1**************************************** PROGRAM MIX1CMA ISOPAC FOR CLUSTERING UNIVARIATE DATA (DATA ON THE LINE) DEVELOPED AND PROGRAMMED BY DR. STANLEY L. SCLOVE VERSION 1.3 12-JAN-92 CMS DSN = MIX1CMA ISOPAC COPYRIGHT (C) 1991 STANLEY LOUIS SCLOVE 3 on 2: Starting with 3 groups when there are really 2 clusters N = 40 MINIMUM OF SAMPLE: 1.00000000 MAXIMUM OF SAMPLE: 7.00000000 MEAN = 4.0000 M.L. ESTIMATE OF VARIANCE = 4.50000 SSDEVS = 180.0000 MINUS 2 LOG LIKELIHOOD = 173.6782 STDDEV = 2.1213 AIC = 177.6782 SCHWARZ CRITERION = 181.0559 KASHYAP CRITERION = 175.8505 1 K = 2 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.5000 0.5000 INITIAL MEANS 3.00 5.00 INITIAL VARIANCE 1.1250 WGSS = 40.8752 MINUS 2 LOG LIKELIHOOD = 178.8196 WGMS = 1.0757 STD.ERROR=SQRT(WGMS) = 1.0371 ITERATION 1 BOUNDARIES: 4.00 MEANS: 2.14 5.86 WGSS = 22.2359 MINUS 2 LOG LIKELIHOOD = 125.2251 WGMS = 0.5852 STD.ERROR=SQRT(WGMS) = 0.7650 ITERATION 2 BOUNDARIES: 4.00 MEANS: 2.01 5.99 SUMS: 40.28 119.72 NUMBERS: 20 20 VARIANCES: 0.56 0.56 STD.DEVS.: 0.75 0.75 M.L. ESTIMATE OF COMMON VARIANCE = 0.55590 NUMBER OF PARAMETERS = 4 AIC = 133.2251 SCHWARZ CRITERION = 139.9806 KASHYAP CRITERION = 141.0490 1 K = 3 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.2703 0.4594 0.2703 INITIAL MEANS 2.50 4.00 5.50 INITIAL VARIANCE 0.7500 WGSS = 31.4170 MINUS 2 LOG LIKELIHOOD = 169.3395 WGMS = 0.8491 STD.ERROR=SQRT(WGMS) = 0.9215 ITERATION 1 BOUNDARIES: 3.20 4.80 MEANS: 1.86 4.00 6.14 WGSS = 22.9603 MINUS 2 LOG LIKELIHOOD = 136.4689 WGMS = 0.6205 STD.ERROR=SQRT(WGMS) = 0.7877 ITERATION 2 BOUNDARIES: 3.33 4.67 MEANS: 1.90 4.00 6.10 WGSS = 20.5250 MINUS 2 LOG LIKELIHOOD = 139.7809 WGMS = 0.5547 STD.ERROR=SQRT(WGMS) = 0.7448 ITERATION 3 BOUNDARIES: 3.48 4.52 MEANS: 1.94 4.00 6.06 SUMS: 36.42 9.76 113.81 NUMBERS: 20 0 20 VARIANCES: 0.47 1.19 0.47 STD.DEVS.: 0.68 1.09 0.68 M.L. ESTIMATE OF COMMON VARIANCE = 0.51312 NUMBER OF PARAMETERS = 6 AIC = 151.7809 SCHWARZ CRITERION = 161.9142 KASHYAP CRITERION = 163.2227 1 K = 4 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.1631 0.3369 0.3369 0.1631 INITIAL MEANS 2.20 3.40 4.60 5.80 INITIAL VARIANCE 0.5625 WGSS = 19.4675 MINUS 2 LOG LIKELIHOOD = 155.4895 WGMS = 0.5408 STD.ERROR=SQRT(WGMS) = 0.7354 ITERATION 1 BOUNDARIES: 2.53 4.00 5.47 MEANS: 1.72 2.68 5.32 6.28 WGSS = 15.0277 MINUS 2 LOG LIKELIHOOD = 132.5002 WGMS = 0.4174 STD.ERROR=SQRT(WGMS) = 0.6461 ITERATION 2 BOUNDARIES: 2.50 4.00 5.50 