1------------------------------------------- PROGRAM MIX1CMA CLUSPAC FOR CLUSTERING UNIVARIATE DATA (DATA ON THE LINE) DEVELOPED AND PROGRAMMED BY DR. STANLEY L. SCLOVE VERSION 1.3 21-MAY-91 CMS DSN = MIX1CMA CLUSPAC COPYRIGHT (C) 1991, 1992 STANLEY L. 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 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 1.00 7.00 INITIAL VARIANCE 1.1250 WGSS = 20.3903 MINUS 2 LOG LIKELIHOOD = 155.2500 WGMS = 0.5366 STD.ERROR=SQRT(WGMS) = 0.7325 ITERATION 1 BOUNDARIES: 4.00 MEANS: 2.00 6.00 WGSS = 20.0306 MINUS 2 LOG LIKELIHOOD = 140.5291 WGMS = 0.5271 STD.ERROR=SQRT(WGMS) = 0.7260 ITERATION 2 BOUNDARIES: 4.00 MEANS: 2.00 6.00 SUMS: 40.00 120.00 NUMBERS: 20 20 VARIANCES: 0.50 0.50 STD.DEVS.: 0.71 0.71 M.L. ESTIMATE OF COMMON VARIANCE = 0.50077 NUMBER OF PARAMETERS = 4 AIC = 148.5291 SCHWARZ CRITERION = 155.2846 KASHYAP CRITERION = 156.6663 1 K = 3 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.2703 0.4594 0.2703 INITIAL MEANS 1.00 4.00 7.00 INITIAL VARIANCE 0.7500 WGSS = 32.1438 MINUS 2 LOG LIKELIHOOD = 184.8588 WGMS = 0.8688 STD.ERROR=SQRT(WGMS) = 0.9321 ITERATION 1 BOUNDARIES: 2.84 5.16 MEANS: 1.66 4.00 6.34 WGSS = 25.6857 MINUS 2 LOG LIKELIHOOD = 145.7912 WGMS = 0.6942 STD.ERROR=SQRT(WGMS) = 0.8332 ITERATION 2 BOUNDARIES: 3.12 4.88 MEANS: 1.81 4.00 6.19 SUMS: 29.19 31.10 99.71 NUMBERS: 15 10 15 VARIANCES: 0.40 1.66 0.40 STD.DEVS.: 0.63 1.29 0.63 M.L. ESTIMATE OF COMMON VARIANCE = 0.64214 NUMBER OF PARAMETERS = 6 AIC = 157.7912 SCHWARZ CRITERION = 167.9244 KASHYAP CRITERION = 168.5601 1 K = 4 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.1631 0.3369 0.3369 0.1631 INITIAL MEANS 1.00 3.00 5.00 7.00 INITIAL VARIANCE 0.5625 WGSS = 12.8806 MINUS 2 LOG LIKELIHOOD = 145.9142 WGMS = 0.3578 STD.ERROR=SQRT(WGMS) = 0.5982 ITERATION 1 BOUNDARIES: 1.79 4.00 6.21 MEANS: 1.42 2.41 5.59 6.58 WGSS = 11.6895 MINUS 2 LOG LIKELIHOOD = 136.7027 WGMS = 0.3247 STD.ERROR=SQRT(WGMS) = 0.5698 ITERATION 2 BOUNDARIES: 1.80 4.00 6.20 MEANS: 1.45 2.38 5.62 6.55 SUMS: 11.81 28.19 66.64 53.36 NUMBERS: 5 15 15 5 VARIANCES: 0.28 0.30 0.30 0.28 STD.DEVS.: 0.53 0.55 0.55 0.53 M.L. ESTIMATE OF COMMON VARIANCE = 0.29224 NUMBER OF PARAMETERS = 8 AIC = 