C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C C C PROGRAM TSPAC: VIT1DTA C C VERSION 1.0 28-DEC-2001 C C C C C C C C PROGRAM TSPAC:VIT1DTA WAS DEVELOPED FROM TSPAC:TSSG1DTA. C C C C PROGRAM VIT1DTA IS FOR TIME-SERIES SEGMENTATION VIA THE C C HIDDEN MARKOV MODEL AND THE VITERBI ALGORITHM. C C C C THE "TSSG" PROGRAMS USE A "GREEDY" ALGORITHM FOR SEGMENTING C C TIME SERIES. THE TSSGP SERIES IS FOR MULTIVARIATE C C TIME SERIES. FOR UNIVARIATE TIME SERIES THE "TSSG1" PROGRAMS C C ARE USED. C C TSPAC INCLUDES PROGRAMS USING DISTANCE IN THE METRIC OF THE C C ESTIMATED COMMON COVARIANCE MATRIX AS WELL AS PROGRAMS USING C C DIFFERENT COVARIANCE MATRICES, WITH ADJUSTMENT BY THE C C DETERMINANTS, I.E., USING ESTIMATED LOG LIKELIHOOD FOR THE C C GAUSSIAN MODEL WITH DIFFERENT COVARIANCE MATRICES. C C C C THERE ARE PROGRAMS IN MANUAL MODE, IN WHICH THE NUMBER OF C C CLASSES AND INITIAL MEANS ARE INPUT AND PROGRAMS IN AUTOMATIC C C MODE, WHICH TRY A RANGE OF NUMBERS OF CLASSES, WITH AUTOMATIC C C SETTING OF INITIAL MEANS. C C C C C C PROGRAMMED BY: C C DR. STANLEY L. SCLOVE 312/996-2681 C C INFORMATION & DECISION SCIENCE DEPT 312/996-2676 C C UNIVERSITY OF ILLINOIS AT CHICAGO C C 601 S. MORGAN ST. C C CHICAGO, IL 60607-7124 C C C C RESEARCH SUPPORTED IN PART BY: C C CENTER FOR HEALTH STATISTICS, C C UNIVERSITY OF ILLINOIS AT CHICAGO C C C C C C RESTRICTIONS (CAN BE MODIFIED): C C N, SERIES LENGTH, AT MOST 9999; C C IP, NUMBER OF VARIABLES, AT MOST 20; C C K, NUMBER OF CLASSES, AT MOST 29; C C ITER, MAXIMUM NUMBER OF ITERATIONS, 20. C C C C C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C DIMENSION X( 9999),SUM(29) DIMENSION D(29),ICLUS( 9999) C DIMENSION IOTA( 9999),JOTA(29) C DIMENSION TITLE(18) DIMENSION NG(29),XMEAN(29) DIMENSION FMT(18) DIMENSION SS(29),SSD(29) DIMENSION ICLSOL( 9999) C C DIMENSION ET(29) DIMENSION PG(29) C DIMENSION NT(29,29),IRSUM(29),TP(29,29) DIMENSION PROB(29) C C DOUBLE PRECISION SS,SUM DOUBLE PRECISION WGSS,SSD DOUBLE PRECISION VARHAT DOUBLE PRECISION P DOUBLE PRECISION DET DOUBLE PRECISION D DOUBLE PRECISION XMEAN DOUBLE PRECISION TEMPIV,TEMPJV DOUBLE PRECISION F DOUBLE PRECISION CF C DOUBLE PRECISION A C DOUBLE PRECISION ET DOUBLE PRECISION PG DOUBLE PRECISION TP,PROB C C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C C C CONTROL CARDS: C C C C DATASET TITLE C C SERIES LENGTH, N, IN FORMAT (2X,I4) C C FMT, IN FORMAT (18A4), E.G., (1X,F4.1) C C "FMT" WILL ALSO BE USED