MEANS: 1.75 2.53 5.47 6.25 SUMS: 23.79 16.24 35.19 84.78 NUMBERS: 15 5 5 15 VARIANCES: 0.39 0.34 0.34 0.39 STD.DEVS.: 0.63 0.58 0.58 0.63 M.L. ESTIMATE OF COMMON VARIANCE = 0.37569 NUMBER OF PARAMETERS = 8 AIC = 148.5002 SCHWARZ CRITERION = 162.0112 KASHYAP CRITERION = 164.2550 1 K = 5 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.1068 0.2444 0.2976 0.2444 0.1068 INITIAL MEANS 2.00 3.00 4.00 5.00 6.00 INITIAL VARIANCE 0.4500 WGSS = 16.6585 MINUS 2 LOG LIKELIHOOD = 154.0183 WGMS = 0.4760 STD.ERROR=SQRT(WGMS) = 0.6899 ITERATION 1 BOUNDARIES: 2.16 3.44 4.56 5.84 MEANS: 1.61 2.38 4.00 5.62 6.39 WGSS = 15.4092 MINUS 2 LOG LIKELIHOOD = 139.6403 WGMS = 0.4403 STD.ERROR=SQRT(WGMS) = 0.6635 ITERATION 2 BOUNDARIES: 2.16 3.62 4.38 5.84 MEANS: 1.66 2.37 4.00 5.63 6.34 SUMS: 18.23 19.81 5.30 47.18 69.49 NUMBERS: 15 5 0 5 15 VARIANCES: 0.36 0.36 1.07 0.36 0.36 STD.DEVS.: 0.60 0.60 1.03 0.60 0.60 M.L. ESTIMATE OF COMMON VARIANCE = 0.38523 NUMBER OF PARAMETERS = 10 AIC = 159.6403 SCHWARZ CRITERION = 176.5291 KASHYAP CRITERION = 178.6977 1 K = 6 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.0739 0.1810 0.2451 0.2451 0.1810 0.0739 INITIAL MEANS 1.86 2.71 3.57 4.43 5.29 6.14 INITIAL VARIANCE 0.3750 WGSS = 13.2341 MINUS 2 LOG LIKELIHOOD = 149.5415 WGMS = 0.3892 STD.ERROR=SQRT(WGMS) = 0.6239 ITERATION 1 BOUNDARIES: 1.90 3.03 4.00 4.97 6.10 MEANS: 1.52 2.21 2.98 5.02 5.79 6.48 WGSS = 11.6841 MINUS 2 LOG LIKELIHOOD = 136.4387 WGMS = 0.3436 STD.ERROR=SQRT(WGMS) = 0.5862 ITERATION 2 BOUNDARIES: 1.90 3.04 4.00 4.96 6.10 MEANS: 1.54 2.21 2.82 5.18 5.79 6.46 SUMS: 13.54 18.54 7.93 14.52 48.45 57.02 NUMBERS: 5 15 0 0 15 5 VARIANCES: 0.30 0.32 0.16 0.16 0.32 0.30 STD.DEVS.: 0.55 0.57 0.40 0.40 0.57 0.55 M.L. ESTIMATE OF COMMON VARIANCE = 0.29210 NUMBER OF PARAMETERS = 12 AIC = 160.4387 SCHWARZ CRITERION = 180.7052 KASHYAP CRITERION = 183.7040 1 K = 7 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.0536 0.1375 0.1986 0.2106 0.1986 0.1375 0.0536 INITIAL MEANS 1.75 2.50 3.25 4.00 4.75 5.50 6.25 INITIAL VARIANCE 0.3214 WGSS = 11.7304 MINUS 2 LOG LIKELIHOOD = 148.8035 WGMS = 0.3555 STD.ERROR=SQRT(WGMS) = 0.5962 ITERATION 1 BOUNDARIES: 1.72 2.73 3.60 4.40 5.27 6.28 MEANS: 1.44 2.08 2.73 4.00 5.27 5.92 6.56 WGSS = 11.1363 MINUS 2 LOG LIKELIHOOD = 138.9698 WGMS = 0.3375 STD.ERROR=SQRT(WGMS) = 0.5809 ITERATION 2 BOUNDARIES: 1.72 2.72 3.84 4.16 5.28 6.28 MEANS: 1.45 2.10 2.72 4.00 5.28 5.90 6.55 SUMS: 10.58 17.39 