1**************************************** CLUSTER ANALYSIS OF CASES USING COMMON COVARIANCE MATRIX CMS FILE: MIXPCM ISOPAC DEVELOPED AND PROGRAMMED BY DR. STANLEY L. SCLOVE MIXPCM ISOPAC VERSION 7.4 07-DEC-89 COPYRIGHT (C) 1989 STANLEY L. SCLOVE. ALL RIGHTS RESERVED. ******************************************************************************** FISHER IRIS DATA NUMBER OF OBSERVATIONS (SAMPLE SIZE), N = 150 NUMBER OF VARIABLES = 4 MINIMUM FOR EACH VARIABLE: 4.3 2.0 1.0 0.1 MAXIMUM FOR EACH VARIABLE: 7.9 4.4 6.9 2.5 1 K = 3 CLUSTERS FIRST ITERATION USES THE INITIAL PARAMETER ESTIMATES PROVIDED BY THE USER. ITERATION 1 MEANS 5.1 3.5 1.4 0.2 6.4 2.9 4.3 1.3 5.9 3.0 5.1 1.8 CURRENT ESTIMATES OF PRIOR PROBABILITIES: MIXING PROBABILITIES: 0.27 0.46 0.27 COMMON COVARIANCE MATRIX (MLE): 1.00000 0.40000 0.40000 0.40000 0.40000 1.00000 0.40000 0.40000 0.40000 0.40000 1.00000 0.40000 0.40000 0.40000 0.40000 1.00000 INVERSE COVARIANCE MATRIX: 1.36364 -0.30303 -0.30303 -0.30303 -0.30303 1.36364 -0.30303 -0.30303 -0.30303 -0.30303 1.36364 -0.30303 -0.30303 -0.30303 -0.30303 1.36364 MINUS 2 LOG LIKELIHOOD = 1361.68311 NUMBER OF PARAMETERS = 24 AIC = 1409.68311 SCHWARZ CRITERION = 1481.93823 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.99 0.01 0.00 1.00 0.00 0.00 0.99 0.01 0.00 ITERATION 2 MEANS 5.0 3.4 1.5 0.2 6.2 2.9 4.7 1.6 6.3 2.9 5.1 1.8 CURRENT ESTIMATES OF PRIOR PROBABILITIES: MIXING PROBABILITIES: 0.33 0.39 0.28 COMMON COVARIANCE MATRIX (MLE): 0.11323 0.03788 0.10584 0.03958 0.03788 0.04089 0.03124 0.01785 0.10584 0.03124 0.16007 0.06615 0.03958 0.01785 0.06615 0.04121 INVERSE COVARIANCE MATRIX: 31.84252 -18.03351 -24.13992 15.98085 -18.03351 40.48194 12.21522 -19.82097 -24.13992 12.21522 36.93493 -41.39940 15.98085 -19.82097 -41.39940 83.96328 MINUS 2 LOG LIKELIHOOD = 1036.89160 NUMBER OF PARAMETERS = 24 AIC = 1084.89160 SCHWARZ CRITERION = 1157.14673 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 ITERATION 3 MEANS 5.0 3.4 1.5 0.2 6.1 2.8 4.5 1.4 6.4 3.0 5.4 2.0 CURRENT ESTIMATES OF PRIOR PROBABILITIES: MIXING PROBABILITIES: 0.33 0.36 0.30 COMMON COVARIANCE MATRIX (MLE): 0.10526 0.03504 0.08682 0.02941 0.03504 0.03838 0.02411 0.01337 0.08682 0.02411 0.10958 0.03849 0.02941 0.01337 0.03849 0.02542 INVERSE COVARIANCE MATRIX: 36.06670 -19.02748 -28.29891 11.13004 -19.02748 42.24194 12.50089 -19.13434 -28.29891 12.50089 41.88191 -37.25082 11.13004 -19.13434 -37.25082 92.93090 MINUS 2 LOG LIKELIHOOD = 988.39648 NUMBER OF PARAMETERS = 24 AIC = 1036.39648 SCHWARZ CRITERION = 1108.65161 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 ITERATION 4 MEANS 5.0 3.4 1.5 0.2 6.0 2.8 4.3 1.3 6.5 3.0 5.5 2.0 CURRENT ESTIMATES OF PRIOR PROBABILITIES: MIXING PROBABILITIES: 0.33 0.34 