FOR OUTPUT: ALLOW AT LEAST ONE BLANK C C AT THE BEGINNING FOR CARRIAGE CONTROL. C C DATA, BY TIME POINT, IN FORMAT SPECIFIED BY FMT C C DATA IS INDEXED BY TIME POINT. C C C C KL, MIN NUMBER OF CLASSES, IN FORMAT (3X,I2) C C KU, MAX NUMBER OF CLASSES, IN FORMAT (3X,I2) C C C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C READ (5,28000) TITLE C C WRITE PROGRAM INFORMATION. WRITE (6,17000) WRITE (6,53000) WRITE (6,35000) TITLE C C READ SERIES LENGTH, N. READ (5,16000) N C WRITE (6,33000) N C C C READ DATA FORMAT. READ (5,28000) FMT WRITE (6,11000) FMT C C C READ DATA. C DO 300 I = 1,N READ (5,FMT) X(I) IF (I .EQ. 1) GO TO 100 GO TO 200 100 CONTINUE C XMAX = X(1) XMIN = X(1) 200 CONTINUE IF (X(I) .LT. XMIN ) XMIN = X(I) IF (X(I) .GT. XMAX ) XMAX = X(I) 300 CONTINUE WRITE (6,54000) WRITE (6,FMT) XMIN WRITE (6,55000) WRITE (6,FMT) XMAX C C READ KL AND KU, THE MIN AND MAX NUMBER OF CLASSES TO BE TRIED. READ (5,15000) KL READ (5,15000) KU WRITE (6,18000) KL,KU C C SET CONSTANTS. C PI = 3.1415927 C C XN = N DO 400 INTEG=1,N IOTA(INTEG) = INTEG 400 CONTINUE C DO 6500 K = KL,KU C K IS THE NUMBER OF CLASSES. C C COMPUTE INITIAL MEANS: C DO 500 IG=1,K DO 500 IVAR = 1,IP XMEAN(IG) = XMIN + IG*(XMAX - XMIN )/(K+1) 500 CONTINUE C WRITE (6,19000) K C WRITE INITIAL MEANS C DO 600 IG = 1,K WRITE (6,20000) IG,XMEAN(IG) 600 CONTINUE C C SET CONSTANTS FOR THIS VALUE OF K. C DO 700 J = 1,K JOTA(J) = J 700 CONTINUE C C PARAMETERS FOR MODEL WITH COMMON COVARIANCE MATRIX ARE C K MEAN VECTORS AND ONE COVARIANCE MATRIX. C IP = 1 NOPARM = K*IP + IP*(IP+1)/2 C PARAMETERS FOR MODEL WITH DIFFERENT COVARIANCE MATRICES ARE C K MEAN VECTORS AND K COVARIANCE MATRICES. NPRMDF = K*IP + K*IP*(IP+1)/2 C C NON-DISTRIBUTIONAL PARAMETERS: C K-BY-K TRANSITION PROB. MATRIX C GIVES K(K-1) FREE TRANSITION PROBABILITIES C NOPARM = NOPARM + K*(K-1) NPRMDF = NPRMDF + K*(K-1) C C C FOR FIRST ITERATION, MARGINAL DISTRIBUTION OF LABELS, PROB, C IS TAKEN TO BE UNIFORM. C DO 800 IG=1,K 800 PROB(IG) = 1.0/K C C ITER = 1 C ITERATIONS BEGIN HERE C 900 CONTINUE IF (ITER .EQ. 1) GO TO 1100 DO 1000 I = 1,N C ICLSOL(I) = ICLUS(I) 1000 CONTINUE C SAVE PREVIOUS VALUE OF -2 LOG MAX LIKELIHOOD: XMN20L = XMN2LL 1100 CONTINUE C C COMMENCE DISTANCE COMPUTATIONS. C DO 2400 I = 1,N C C INITIALIZE DISTANCES (TO BE ACCUMULATED) AT ZERO. DO 1200 L = 1,K D(L) = 0.0 1200 CONTINUE C FOR FIRST ITERATION, EUCLIDEAN DISTANCE IS USED BECAUSE C NO COVARIANCE MATRIX IS YET