11.35 1.82 22.08 48.92 47.87 NUMBERS: 5 10 5 0 5 10 5 VARIANCES: 0.27 0.29 0.21 1.01 0.21 0.29 0.27 STD.DEVS.: 0.52 0.54 0.46 1.01 0.46 0.54 0.52 M.L. ESTIMATE OF COMMON VARIANCE = 0.27841 NUMBER OF PARAMETERS = 14 AIC = 166.9698 SCHWARZ CRITERION = 190.6141 KASHYAP CRITERION = 193.7570 1 K = 8 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.0402 0.1067 0.1613 0.1918 0.1918 0.1613 0.1067 0.0402 INITIAL MEANS 1.67 2.33 3.00 3.67 4.33 5.00 5.67 6.33 INITIAL VARIANCE 0.2813 WGSS = 10.0845 MINUS 2 LOG LIKELIHOOD = 146.6161 WGMS = 0.3151 STD.ERROR=SQRT(WGMS) = 0.5614 ITERATION 1 BOUNDARIES: 1.58 2.50 3.33 4.00 4.67 5.50 6.42 MEANS: 1.36 1.97 2.58 3.11 4.89 5.42 6.03 6.64 WGSS = 9.0673 MINUS 2 LOG LIKELIHOOD = 136.2411 WGMS = 0.2834 STD.ERROR=SQRT(WGMS) = 0.5323 ITERATION 2 BOUNDARIES: 1.59 2.48 3.52 4.00 4.48 5.52 6.41 MEANS: 1.36 1.98 2.60 2.93 5.07 5.40 6.02 6.64 SUMS: 8.42 15.31 11.85 4.42 7.66 24.65 46.54 41.14 NUMBERS: 5 10 5 0 0 5 10 5 VARIANCES: 0.24 0.23 0.25 0.07 0.07 0.25 0.23 0.24 STD.DEVS.: 0.49 0.48 0.50 0.27 0.27 0.50 0.48 0.49 M.L. ESTIMATE OF COMMON VARIANCE = 0.22668 NUMBER OF PARAMETERS = 16 AIC = 168.2411 SCHWARZ CRITERION = 195.2632 KASHYAP CRITERION = 199.0227 1 K = 9 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.0310 0.0845 0.1324 0.1643 0.1756 0.1643 0.1324 0.0845 0.0310 INITIAL MEANS 1.60 2.20 2.80 3.40 4.00 4.60 5.20 5.80 6.40 INITIAL VARIANCE 0.2500 WGSS = 9.2771 MINUS 2 LOG LIKELIHOOD = 146.7874 WGMS = 0.2993 STD.ERROR=SQRT(WGMS) = 0.5470 ITERATION 1 BOUNDARIES: 1.48 2.33 3.02 3.68 4.32 4.98 5.67 6.52 MEANS: 1.30 1.89 2.43 2.91 4.00 5.09 5.57 6.11 6.70 WGSS = 8.6596 MINUS 2 LOG LIKELIHOOD = 137.4124 WGMS = 0.2793 STD.ERROR=SQRT(WGMS) = 0.5285 ITERATION 2 BOUNDARIES: 1.50 2.34 3.01 3.94 4.06 4.99 5.66 6.50 MEANS: 1.29 1.91 2.45 2.88 4.00 5.12 5.55 6.09 6.71 SUMS: 6.89 13.76 11.99 7.09 0.73 12.65 27.12 43.83 35.95 NUMBERS: 5 10 5 0 0 0 5 10 5 VARIANCES: 0.21 0.21 0.27 0.11 1.00 0.11 0.27 0.21 0.21 STD.DEVS.: 0.46 0.46 0.52 0.33 1.00 0.33 0.52 0.46 0.46 M.L. ESTIMATE OF COMMON VARIANCE = 0.21649 NUMBER OF PARAMETERS = 18 AIC = 173.4124 SCHWARZ CRITERION = 203.8122 KASHYAP CRITERION = 207.7097 MODEL SELECTION CRITERIA AIC SCHWARZ KASHYAP K= 1 177.68 181.06 175.85 K= 2 133.23 139.98 141.05 K= 3 151.78 161.91 163.22 K= 4 148.50 162.01 164.25 K= 5 159.64 176.53 178.70 K= 6 160.44 180.71 183.70 K= 7 166.97 190.61 193.76 K= 8 168.24 195.26 199.02 K= 9 173.41 203.81 207.71