152.7027 SCHWARZ CRITERION = 166.2137 KASHYAP CRITERION = 169.2111 1 K = 5 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.1068 0.2444 0.2976 0.2444 0.1068 INITIAL MEANS 1.00 2.50 4.00 5.50 7.00 INITIAL VARIANCE 0.4500 WGSS = 14.2874 MINUS 2 LOG LIKELIHOOD = 144.8160 WGMS = 0.4082 STD.ERROR=SQRT(WGMS) = 0.6389 ITERATION 1 BOUNDARIES: 1.45 3.34 4.66 6.55 MEANS: 1.28 2.20 4.00 5.80 6.72 WGSS = 13.9881 MINUS 2 LOG LIKELIHOOD = 142.3899 WGMS = 0.3997 STD.ERROR=SQRT(WGMS) = 0.6322 ITERATION 2 BOUNDARIES: 1.45 3.53 4.47 6.55 MEANS: 1.36 2.22 4.00 5.78 6.64 SUMS: 7.90 29.78 6.19 77.50 38.62 NUMBERS: 5 15 0 15 5 VARIANCES: 0.26 0.35 1.04 0.35 0.26 STD.DEVS.: 0.51 0.59 1.02 0.59 0.51 M.L. ESTIMATE OF COMMON VARIANCE = 0.34970 NUMBER OF PARAMETERS = 10 AIC = 162.3899 SCHWARZ CRITERION = 179.2787 KASHYAP CRITERION = 181.7375 1 K = 6 CLUSTERS INITIAL VALUES OF PRIOR PROBS 0.0739 0.1810 0.2451 0.2451 0.1810 0.0739 INITIAL MEANS 1.00 2.20 3.40 4.60 5.80 7.00 INITIAL VARIANCE 0.3750 WGSS = 9.6635 MINUS 2 LOG LIKELIHOOD = 133.6548 WGMS = 0.2842 STD.ERROR=SQRT(WGMS) = 0.5331 ITERATION 1 BOUNDARIES: 1.34 2.68 4.00 5.32 6.66 MEANS: 1.20 2.00 2.87 5.13 6.00 6.80 WGSS = 7.6328 MINUS 2 LOG LIKELIHOOD = 130.1540 WGMS = 0.2245 STD.ERROR=SQRT(WGMS) = 0.4738 ITERATION 2 BOUNDARIES: 1.41 2.62 4.00 5.38 6.59 MEANS: 1.20 2.00 2.84 5.16 6.00 6.80 SUMS: 5.71 21.51 12.78 23.23 64.53 32.25 NUMBERS: 5 10 5 5 10 5 VARIANCES: 0.16 0.23 0.14 0.14 0.23 0.16 STD.DEVS.: 0.40 0.47 0.37 0.37 0.47 0.40 M.L. ESTIMATE OF COMMON VARIANCE = 0.19082 NUMBER OF PARAMETERS = 12 AIC = 154.1540 SCHWARZ CRITERION = 174.4205 KASHYAP CRITERION = 178.6967 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 1.00 2.00 3.00 4.00 5.00 6.00 7.00 INITIAL VARIANCE 0.3214 WGSS = 10.0123 MINUS 2 LOG LIKELIHOOD = 138.0016 WGMS = 0.3034 STD.ERROR=SQRT(WGMS) = 0.5508 ITERATION 1 BOUNDARIES: 1.20 2.41 3.54 4.46 5.59 6.80 MEANS: 1.16 1.87 2.62 4.00 5.38 6.13 6.84 WGSS = 9.3074 MINUS 2 LOG LIKELIHOOD = 137.7216 WGMS = 0.2820 STD.ERROR=SQRT(WGMS) = 0.5311 ITERATION 2 BOUNDARIES: 1.23 2.40 3.79 4.21 5.60 6.77 MEANS: 1.19 1.88 2.65 4.00 5.35 6.12 6.81 SUMS: 4.62 18.20 16.55 1.69 33.38 59.05 26.50 NUMBERS: 5 10 5 0 5 10 5 VARIANCES: 0.15 0.25 