CLUSTER ANALYSIS OF CASES BY MIXTURE-MODEL WITH VARYING COVARIANCE MATRICES CMS FILE: MIXPDT ISOPAC 0DEVELOPED AND PROGRAMMED BY: 0 DR. STANLEY L. SCLOVE INFORMATION & DECISION SCIENCES DEPT. M/C 294 COLLEGE OF BUSINESS ADMINISTRATION UNIVERSITY OF ILLINOIS AT CHICAGO BOX 4348, CHICAGO, IL 60680 0 312/996-2681 0MIXPDT ISOPAC VERSION 2.0 13-NOV-89 0COPYRIGHT (C) 1989 STANLEY L. SCLOVE. ALL RIGHTS RESERVED. 0CMS DSN = REALEST DATAORIG; Xs: STYLE;SFLA;GRADE;ASSESSED;MARKET N = 60 NUMBER OF VARIABLES = 5 MINIMUM FOR EACH VARIABLE: 1.00 5.21 0.75 6.90 29.1 MAXIMUM FOR EACH VARIABLE: 2.00 18.04 1.00 48.30 72.6 1 K = 3 CLUSTERS FIRST ITERATION USES THE INITIAL PARAMETER ESTIMATES PROVIDED BY THE USER. ITERATION 1 MEANS 1.00000 6.21500 0.75000 11.40000 38.70000 1.12094 8.39344 0.85312 32.67281 52.03125 1.34615 10.92385 0.91538 41.61923 63.83077 CURRENT ESTIMATES OF MIXING PROBABILITIES: MIXTURE PROBABILITIES: 0.05 0.50 0.45 0COVARIANCE MATRICES: 0POPULATION 1 0.07883 0.40628 0.00382 -0.14367 0.67602 0.40628 4.12050 0.03546 -1.01970 7.20613 0.00382 0.03546 0.00331 -0.03200 0.18578 -0.14367 -1.01970 -0.03200 22.75293 -4.66111 0.67602 7.20613 0.18578 -4.66111 35.79482 0POPULATION 2 0.07883 0.40628 0.00382 -0.14367 0.67602 0.40628 4.12050 0.03546 -1.01970 7.20613 0.00382 0.03546 0.00331 -0.03200 0.18578 -0.14367 -1.01970 -0.03200 22.75293 -4.66111 0.67602 7.20613 0.18578 -4.66111 35.79482 0POPULATION 3 0.07883 0.40628 0.00382 -0.14367 0.67602 0.40628 4.12050 0.03546 -1.01970 7.20613 0.00382 0.03546 0.00331 -0.03200 0.18578 -0.14367 -1.01970 -0.03200 22.75293 -4.66111 0.67602 7.20613 0.18578 -4.66111 35.79482 MINUS 2 LOG LIKELIHOOD = 274.77881 NUMBER OF PARAMETERS = 62 AIC = 398.77881 SCHWARZ CRITERION = 528.62793 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.00 0.33 0.67 0.00 1.00 0.00 0.00 0.62 0.38 0.00 1.00 0.00 ITERATION 2 MEANS 1.00001 7.22095 0.75013 9.91088 40.81006 1.13142 8.44191 0.85576 32.63852 52.38750 1.33259 10.76754 0.91454 41.25284 63.36353 CURRENT ESTIMATES OF MIXING PROBABILITIES: MIXTURE PROBABILITIES: 0.05 0.50 0.45 0COVARIANCE MATRICES: 0POPULATION 1 0.00000 0.00002 0.00000 0.00011 0.00014 0.00002 2.69220 0.00014 -3.20205 4.02750 0.00000 0.00014 0.00002 0.00152 0.00145 0.00011 -3.20205 0.00152 4.69049 -6.11468 0.00014 4.02750 0.00145 -6.11468 8.98600 0POPULATION 2 0.06176 0.32910 0.00110 -0.04759 0.67841 0.32910 3.70962 0.04870 -2.51738 9.61844 0.00110 0.04870 0.00471 -0.05103 0.28842 -0.04759 -2.51738 -0.05103 27.12666 -8.39278 0.67841 9.61844 0.28842 -8.39278 52.44673 0POPULATION 3 0.10201 0.54847 0.00704 -0.08988 0.82271 0.54847 5.07047 0.03094 2.20715 6.82706 0.00704 0.03094 0.00131 0.02065 0.05987 -0.08988 2.20715 0.02065 21.32265 6.08449 0.82271 6.82706 0.05987 6.08449 21.91360 MINUS 2 LOG LIKELIHOOD = 147.35327 NUMBER OF PARAMETERS = 62 AIC = 271.35327 SCHWARZ CRITERION = 401.20239 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.00 0.18 0.82 0.00 0.98 0.02 0.00 0.47 0.53 0.00 0.94 0.06 ITERATION 3 MEANS 1.00000 7.22000 0.75000 9.90000 40.80001 1.11867 8.29798 0.84911 32.23736 51.70503 1.31889 10.60626 0.91308 40.53992 62.60514 CURRENT ESTIMATES OF MIXING PROBABILITIES: MIXTURE PROBABILITIES: 0.05 0.44 0.51 0COVARIANCE MATRICES: 0POPULATION 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2.69340 0.00000 -3.21600 4.02000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -3.21600 0.00000 4.56000 -6.24000 0.00000 