@PAGE 135 @heading number right $$ AFCLSTKS MIXPDTA p.$$ @end MIXPDTA CLUSPAC - MIXTURE-MODEL CLUSTERING OF CASES VARYING COVARIANCE MATRICES AUTOMATIC SETTING OF INITIAL PARAMETER ESTIMATES Copyright (C) Stanley L. Sclove Developed and programmed by: Prof. Stanley L. Sclove, Ph.D. Phone (312) 996-2681 Information & Decision Sciences Dept. M/C 294 College of Business Administration University of Illinois at Chicago Box 4348, Chicago, IL 60680-4348 Program Version: 2.8 01-Jan-90 (VM/CMS) ................................................................................ PROBLEM TITLE IS STOCK DATA FROM AFIFI & CLARK TABLES 8.1 AND 16.1 COMBINED 1/ 1/1990 AT 16: 2: 4 NUMBER OF VARIABLES . . . . . . . . . . . . 7 NUMBER OF OBSERVATIONS (SAMPLE SIZE), N . . 41 MINIMUM FOR EACH VARIABLE: 3.8 0.0 6.8 -3.1 0.8 5. 0.10 MAXIMUM FOR EACH VARIABLE: 24.9 2.7 39.8 48.9 21.9 22. 1.00 FIRST FOUR DATA POINTS ----- ---- ---- ------ 10.0 0.4 13.6 8.0 6.7 5. 0.32 Chem05 14.9 1.1 13.7 48.9 5.8 5. 0.10 Chem17 9.8 0.5 12.1 14.5 3.8 6. 0.51 Chem06 13.8 0.6 20.9 36.0 10.9 6. 0.16 Chem18 NUMBER OF CLUSTERS TO REPORT. . . . . . . . 1 TO 9 STATISTICS FOR WHOLE (UNCLUSTERED) SAMPLE: MEAN VECTOR: 11.74 0.58 16.45 15.08 5.68 10.24 0.39 COVARIANCE MATRIX: 16.965 -0.751 0.284 11.033 7.665 0.226 -0.083 -0.751 0.226 1.692 2.043 -0.422 0.605 -0.013 0.284 1.692 44.780 28.755 3.769 18.831 -0.344 11.033 2.043 28.755 93.201 7.694 10.111 -0.627 7.665 -0.422 3.769 7.694 14.361 4.333 -0.241 0.226 0.605 18.831 10.111 4.333 17.794 -0.022 -0.083 -0.013 -0.344 -0.627 -0.241 -0.022 0.025 MINUS 2 LOG LIKELIHOOD = 1175.1 NUMBER OF PARAMETERS = 35 AIC = 1245.1 SCHWARZ CRITERION = 1305.1 ................................................................................ K = 2 CLUSTERS NUMBER OF PARAMETERS = 71 INITIAL MEANS MEAN VECTOR FOR CLUSTER 1: 10.0 0.4 13.6 8.0 6.7 5. 0.32 MEAN VECTOR FOR CLUSTER 2: 9.9 0.4 12.1 4.2 4.6 9. 0.49 ITERATION 1 MINUS 2 LOG LIKELIHOOD = 1383.2 AIC = 1525.2 SCHWARZ CRITERION = 1646.9 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.89 0.11 1.00 0.00 0.35 0.65 1.00 0.00 NUMBERS IN CLUSTERS: 26 15 ITERATION 2 MINUS 2 LOG LIKELIHOOD = 1126.9 AIC = 1268.9 SCHWARZ CRITERION = 1390.6 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.74 0.26 1.00 0.00 0.06 0.94 1.00 0.00 NUMBERS IN CLUSTERS: 19 22 ITERATION 3 MINUS 2 LOG LIKELIHOOD = 1074.1 AIC = 1216.1 SCHWARZ CRITERION = 1337.8 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.12 0.88 1.00 0.00 0.00 1.00 1.00 0.00 NUMBERS IN CLUSTERS: 12 29 ITERATION 4 MINUS 2 LOG LIKELIHOOD = 1048.6 AIC = 1190.6 SCHWARZ CRITERION = 1312.3 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.01 0.99 1.00 0.00 0.00 1.00 1.00 0.00 MIXING PROBABILITIES: 0.29 0.71 MEAN VECTOR FOR CLUSTER 1: 13.826 0.813 21.105 22.165 7.535 11.456 0.304 MEAN VECTOR FOR