0.33 COMMON COVARIANCE MATRIX (MLE): 0.09336 0.03022 0.06424 0.01664 0.03022 0.03667 0.01607 0.00910 0.06424 0.01607 0.07037 0.01684 0.01664 0.00910 0.01684 0.01379 INVERSE COVARIANCE MATRIX: 36.74386 -18.10964 -30.60616 5.00090 -18.10964 42.07476 11.78670 -20.31858 -30.60616 11.78670 45.90397 -26.92245 5.00090 -20.31858 -26.92245 112.80749 MINUS 2 LOG LIKELIHOOD = 1042.17090 NUMBER OF PARAMETERS = 24 AIC = 1090.17090 SCHWARZ CRITERION = 1162.42603 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 ITERATION 5 MEANS 5.0 3.4 1.5 0.2 6.0 2.8 4.3 1.3 6.6 3.0 5.5 2.0 CURRENT ESTIMATES OF PRIOR PROBABILITIES: MIXING PROBABILITIES: 0.33 0.33 0.33 COMMON COVARIANCE MATRIX (MLE): 0.08929 0.02973 0.05834 0.01357 0.02973 0.03698 0.01625 0.00935 0.05834 0.01625 0.06396 0.01388 0.01357 0.00935 0.01388 0.01255 INVERSE COVARIANCE MATRIX: 34.52202 -16.91121 -28.71432 7.02584 -16.91121 42.42754 9.91822 -24.30634 -28.71432 9.91822 44.95925 -26.06415 7.02584 -24.30634 -26.06415 119.05632 MINUS 2 LOG LIKELIHOOD = 1054.31006 NUMBER OF PARAMETERS = 24 AIC = 1102.31006 SCHWARZ CRITERION = 1174.56519 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 ITERATION 6 MEANS 5.0 3.4 1.5 0.2 5.9 2.8 4.3 1.3 6.6 3.0 5.5 2.0 CURRENT ESTIMATES OF PRIOR PROBABILITIES: MIXING PROBABILITIES: 0.33 0.33 0.34 COMMON COVARIANCE MATRIX (MLE): 0.08846 0.02989 0.05686 0.01306 0.02989 0.03724 0.01673 0.00979 0.05686 0.01673 0.06170 0.01336 0.01306 0.00979 0.01336 0.01280 INVERSE COVARIANCE MATRIX: 34.24591 -16.62078 -28.74102 7.79209 -16.62078 42.71716 9.22574 -25.35651 -28.74102 9.22574 45.70951 -25.46758 7.79209 -25.35651 -25.46758 116.16780 MINUS 2 LOG LIKELIHOOD = 1053.26562 NUMBER OF PARAMETERS = 24 AIC = 1101.26562 SCHWARZ CRITERION = 1173.52075 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 1.00 0.00 0.00 NUMBERS IN CLUSTERS: 50 49 51 MIXING PROBABILITIES: 0.33 0.33 0.34 MEAN VECTOR FOR CLUSTER 1: 5.00600 3.42800 1.46200 0.24600 MEAN VECTOR FOR CLUSTER 2: 5.94227 2.76207 4.24952 1.31430 MEAN VECTOR FOR CLUSTER 3: 6.56961 2.97777 5.53756 2.02396 COMMON COVARIANCE MATRIX (MLE): 0.08864 0.03018 0.05691 0.01317 0.03018 0.03744 0.01724 0.01014 0.05691 0.01724 0.06131 0.01339 0.01317 0.01014 0.01339 0.01302 CASE, LABEL / DATA 1 1 5.1 3.5 1.4 0.2 2 1 4.9 3.0 1.4 0.2 3 1 4.7 3.2 1.3 0.2 4 1 4.6 3.1 1.5 0.2 5 1 5.0 3.6 1.4 0.2 6 1 5.4 3.9 1.7 0.4 7 1 4.6 3.4 1.4 0.3 8 1 5.0 3.4 1.5 0.2 9 1 4.4 2.9 1.4 0.2 10 1 4.9 3.1 1.5 0.1 11 1 5.4 3.7 1.5 0.2 12 1 4.8 3.4 1.6 0.2 13 1 4.8 3.0 1.4 0.1 14 1 4.3 3.0 1.1 0.1 15 1 5.8 4.0 1.2 0.2 16 1 5.7 4.4 1.5 0.4 17 1 5.4 3.9 1.3 0.4 18 1 5.1 3.5 1.4 0.3 19 1 5.7 3.8 1.7 0.3 20 1 5.1 3.8 1.5 0.3 21 1 5.4 3.4 1.7 0.2 22 1 5.1 3.7 1.5 0.4 23 1 4.6 3.6 1.0 0.2 24 1 5.1 3.3 