0.24 1.01 0.24 0.25 0.15 STD.DEVS.: 0.39 0.50 0.49 1.00 0.49 0.50 0.39 M.L. ESTIMATE OF COMMON VARIANCE = 0.23269 NUMBER OF PARAMETERS = 14 AIC = 165.7216 SCHWARZ CRITERION = 189.3659 KASHYAP CRITERION = 193.0469 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 1.00 1.86 2.71 3.57 4.43 5.29 6.14 7.00 INITIAL VARIANCE 0.2813 WGSS = 8.7311 MINUS 2 LOG LIKELIHOOD = 137.2970 WGMS = 0.2728 STD.ERROR=SQRT(WGMS) = 0.5223 ITERATION 1 BOUNDARIES: 1.14 2.17 3.08 4.00 4.92 5.83 6.86 MEANS: 1.12 1.77 2.41 3.03 4.97 5.59 6.23 6.88 WGSS = 8.0438 MINUS 2 LOG LIKELIHOOD = 137.1053 WGMS = 0.2514 STD.ERROR=SQRT(WGMS) = 0.5014 ITERATION 2 BOUNDARIES: 1.20 2.18 3.06 4.00 4.94 5.82 6.80 MEANS: 1.13 1.78 2.41 2.93 5.07 5.59 6.22 6.87 SUMS: 3.87 14.30 15.16 6.68 11.57 35.14 49.81 23.48 NUMBERS: 5 10 5 0 0 5 10 5 VARIANCES: 0.11 0.23 0.26 0.07 0.07 0.26 0.23 0.11 STD.DEVS.: 0.34 0.48 0.51 0.26 0.26 0.51 0.48 0.34 M.L. ESTIMATE OF COMMON VARIANCE = 0.20110 NUMBER OF PARAMETERS = 16 AIC = 169.1053 SCHWARZ CRITERION = 196.1273 KASHYAP CRITERION = 200.2461 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 1.00 1.75 2.50 3.25 4.00 4.75 5.50 6.25 7.00 INITIAL VARIANCE 0.2500 WGSS = 8.3025 MINUS 2 LOG LIKELIHOOD = 139.0126 WGMS = 0.2678 STD.ERROR=SQRT(WGMS) = 0.5175 ITERATION 1 BOUNDARIES: 1.07 1.97 2.77 3.67 4.33 5.23 6.03 6.93 MEANS: 1.09 1.68 2.22 2.87 4.00 5.13 5.78 6.32 6.91 WGSS = 7.6677 MINUS 2 LOG LIKELIHOOD = 136.7457 WGMS = 0.2473 STD.ERROR=SQRT(WGMS) = 0.4973 ITERATION 2 BOUNDARIES: 1.13 1.96 2.71 3.96 4.04 5.29 6.04 6.87 MEANS: 1.11 1.69 2.21 2.88 4.00 5.12 5.79 6.31 6.89 SUMS: 3.30 11.33 14.50 10.62 0.70 18.87 37.91 42.25 20.53 NUMBERS: 5 0 10 5 0 5 10 0 5 VARIANCES: 0.10 0.24 0.22 0.11 1.00 0.11 0.22 0.24 0.10 STD.DEVS.: 0.31 0.49 0.47 0.33 1.00 0.32 0.47 0.49 0.31 M.L. ESTIMATE OF COMMON VARIANCE = 0.19169 NUMBER OF PARAMETERS = 18 AIC = 172.7457 SCHWARZ CRITERION = 203.1455 KASHYAP CRITERION = 207.4079 MODEL SELECTION CRITERIA AIC SCHWARZ KASHYAP K= 1 177.68 181.06 175.85 K= 2 148.53 155.28 156.67 K= 3 157.79 167.92 168.56 K= 4 152.70 166.21 169.21 K= 5 162.39 179.28 181.74 K= 6 154.15 174.42 178.70 K= 7 165.72 189.37 193.05 K= 8 169.11 196.13 200.25 K= 9 172.75 203.15 207.41