CLUSTER 2: 10.886 0.485 14.541 12.165 4.923 9.746 0.421 COMMON COVARIANCE MATRIX (MLE): 6.896 -0.367 -0.396 3.043 2.032 -0.603 -0.019 -0.367 0.077 0.479 0.420 -0.200 0.228 -0.002 -0.396 0.479 14.845 8.023 1.252 7.482 -0.169 3.043 0.420 8.023 31.603 1.577 5.511 -0.171 2.032 -0.200 1.252 1.577 5.270 1.709 -0.120 -0.603 0.228 7.482 5.511 1.709 9.286 -0.020 -0.019 -0.002 -0.169 -0.171 -0.120 -0.020 0.014 CONVERGENCE: NO CASE CHANGED CLUSTERS AFTER ITERATION 4. CLUSTER 1 Chem17 Chem18 Groc03 Groc04 Chem01 Chem14 Chem20 Chem15 Chem21 Chem16 Heal03 Heal01 CLUSTER 2 Chem05 Chem06 Chem27 Groc05 Chem11 Chem12 Chem13 Chem25 Chem26 Groc06 Chem02 Chem03 Groc01 Chem08 Chem04 Chem10 Chem29 Groc02 Chem07 Chem19 Chem09 Chem23 Chem24 Chem28 Chem22 Chem30 Heal05 Heal04 Heal02 ................................................................................ K = 3 CLUSTERS NUMBER OF PARAMETERS = 107 INITIAL MEANS MEAN VECTOR FOR CLUSTER 1: 10.0 0.4 13.6 8.0 6.7 5. 0.32 MEAN VECTOR FOR CLUSTER 2: 13.0 0.7 17.2 12.7 7.3 8. 0.38 MEAN VECTOR FOR CLUSTER 3: 9.5 0.4 13.5 5.9 3.5 11. 0.57 ITERATION 1 MINUS 2 LOG LIKELIHOOD = 1662.3 AIC = 1876.3 SCHWARZ CRITERION = 2059.7 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.66 0.34 0.00 0.01 0.99 0.00 0.31 0.39 0.30 0.09 0.91 0.00 NUMBERS IN CLUSTERS: 5 24 12 ITERATION 2 MINUS 2 LOG LIKELIHOOD = 1021.9 AIC = 1235.9 SCHWARZ CRITERION = 1419.3 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.95 0.05 0.01 0.00 1.00 0.00 0.44 0.01 0.55 0.00 1.00 0.00 NUMBERS IN CLUSTERS: 10 18 13 ITERATION 3 MINUS 2 LOG LIKELIHOOD = 974.5 AIC = 1188.5 SCHWARZ CRITERION = 1371.9 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.00 1.00 0.00 0.57 0.00 0.43 0.00 1.00 0.00 NUMBERS IN CLUSTERS: 13 16 12 ITERATION 4 MINUS 2 LOG LIKELIHOOD = 966.8 AIC = 1180.8 SCHWARZ CRITERION = 1364.2 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.00 1.00 0.00 0.53 0.00 0.47 0.00 1.00 0.00 MIXING PROBABILITIES: 0.31 0.38 0.31 MEAN VECTOR FOR CLUSTER 1: 10.906 0.478 14.114 10.951 6.956 8.225 0.349 MEAN VECTOR FOR CLUSTER 2: 13.313 0.782 21.024 23.510 6.575 12.834 0.292 MEAN VECTOR FOR CLUSTER 3: 10.640 0.435 13.150 8.798 3.290 9.078 0.543 COMMON COVARIANCE MATRIX (MLE): 5.428 -0.352 -1.740 0.668 2.354 -0.852 0.010 -0.352 0.075 0.428 0.385 -0.202 0.112 0.000 -1.740 0.428 11.831 1.875 0.190 4.450 -0.010 0.668 0.385 1.875 17.304 0.565 -1.188 -0.037 2.354 -0.202 0.190 0.565 3.913 1.100 -0.023 -0.852 0.112 4.450 -1.188 1.100 4.935 0.036 0.010 0.000 -0.010 -0.037 -0.023 0.036 0.004 CONVERGENCE: NO CASE CHANGED CLUSTERS AFTER ITERATION 4. CLUSTER 1 Chem05 Chem06 Groc05 Chem12 Chem13 Chem25 Chem26 Chem02 Chem03 Chem29 Chem07 Chem19 Chem21 CLUSTER 2 Chem17 Chem18 Groc03 Groc04 Chem01 Chem20 Chem23 Chem24 Chem15 Chem22 Chem16 Heal05 Heal03 Heal04 Heal01 Heal02 CLUSTER 3 Chem27 Chem11 Groc06 Groc01 Chem08 Chem04 Chem10 Groc02 Chem14 Chem09 Chem28 Chem30 ................................................................................ K = 4 CLUSTERS NUMBER OF PARAMETERS = 143 INITIAL MEANS MEAN VECTOR FOR CLUSTER 1: 10.0 0.4 13.6 8.0 6.7 5. 0.32 MEAN VECTOR FOR CLUSTER 2: 12.0 0.5 15.0 14.9 3.6 7. 0.36 MEAN VECTOR FOR CLUSTER 3: 9.9 0.4 12.1 4.2 4.6 9. 0.49 MEAN VECTOR FOR CLUSTER 4: 11.5 0.4 15.4 11.7 7.2 12. 0.51 ITERATION 1 MINUS 2 LOG LIKELIHOOD = 2021.1 AIC = 2307.1 SCHWARZ CRITERION = 2552.2 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.99 0.01 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.70 0.24 0.05 0.02 0.98 0.00 0.00 NUMBERS IN CLUSTERS: 8 21 10 2 ITERATION 2 MINUS 2 LOG LIKELIHOOD = 950.6 AIC = 1236.6 SCHWARZ CRITERION = 1481.6 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.08 0.53 0.15 0.24 0.00 1.00 0.00 0.00 NUMBERS IN CLUSTERS: 11 16 9 5 ITERATION 3 MINUS 2 LOG LIKELIHOOD = 902.5 AIC = 1188.5 SCHWARZ CRITERION = 1433.6 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.24 0.36 0.02 0.38 0.00 1.00 0.00 0.00 NUMBERS IN CLUSTERS: 11 16 7 7 ITERATION 4 MINUS 2 LOG LIKELIHOOD = 882.5 AIC = 1168.5 SCHWARZ CRITERION = 1413.5 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.27 0.01 0.00 0.72 0.00 1.00 0.00 0.00 MIXING PROBABILITIES: 0.27 0.38 0.17 0.17 MEAN VECTOR FOR CLUSTER 1: 12.329 0.411 14.619 10.232 8.226 8.480 0.324 MEAN VECTOR FOR CLUSTER 2: 11.424 0.859 20.544 23.069 5.232 11.851 0.294 MEAN VECTOR FOR CLUSTER 3: 10.332 0.524 13.232 6.545 2.099 9.682 0.597 MEAN VECTOR FOR CLUSTER 4: 12.945 0.290 13.553 13.672 6.313 10.036 0.478 COMMON COVARIANCE MATRIX (MLE): 3.815 -0.188 -0.284 2.888 1.550 -0.190 -0.010 -0.188 0.062 0.396 0.335 -0.073 0.149 0.000 -0.284 0.396 12.352 3.261 1.284 5.619 -0.005 2.888 0.335 3.261 16.579 2.263 0.410 -0.058 1.550 -0.073 1.284 2.263 2.898 1.542 -0.027 -0.190 0.149 5.619 0.410 1.542 5.450 0.006 -0.010 0.000 -0.005 -0.058 -0.027 0.006 0.003 CONVERGENCE: NO CASE CHANGED CLUSTERS AFTER ITERATION 4. CLUSTER 1 Chem05 Chem27 Chem12 Chem13 Chem26 Chem02 Chem03 Chem29 Chem19 Chem15 Chem21 CLUSTER 2 Chem17 Chem18 Groc03 Groc05 Chem25 Groc04 Chem01 Chem07 Chem20 Chem24 Chem22 Heal05 Heal03 Heal04 Heal01 Heal02 CLUSTER 3 Groc06 Groc01 Chem10 Groc02 Chem14 Chem09 Chem30 CLUSTER 4 Chem06 Chem11 Chem08 Chem04 Chem23 Chem28 Chem16 ................................................................................ K = 5 CLUSTERS NUMBER OF PARAMETERS = 179 INITIAL MEANS MEAN VECTOR FOR CLUSTER 1: 10.0 0.4 13.6 8.0 6.7 5. 0.32 MEAN VECTOR FOR CLUSTER 2: 7.3 0.6 15.4 4.9 5.1 7. 0.27 MEAN VECTOR FOR CLUSTER 3: 9.9 1.1 17.9 15.3 1.6 8. 0.32 MEAN VECTOR FOR CLUSTER 4: 6.5 0.4 18.7 -3.1 1.3 10. 0.38 MEAN VECTOR FOR CLUSTER 5: 11.6 0.4 18.7 22.1 8.1 13. 