AVAILABLE. AFTER THE FIRST C ITERATION, DISTANCE WILL BE TAKEN IN THE METRIC OF THE C GROUP COVARIANCE MATRIX. C IF (ITER .GT. 1) GO TO 1400 DO 1300 L=1,K C D(L) = D(L) + ( XMEAN(L) - X(I) )**2 1300 CONTINUE GO TO 1700 1400 CONTINUE DO 1600 L=1,K TEMPIV = XMEAN(L) - X(I) TEMPJV = XMEAN(L) - X(I) C D(L) = D(L) + TEMPIV*PG(L)*TEMPJV C 1500 CONTINUE C 1600 CONTINUE 1700 CONTINUE C DO 2200 L = 1,K C FOR FIRST ITERATION, CLASSIFICATION IS SIMPLY BY C MINIMUM DISTANCE. OTHERWISE, THE TRANSITION C PROBABILITIES AND DETERMINANTS ENTER: C IF (ITER .EQ. 1) GO TO 2200 C C UP TO NOW, D(L) IS (SQUARED) DISTANCE C IT MUST NOW BE MODIFIED TO PROBABILITY, C FOR MULTIPLICATION BY THE TRANSITION PROBABILITIES. C ADD DETERMINANT OF COVARIANCE MATRIX TO DISTANCE: D(L) = D(L) + ET(L) ARG = -D(L)/2.0 IF (ARG .LT. -180.2) GO TO 1800 GO TO 1900 1800 D(L) = 0.0 GO TO 2000 1900 CONTINUE C C MOVE FROM LOG PROB SCALE TO PROB SCALE: D(L) = EXP(ARG) C D(L) IS NO LONGER A DISTANCE: C IT IS (PROPORTIONAL TO) THE BELONGING PROBABILITY 2000 CONTINUE C IF (I .EQ. 1) GO TO 2100 IG1 = ICLUS(I-1) C D(L) = -TP(IG1,L)*D(L) GO TO 2200 2100 CONTINUE C CLASSIFY FIRST OBSERVATION D(L) = -D(L)*PROB(L) 2200 CONTINUE C F = D(1) ICLUS(I) = 1 DO 2400 L = 2,K IF ( D(L) - F ) 2300,2400,2400 2300 F = D(L) ICLUS(I) = L 2400 CONTINUE WRITE (6,10000) C WRITE (6,12000) (IOTA(J), J=1,N) C WRITE (6,12000) (ICLUS(I),I=1,N) C DO 2600 IG = 1,K NG(IG) = 0 SUM(IG) = 0.0 SS(IG) = 0.0 SSD(IG) = 0.0 2600 CONTINUE DO 2700 I = 1,N C IGROUP = ICLUS(I) NG(IGROUP) = NG(IGROUP) + 1 SUM(IGROUP) = SUM(IGROUP) + X(I) SS(IGROUP) = SS(IGROUP) + X(I)*X(I) 2700 CONTINUE C WRITE (6,27000) (NG(IG),IG=1,K) C WGSS = 0.0 2800 CONTINUE C C DO 3100 IG = 1,K IF (NG(IG) .EQ. 0) GO TO 2900 GO TO 3000 2900 WRITE (6,60000) IG GO TO 6600 3000 CONTINUE C C COMPUTE MEAN VECTORS XMEAN(IG) = SUM(IG)/NG(IG) C COMPUTE SUM-OF-PRODUCTS MATRICES CF = SUM(IG)*SUM(IG)/NG(IG) SSD(IG) = SS(IG) - CF 3100 CONTINUE C C C POOL: C DO 3200 IG = 1,K WGSS = WGSS + SSD(IG) 3200 CONTINUE C C C COMPUTE VARHAT, MLE OF COMMON VARIANCE: VARHAT = WGSS/N 3300 CONTINUE C XLGVAR = DLOG(VARHAT) XMN2LL = N*(IP*ALOG(2.0*PI) + IP + XLGVAR) C C IF (ITER .EQ. 1) GO TO 3600 C C COMPARE NEW SEGMENTATION WITH OLD C DO 3500 I = 1,N C IF (ICLUS(I) .EQ. ICLSOL(I)) GO TO 3500 GO TO 3600 3500 CONTINUE GO TO 6000 3600 CONTINUE C C IF NEW SEGMENTATION DIFFERS FROM OLD, C COMPUTE AND WRITE NEW STATISTICS C DO 3700 IG = 1,K WRITE (6,26000) IG,XMEAN(IG) 