4.02000 0.00000 -6.24000 8.88001 0POPULATION 2 0.05544 0.27096 0.00042 -0.04055 0.67746 0.27096 3.36467 0.04783 -3.14409 10.00840 0.00042 0.04783 0.00505 -0.07929 0.29289 -0.04055 -3.14409 -0.07929 28.37085 -11.39232 0.67746 10.00840 0.29289 -11.39232 55.66487 0POPULATION 3 0.10274 0.57484 0.00645 -0.05687 0.81878 0.57484 5.24253 0.02885 2.58575 7.01407 0.00645 0.02885 0.00114 0.02507 0.06015 -0.05687 2.58575 0.02507 23.46062 8.84629 0.81878 7.01407 0.06015 8.84629 23.70482 0AFB263I LLGN : ARG = -0.13733109097988874D-37, LESS THAN OR EQUAL TO ZERO LLGN : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 102 (OFFSET 0A0C36). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- D#LOG (1BB972) CALLED BY MAIN (117010) AT ISN 102 AT OFFSET 0A0C36. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. 0AFB251I SSQRT : ARG=-0.13733109E-37, LESS THAN ZERO SSQRT : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 119 (OFFSET 0A0F2A). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- S#QRT (1BD58A) CALLED BY MAIN (117010) AT ISN 119 AT OFFSET 0A0F2A. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. 0AFB251I SSQRT : ARG=-0.13733109E-37, LESS THAN ZERO SSQRT : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 119 (OFFSET 0A0F2A). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- S#QRT (1BD58A) CALLED BY MAIN (117010) AT ISN 119 AT OFFSET 0A0F2A. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. 0AFB251I SSQRT : ARG=-0.13733109E-37, LESS THAN ZERO SSQRT : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 119 (OFFSET 0A0F2A). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- S#QRT (1BD58A) CALLED BY MAIN (117010) AT ISN 119 AT OFFSET 0A0F2A. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. MINUS 2 LOG LIKELIHOOD = -55.03671 NUMBER OF PARAMETERS = 62 AIC = 68.96329 SCHWARZ CRITERION = 198.81262 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.00 0.07 0.93 0.00 0.92 0.08 0.00 0.27 0.73 0.00 0.77 0.23 ITERATION 4 MEANS 1.00000 7.22000 0.75000 9.90000 40.80001 1.10214 8.10772 0.83967 31.69686 50.70553 1.30566 10.45354 0.91154 39.89772 61.94924 CURRENT ESTIMATES OF MIXING PROBABILITIES: MIXTURE PROBABILITIES: 0.05 0.37 0.58 0COVARIANCE MATRICES: 0POPULATION 1 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 2.69340 0.00000 -3.21600 4.02000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -3.21600 0.00000 4.56000 -6.24000 0.00000 4.02000 0.00000 -6.24000 8.88001 0POPULATION 2 0.04536 0.18261 -0.00053 -0.02221 0.63340 0.18261 2.83418 0.04507 -3.98824 10.07355 -0.00053 0.04507 0.00542 -0.12678 0.28632 -0.02221 -3.98824 -0.12678 29.41368 -16.41422 0.63340 10.07355 0.28632 -16.41422 57.38344 0POPULATION 3 0.10376 0.59751 0.00585 -0.04105 0.82602 0.59751 5.38316 0.02720 2.74471 7.28143 0.00585 0.02720 0.00102 0.02948 0.06060 -0.04105 2.74471 0.02948 25.20670 10.54480 0.82602 7.28143 0.06060 10.54480 25.45012 0AFB263I LLGN : ARG = -0.13733109097988874D-37, LESS THAN OR EQUAL TO ZERO LLGN : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 102 (OFFSET 0A0C36). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- D#LOG (1BB972) CALLED BY MAIN (117010) AT ISN 102 AT OFFSET 0A0C36. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. 0AFB251I SSQRT : ARG=-0.13733109E-37, LESS THAN ZERO SSQRT : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 119 (OFFSET 0A0F2A). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- S#QRT (1BD58A) CALLED BY MAIN (117010) AT ISN 119 AT OFFSET 0A0F2A. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. 0AFB251I SSQRT : ARG=-0.13733109E-37, LESS THAN ZERO SSQRT : LAST EXECUTED FORTRAN STATEMENT IN PROGRAM MAIN AT ISN 119 (OFFSET 0A0F2A). 0TRACEBACK OF CALLING ROUTINES; MODULE ENTRY ADDRESS = 117010. ----------------------------------------------------------------------------- S#QRT (1BD58A) CALLED BY MAIN (117010) AT ISN 119 AT OFFSET 0A0F2A. ----------------------------------------------------------------------------- MAIN (117010) CALLED BY OPERATING SYSTEM. ----------------------------------------------------------------------------- 0STANDARD CORRECTIVE ACTION TAKEN. EXECUTION CONTINUING. MINUS 2 LOG LIKELIHOOD = -66.62759 NUMBER OF PARAMETERS = 62 AIC = 57.37241 SCHWARZ CRITERION = 187.22174 POSTERIOR PROBS OF GROUP MEMBERSHIP FOR 1ST 4 CASES: 0.00 0.02 0.98 0.00 0.83 0.17 0.00 0.11 0.89 0.00 0.54 0.46 NUMBERS: 3 18 39 MIXTURE PROBABILITIES: 0.05 0.32 0.63 MEAN VECTOR FOR CLUSTER 1: 1.00000 7.22000 0.75000 9.90000 40.80001 MEAN VECTOR FOR CLUSTER 2: 1.08971 7.93339 0.82858 31.23101 49.47908 MEAN VECTOR FOR CLUSTER 3: 1.29331 10.32665 0.91050 39.38288 61.53497 0COVARIANCE MATRICES: 0.04505 0.25258 0.00205 -0.00470 0.40214 0.25258 2.42297 0.01456 0.68220 4.03731 0.00205 0.01456 0.00094 -0.00522 0.04888 -0.00470 0.68220 -0.00522 13.99213 2.33263 0.40214 4.03731 0.04888 2.33263 16.20165 CASE, LABEL / DATA 1 3 1.25 10.11 0.90 39.00 57.6 2 2 1.00 7.21 0.90 32.40 49.2 3 3 1.00 7.60 0.90 39.90 53.7 4 2 1.00 6.62 0.90 29.40 51.9 5 3 1.25 9.31 0.90 36.90 57.0 6 1 1.00 7.22 0.75 11.10 38.4 7 3 1.75 16.02 1.00 46.50 71.1 8 3 1.00 6.77 0.90 34.20 54.6 9 3 1.25 10.47 0.90 45.00 65.4 10 3 1.00 8.38 0.90 38.40 53.4 11 3 1.25 9.18 0.90 48.30 61.8 12 3 1.00 7.87 0.90 33.60 58.8 13 2 1.75 8.58 0.75 33.60 53.7 14 3 1.25 11.71 0.90 48.30 72.6 15 3 1.00 8.99 0.90 34.80 56.4 16 2 1.00 5.77 0.75 33.30 39.3 17 2 1.00 5.38 0.75 42.30 29.1 18 3 1.25 10.56 0.90 38.70 62.7 19 3 1.25 8.83 0.90 38.70 59.4 20 3 1.25 10.33 0.90 37.80 60.6 21 3 1.25 10.75 0.90 45.60 64.2 22 3 1.25 10.70 0.90 34.20 65.4 23 3 1.00 10.60 0.90 36.00 57.6 24 3 1.25 11.38 0.90 38.40 58.5 25 2 1.00 5.44 0.90 34.80 37.8 26 3 1.00 8.25 0.90 42.30 57.0 27 3 2.00 14.35 0.90 32.10 58.2 28 2 1.00 8.34 0.75 27.00 51.9 29 2 1.00 7.80 0.75 33.90 46.5 30 2 1.00 7.67 0.75 33.30 50.4 31 3 1.25 10.11 0.90 42.00 65.4 32 3 1.25 10.24 0.90 40.50 63.3 33 2 1.00 6.91 0.75 33.90 49.5 34 3 1.00 9.66 0.90 45.30 66.0 35 3 1.25 11.06 0.90 47.40 64.2 36 3 1.00 11.00 0.90 45.00 62.4 37 2 1.00 8.90 0.90 30.30 52.5 38 2 1.00 9.20 0.75 31.20 46.8 39 3 2.00 18.04 0.90 45.90 68.1 40 2 1.12 9.65 0.90 21.90 55.8 41 2 1.25 6.61 0.75 35.70 46.5 42 3 1.75 11.64 1.00 44.10 62.7 43 3 1.25 10.79 0.90 36.30 60.9 44 2 1.00 8.15 0.90 21.60 51.6 45 3 1.75 10.60 1.00 43.80 67.2 46 3 2.00 12.98 1.00 35.40 67.8 47 3 2.00 12.49 0.90 33.00 70.8 48 2 1.00 8.14 0.90 22.20 52.2 49 1 1.00 5.21 0.75 11.70 39.0 50 3 1.50 10.40 0.90 33.60 60.6 51 3 1.25 10.51 0.90 39.60 62.1 52 3 1.00 7.12 0.90 31.80 63.6 53 3 1.00 6.94 0.90 42.00 56.1 54 3 1.50 10.52 0.90 30.30 59.4 55 1 1.00 9.23 0.75 6.90 45.0 56 3 1.00 9.67 0.90 39.00 66.3 57 3 1.00 7.43 0.90 39.30 52.2 58 2 1.50 12.37 0.90 25.50 59.7 59 2 1.00 9.26 0.90 27.33 56.1 60 3 1.00 8.02 0.90 38.10 54.0 PROGRAM ENDED NORMALLY. 0 MESSAGE SUMMARY: MESSAGE NUMBER - COUNT 0 251 6 0 263 2