0.20 ITERATION 1 MINUS 2 LOG LIKELIHOOD = 2191.9 AIC = 2549.9 SCHWARZ CRITERION = 2856.6 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.98 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.99 0.00 0.01 0.00 0.00 0.00 0.00 0.00 0.00 1.00 NUMBERS IN CLUSTERS: 17 3 6 5 10 ITERATION 2 MINUS 2 LOG LIKELIHOOD = 794.3 AIC = 1152.3 SCHWARZ CRITERION = 1459.1 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 PREC.MX. OF CLUSTER 4 HAS BEEN SET TO POOLED PREC.MX. NUMBERS IN CLUSTERS: 16 4 5 6 10 ITERATION 3 MINUS 2 LOG LIKELIHOOD = 651.4 AIC = 1009.4 SCHWARZ CRITERION = 1316.2 CASE POSTERIOR PROBS OF CLUSTER MEMBERSHIP: POSTERIOR PROB OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 PREC.MX. OF CLUSTER 3 HAS BEEN SET TO POOLED PREC.MX. NUMBERS IN CLUSTERS: 18 4 6 4 9 ITERATION 4 -0.1819248E+18 0.4667656E-66 0AFB262I LEXP : ARG = 0.90962421501851008D+17, GREATER THAN 174.673 LEXP : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 274 (OFFSET 115056). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- D#EXP (232042) CALLED BY MAIN (117010) AT ISN 274 AT OFFSET 115056. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. -0.1044852E+19 0.4667656E-66 0AFB262I LEXP : ARG = 0.52242577161098267D+18, GREATER THAN 174.673 LEXP : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 274 (OFFSET 115056). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- D#EXP (232042) CALLED BY MAIN (117010) AT ISN 274 AT OFFSET 115056. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. -0.1962165E+19 0.4667656E-66 0AFB262I LEXP : ARG = 0.98108272422805573D+18, GREATER THAN 174.673 LEXP : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 274 (OFFSET 115056). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- D#EXP (232042) CALLED BY MAIN (117010) AT ISN 274 AT OFFSET 115056. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. -0.3762737E+18 0.4667656E-66 0AFB262I LEXP : ARG = 0.18813686666264178D+18, GREATER THAN 174.673 LEXP : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 274 (OFFSET 115056). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- D#EXP (232042) CALLED BY MAIN (117010) AT ISN 274 AT OFFSET 115056. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. -0.1051009E+17 0.4667656E-66 0AFB262I LEXP : ARG = 0.52550449478061330D+16, GREATER THAN 174.673 LEXP : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 274 (OFFSET 115056). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- D#EXP (232042) CALLED BY MAIN (117010) AT ISN 274 AT OFFSET 115056. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. -0.5033393E+17 0.4667656E-66 -0.9971615E+17 0.4667656E-66 -0.6668149E+17 0.4667656E-66 -0.3890439E+18 0.4667656E-66 -0.3933527E+18 0.4667656E-66 0AFB900I VEMG2 : EXECUTION TERMINATING DUE TO ERROR COUNT FOR ERROR NUMBER 262 0 MESSAGE SUMMARY: MESSAGE NUMBER - COUNT 0 262 10 3 274 F(I,L) = DEXP( F(I,L) ) 522.