3700 CONTINUE C C COMPUTE TRANSITION PROBABILITY MATRIX: C DO 3800 I1 = 1,K C DO 3800 J = 1,K NT(I1,J) = 0 3800 CONTINUE DO 3900 I = 2,N C IM1 = I-1 C IBEFOR = ICLUS(IM1) C IY = ICLUS(I) NT(IBEFOR,IY) = NT(IBEFOR,IY) + 1 3900 CONTINUE DO 4000 I1 = 1,K C IRSUM(I1) = 0 4000 CONTINUE DO 4100 I1 = 1,K C DO 4100 J = 1,K IRSUM(I1) = IRSUM(I1) + NT(I1,J) 4100 CONTINUE DO 4400 I1=1,K C XDENOM=IRSUM(I1) IF (XDENOM .EQ. 0.0) GO TO 4200 GO TO 4300 4200 XDENOM = K 4300 CONTINUE C DO 4400 J = 1,K XNUM = NT(I1,J) C IF THERE ARE NO TRANSITIONS FROM I1) THEN TP(I1,J) C IS SET EQUAL TO ZERO, FOR ALL J = 1,2,...,K. C 4400 TP(I1,J) = XNUM/XDENOM 4500 CONTINUE C C COMPUTE MARGINAL DISTRIBUTION OF LABELS: DO 4600 IG = 1,K PROB(IG) = NG(IG) PROB(IG) = PROB(IG)/N 4600 CONTINUE C TRANS = 0.0 DO 4700 I1=1,K C DO 4700 J=1,K ITEST = NT(I1,J) IF (ITEST .EQ. 0) GO TO 4700 IF (TP(I1,J) .EQ. 0.) GO TO 4700 TRANS = TRANS + NT(I1,J)*DLOG(TP(I1,J)) 4700 CONTINUE C TRANS = -2.0*TRANS C C WRITE TRANSITION PROBABILITIES: WRITE (6,13000) WRITE (6,37000) (JOTA(JAY),JAY=1,K) DO 4800 I1 = 1,K C WRITE (6,38000) I1, (NT(I1,J),J=1,K) 4800 CONTINUE WRITE (6,39000) WRITE (6,37000) (JOTA(JAY),JAY=1,K) DO 4900 I1=1,K C WRITE (6,40000) I1, (TP(I1,J),J=1,K) 4900 CONTINUE WRITE (6,63000) (PROB(IG),IG=1,K) WRITE (6,32000) TRANS WRITE (6,50000) WRITE (6,22000) XMN2LL C C ACCOUNT FOR LABEL OF FIRST OBSERVATION: C C LABEL1 = ICLUS(1) PROBAB = PROB(LABEL1) FIRST = ALOG(PROBAB) C FIRST = -2.0*FIRST C C C COMPUTE MODEL SELECTION CRITERIA: C COMPUTE VALUES CORRESPONDING TO NEW SEGMENTATION AND OLD C COVARIANCE MATRIX (OMIT ON FIRST ITERATION) C IF (ITER .EQ. 1) GO TO 5200 C C FOR MODEL WITH COMMON COVARIANCE MATRIX C (NOT OPTIMIZED IN THIS PROGRAM; HOWEVER, IT IS CLEAR C THAT ONE SHOULD USE THE COMMON-COVARIANCE-MATRIX MODEL IF C THE VALUES OF THE MODEL SELECTION CRITERIA HERE FOR THAT MODEL C ARE LESS THAN THOSE FOR THE MODEL WITH DIFFERENT COVARIANCE C MATRICES): C AICOLD = XMN2OL + TRANS + FIRST + 2.0*NOPARM SCHOLD = XMN2OL + TRANS + FIRST + ALOG(XN)*NOPARM WRITE (6,59000) NOPARM WRITE (6,46000) AICOLD WRITE (6,47000) SCHOLD 5200 CONTINUE AIC = XMN2LL + TRANS + FIRST + 2.0*NOPARM WRITE (6,48000) AIC SCH = XMN2LL + TRANS + FIRST + ALOG(XN)*NOPARM WRITE (6,49000) SCH C C C COMPUTE PRECISION MATRICES FOR ALL GROUPS. C IP = 1 TERM=0.0 DO 5700 L=1,K IF (NG(L) .GT. IP) GO TO 5300 WRITE (6,52000) L,NG(L) GO TO 5600 5300 CONTINUE C C H E R E A = SSD(L)/NG(L) 5400 