 2 Vector 3 3.40115 6.46183 188.41702 Eigenvectors: Vector 1 Vector 2 Vector 3 Length 0.49674 0.55815 -0.66462 Width -0.7324 -0.14129 -0.66605 Height 0.46566 -0.81762 -0.33861 Eigenstructure of OchMales: Eigenvalues: Vector 1 Vector 2 Vector 3 3.52907 6.521 133.94992 Eigenvectors: Vector 1 Vector 2 Vector 3 Length 0.71788 0.10242 -0.68859 Width -0.68371 0.28995 -0.66968 Height -0.13107 -0.95155 -0.27817 Eigenstructure of OchFemales: Eigenvalues: Vector 1 Vector 2 Vector 3 5.46167 3.81944 183.9189 Eigenvectors: Vector 1 Vector 2 Vector 3 Length 0.62937 0.36937 -0.68371 Width -0.75595 0.08711 -0.6488 Height 0.18009 -0.92519 -0.33405 *** Flury Decomposition of Chi Square *** (Step-up & model building approaches) _______Model______ Higher Lower Chi Sqr df p-val CS/df AIC -------------------------------------------------------- Equality Proport 0.690 3 0.8756 0.230 53.868 Proport CPC 37.708 6 0.0000 6.285 59.178 CPC CPC(1) 8.449 3 0.0376 2.816 33.471 CPC(1) Unrelated 7.022 6 0.3188 1.170 31.022 Unrelated --- 36.000 *** Test against Unrelated/Arbitrary Structure *** (Jump-up approach) _______Model______ Higher Lower Chi Sqr df p-val ----------------------------------------- Equality Unrelated 53.868 18 0.0000 Proport Unrelated 53.178 15 0.0000 CPC Unrelated 15.471 9 0.0788 CPC(1) Unrelated 7.022 6 0.3188