1.7 0.5 25 1 4.8 3.4 1.9 0.2 26 1 5.0 3.0 1.6 0.2 27 1 5.0 3.4 1.6 0.4 28 1 5.2 3.5 1.5 0.2 29 1 5.2 3.4 1.4 0.2 30 1 4.7 3.2 1.6 0.2 31 1 4.8 3.1 1.6 0.2 32 1 5.4 3.4 1.5 0.4 33 1 5.2 4.1 1.5 0.1 34 1 5.5 4.2 1.4 0.2 35 1 4.9 3.1 1.5 0.2 36 1 5.0 3.2 1.2 0.2 37 1 5.5 3.5 1.3 0.2 38 1 4.9 3.6 1.4 0.1 39 1 4.4 3.0 1.3 0.2 40 1 5.1 3.4 1.5 0.2 41 1 5.0 3.5 1.3 0.3 42 1 4.5 2.3 1.3 0.3 43 1 4.4 3.2 1.3 0.2 44 1 5.0 3.5 1.6 0.6 45 1 5.1 3.8 1.9 0.4 46 1 4.8 3.0 1.4 0.3 47 1 5.1 3.8 1.6 0.2 48 1 4.6 3.2 1.4 0.2 49 1 5.3 3.7 1.5 0.2 50 1 5.0 3.3 1.4 0.2 51 2 7.0 3.2 4.7 1.4 52 2 6.4 3.2 4.5 1.5 53 2 6.9 3.1 4.9 1.5 54 2 5.5 2.3 4.0 1.3 55 2 6.5 2.8 4.6 1.5 56 2 5.7 2.8 4.5 1.3 57 2 6.3 3.3 4.7 1.6 58 2 4.9 2.4 3.3 1.0 59 2 6.6 2.9 4.6 1.3 60 2 5.2 2.7 3.9 1.4 61 2 5.0 2.0 3.5 1.0 62 2 5.9 3.0 4.2 1.5 63 2 6.0 2.2 4.0 1.0 64 2 6.1 2.9 4.7 1.4 65 2 5.6 2.9 3.6 1.3 66 2 6.7 3.1 4.4 1.4 67 2 5.6 3.0 4.5 1.5 68 2 5.8 2.7 4.1 1.0 69 2 6.2 2.2 4.5 1.5 70 2 5.6 2.5 3.9 1.1 71 3 5.9 3.2 4.8 1.8 72 2 6.1 2.8 4.0 1.3 73 2 6.3 2.5 4.9 1.5 74 2 6.1 2.8 4.7 1.2 75 2 6.4 2.9 4.3 1.3 76 2 6.6 3.0 4.4 1.4 77 2 6.8 2.8 4.8 1.4 78 2 6.7 3.0 5.0 1.7 79 2 6.0 2.9 4.5 1.5 80 2 5.7 2.6 3.5 1.0 81 2 5.5 2.4 3.8 1.1 82 2 5.5 2.4 3.7 1.0 83 2 5.8 2.7 3.9 1.2 84 3 6.0 2.7 5.1 1.6 85 2 5.4 3.0 4.5 1.5 86 2 6.0 3.4 4.5 1.6 87 2 6.7 3.1 4.7 1.5 88 2 6.3 2.3 4.4 1.3 89 2 5.6 3.0 4.1 1.3 90 2 5.5 2.5 4.0 1.3 91 2 5.5 2.6 4.4 1.2 92 2 6.1 3.0 4.6 1.4 93 2 5.8 2.6 4.0 1.2 94 2 5.0 2.3 3.3 1.0 95 2 5.6 2.7 4.2 1.3 96 2 5.7 3.0 4.2 1.2 97 2 5.7 2.9 4.2 1.3 98 2 6.2 2.9 4.3 1.3 99 2 5.1 2.5 3.0 1.1 100 2 5.7 2.8 4.1 1.3 101 3 6.3 3.3 6.0 2.5 102 3 5.8 2.7 5.1 1.9 103 3 7.1 3.0 5.9 2.1 104 3 6.3 2.9 5.6 1.8 105 3 6.5 3.0 5.8 2.2 106 3 7.6 3.0 6.6 2.1 107 3 4.9 2.5 4.5 1.7 108 3 7.3 2.9 6.3 1.8 109 3 6.7 2.5 5.8 1.8 110 3 7.2 3.6 6.1 2.5 111 3 6.5 3.2 5.1 2.0 112 3 6.4 2.7 5.3 1.9 113 3 6.8 3.0 5.5 2.1 114 3 5.7 2.5 5.0 2.0 115 3 5.8 2.8 5.1 2.4 116 3 6.4 3.2 5.3 2.3 117 3 6.5 3.0 5.5 1.8 118 3 7.7 3.8 6.7 2.2 119 3 7.7 2.6 6.9 2.3 120 3 6.0 2.2 5.0 1.5 121 3 6.9 3.2 5.7 2.3 122 3 5.6 2.8 4.9 2.0 123 3 7.7 2.8 6.7 2.0 124 3 6.3 2.7 4.9 1.8 125 3 6.7 3.3 5.7 2.1 126 3 7.2 3.2 6.0 1.8 127 3 6.2 2.8 4.8 1.8 128 3 6.1 3.0 4.9 1.8 129 3 6.4 2.8 5.6 2.1 130 3 7.2 3.0 5.8 1.6 131 3 7.4 2.8 6.1 1.9 132 3 7.9 3.8 6.4 2.0 133 3 6.4 2.8 5.6 2.2 134 2 6.3 2.8 5.1 1.5 135 3 6.1 2.6 5.6 1.4 136 3 7.7 3.0 6.1 2.3 137 3 6.3 3.4 5.6 2.4 138 3 6.4 3.1 5.5 1.8 139 3 6.0 3.0 4.8 1.8 140 3 6.9 3.1 5.4 2.1 141 3 6.7 3.1 5.6 2.4 142 3 6.9 3.1 5.1 2.3 143 3 5.8 2.7 5.1 1.9 144 3 6.8 3.2 5.9 2.3 145 3 6.7 3.3 5.7 2.5 146 3 6.7 3.0 5.2 2.3 147 3 6.3 2.5 5.0 1.9 148 3 6.5 3.0 5.2 2.0 149 3 6.2 3.4 5.4 2.3 150 3 5.9 3.0 5.1 1.8 PROGRAM ENDED NORMALLY.