CONTINUE PG(L) = P 5500 CONTINUE C ET(L) = DLOG(A) C 5600 CONTINUE C TERM = TERM + NG(L)*ET(L) 5700 CONTINUE C COMPUTE MODEL SELECTION CRITERIA WITH DIFFERENT COVARIANCE C MATRICES: C C PARAMETERS: C K MEAN VECTORS OF DIMENSION P AND K P-BY-P COVARIANCE MATRICES, C WHERE P IS THE NUMBER OF VARIABLES XM2LLD = N*IP*ALOG(2*PI) + N*IP + TERM XM2LLD = XM2LLD + TRANS + FIRST SCHD = XM2LLD + ALOG(XN)*NPRMDF AICD = XM2LLD + 2.0*NPRMDF WRITE (6,23000) WRITE (6,59000) NPRMDF WRITE (6,24000) XM2LLD WRITE (6,57000) AICD WRITE (6,58000) SCHD C C WRITE (6,25000) ITER DO 5800 IG = 1,K WRITE (6,21000) IG, (XMEAN(IG),IVAR=1,IP) 5800 CONTINUE ITER = ITER + 1 IF (ITER .GE. 21) GO TO 5900 C UNLESS 20 ITERATIONS, HAVE ALREADY BEEN PERFORMED, GO BACK C AND DO ANOTHER. GO TO 900 5900 WRITE (6,44000) GO TO 6500 C C 6000 CONTINUE C C OUTPUT TO BE WRITTEN UPON CONVERGENCE: C WRITE (6,41000) ITER WRITE (6,30000) C COMPUTE AND WRITE COMMON VARIANCE C WGMS = WGSS/(N-K) 6100 CONTINUE WRITE (6,31000) WGMS 6200 CONTINUE C WRITE (6,62000) C COMPUTE AND WRITE CLASS VARIANCES C DO 6400 L = 1,K WGMS = SSD(L)/(NG(L)-1) 6300 CONTINUE WRITE (6,61000) L WRITE (6,31000) WGMS 6400 CONTINUE C C C C WRITE (6,45000) K C 6500 CONTINUE C WRITE (6,42000) 6600 STOP C C 10000 FORMAT(//1X,'SEGMENTATION:'/) 11000 FORMAT(/1X,'DATA READ IN UNDER FORMAT ',18A4) 12000 FORMAT(1X, (40I3/) ) 13000 FORMAT(//1X,'TRANSITIONS') 14000 FORMAT(/1X,'NUMBER OF VARIABLES = ',I2/) 15000 FORMAT(3X,I2) 16000 FORMAT(2X,I4) 17000 FORMAT('1','###################################################', X//,1X,'PROGRAM TSPAC:VIT1DTA '/ X,1X,'FOR TIME SERIES SEGMENTATION '/ X,1X,'USING DIFFERENT VARIANCES'/ X,1X,' '/ X//,1X,'DEVELOPED AND PROGRAMMED BY '// X1X,' DR. STANLEY L. SCLOVE 312/996-2681'/ X1X,' IDS DEPT (MC 294) 312/996-2676'/ X1X,' UNIVERSITY OF ILLINOIS AT CHICAGO '/ X1X,' 601 S. MORGAN ST., CHICAGO, IL 60607-7124 '// X//,1X,'VERSION 1.0 28-Dec-2001 '//) 18000 FORMAT('1',//,1X,'MIN AND MAX NUMBER OF CLASSES TO BE TRIED ARE ', XI2,' AND ',I2//) 19000 FORMAT(1H1,'K = ',I2,' CLASSES'//) 20000 FORMAT(/1X,'INITIAL MEAN FOR CLASS ',I2,': ',(4E14.5/)) 21000 FORMAT(1X,'MEAN FOR CLASS ',I2,': ',(8E13.5/)) 22000 FORMAT(/,1X,'MINUS 2 LOG LIKELIHOOD FOR MODEL WITH COMMON', X' VARIANCE = ', E13.5//) 23000 FORMAT(//1X,'FOR MODEL WITH DIFFERENT VARIANCES:'//) 24000 FORMAT(/,1X,'MINUS 2 LOG LIKELIHOOD FOR MODEL WITH DIFFERENT ', X'VARIANCES = ', E13.5//) 25000 FORMAT(///,1X,'ITERATION ', I2,//) 26000 FORMAT(1X,'MEAN FOR CLASS ',I2,': ',(8E13.5/)) 27000 FORMAT(/,1X,'NUMBERS IN CLASSES:'/,(9I12/)/) 28000 FORMAT(18A4) 29000 FORMAT(3X,I2) 30000 FORMAT(///,1X,'COMMON VARIANCE (DIVISOR IS DF):',//) 31000 FORMAT(1X,(8E13.5/)) 32000 FORMAT(//,' CONTRIBUTION OF TRANS. PROBS. TO LOG LIKELIHOOD =', XE15.5/) 33000 FORMAT(1X,'SERIES LENGTH = ',I4) 35000 FORMAT(1X,18A4) 36000 FORMAT(/9X,(9I7/)) 37000 FORMAT(/5X,(9I7/)) 38000 FORMAT(1X, I4, (9I7/)) 39000 FORMAT(//1X,'TRANSITION PROBABILITIES') 40000 FORMAT(1X, I4,3X,(9F7.4/)) 41000 FORMAT(/1X,'CONVERGENCE: NO CASE CHANGED CLASSES AFTER ', X'ITERATION ',I2,'. SOME ADDITIONAL RESULTS ARE PRINTED BELOW.'//) 42000 FORMAT(/1X,'PROGRAM ENDED SUCCESSFULLY.') 44000 FORMAT(1X,'ROUTINE HAS NOT CONVERGED IN 20 ITERATIONS. STOP') 45000 FORMAT(/,1X,'PROGRAM ENDED SUCCESSFULLY FOR THE CASE ', X'K = ',I2,'.'/) 46000 FORMAT(/1X,'AIC WITH NEW LABELS AND OLD DISTRIBUTIONAL ', X'PARAMETERS: ', E15.5) 47000 FORMAT(/1X,'SCHWARZ CRITERION WITH NEW LABELS AND OLD ', X'DISTRIBUTIONAL PARAMETERS: ', E15.5) 48000 FORMAT(/1X,'AIC WITH NEW LABELS AND NEW DISTRIBUTIONAL ', X'PARAMETERS: ',E15.5) 49000 FORMAT(/1X,'SCHWARZ CRITERION WITH NEW LABELS AND NEW ', X'DISTRIBUTIONAL PARAMETERS: ',E15.5) 50000 FORMAT(//1X,'FOR MODEL WITH COMMON VARIANCE ', X'(NOT OPTIMIZED IN THIS PROGRAM): '//) 51000 FORMAT(1X,'AIC FOR MODEL WITH COMMON VARIANCE = ',E15.5/) 52000 FORMAT(/1X,'CLASS ',I2,' CONTAINS ONLY ',I4,' OBSERVATIONS: ', X'PRECISION MATRIX FROM PREVIOUS ITERATION IS BEING RETAINED'/) 53000 FORMAT(/1X,'MODEL WITH COMMON VARIANCE IS NOT'/ X1X,'OPTIMIZED IN THIS PROGRAM; HOWEVER, IT IS CLEAR'/ X1X,'THAT ONE SHOULD USE IT IF HERE THE VALUES OF THE MODEL-'/ X1X,'SELECTION CRITERIA FOR THAT MODEL ARE LESS THAN THOSE '/ X1X,'FOR THE MODEL WITH DIFFERENT VARIANCES,'/ X1X,'WHICH IS OPTIMIZED HERE.'//) 54000 FORMAT(/1X,'MINIMUM: ',/) 55000 FORMAT(/1X,'MAXIMUM: ',/) 56000 FORMAT(1X,'SCHWARZ CRITERION FOR MODEL WITH COMMON VARIANCE ', X'MATRIX = ',E15.5/) 57000 FORMAT(1X,'AIC FOR MODEL WITH DIFFERENT VARIANCES = ', XE15.5/) 58000 FORMAT(1X,'SCHWARZ CRITERION FOR MODEL WITH DIFFERENT ', X'VARIANCES = ', E15.5/) 59000 FORMAT(/,1X,'NUMBER OF PARAMETERS = ',I4//) 60000 FORMAT(1X,'NO OBSERVATIONS IN GROUP ',I3,'. STOP') 61000 FORMAT(//1X,'VARIANCE FOR CLASS ',I2/) 62000 FORMAT(///1X,'CLASS VARIANCES ', X' (DIVISORS ARE ONE LESS THAN NUMBER IN GROUP):'/) 63000 FORMAT(/1X,'MARGINAL PROB.VECTOR:',(9F11.4/)) END