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PROGRAM MULTIMIX
* This program fits a mixture of multivariate distributions using
* the EM algorithm. The data file contains both categorical and
* continuous variables.
* If the program does not converge after iter=200 iterations, the
* estimates of the parameters will be entered into
* EMPARAMEST.OUT. This file can then be used as the parameter
* input file for PROGRAM MULTIMIX if desired.
* The assignment of the observations to groups (IGP(i)) and the
* posterior probabilities (Zij's) are entered into GROUPS.OUT.
* This file can be used in MINITAB etc. for further analysis.
* NOTE:
* (1) THIS PROGRAM REQUIRES VARIABLES IN A PARTITION TO BE STORED
* CONTIGUOUSLY. HENCE THE DATA IS READ IN WITH THE VARIABLE ORDER
* BEING SPECIFIED BY JP(J). INTYPE(J) AND NCAT(J) BOTH REFER TO
* THE REARRANGED DATA
* (2) IF SDENS=0, THEN Z(II,K) IS SET TO 0.01
* (3) THE PROGRAM CURRENTLY HAS A MAXIMUM OF
* 1500 OBSERVATIONS (iob=1500)
* 6 GROUPS (ik6=6)
* 15 ATTRIBUTES & 15 PARTITIONS (ip15=15)
* 10 LEVELS OF CATEGORIES (im10=10)
* 200 ITERATIONS FOR CONVERGENCE (iter=200)
* ******ALTER IF REQUIRED******
* (REMEMBER TO ALTER PARAMETERS IN DETINV ALSO)
* The parameter file contains:-
* NG - the number of groups
* NOBS - the number of observations
* NVAR - the number of variables
* NPAR - the number of partitions
* ISPEC - an indicator variable for a specified grouping of the
* observations (1 = observations are not specified into
* groups, 2 = observations are specified into groups)
* JP(j) - column in the data array in which the jTH variable of
* the file will be stored
* IP(l) - number of variables in the lTH partition, l=1,NPAR
* IPC(l) - number of continuous variables in partition l, l=1,NPAR
* ISV(l) - indicator starting value for the partition, l=1,NPAR
* IEV(l) - indicator end value for the partition, l=1,NPAR
* ITYPE(l) - indicator giving the type of model each partition is
* (1 = categorical, 2 = MVN, 3 = location models), l=1,NPAR
* INTYPE(j) - an indicator variable giving type of variable, j=1,NVAR
* (1 = categorical variable, 2 = continuous variable,
* 3 = categorical variable involved in location model,
* 4 = continuous variable involved in the location model)
* NCAT(j) - number of categories of jTH variable.
* (For continuous variables, set NCAT(J)=0)
* PI(k) - estimated mixing proportions for each group, k=1,NG
* THETA(K,J,M) - estimated probability that the jTH categorical
* variable is at level M, given that in group k
* EMUL(k,l,j,m)- estimated mean vector for each group, each
* partition, and each location of the location model variables
* EMU(K,L,J) -estimated mean vector for each group and each
* partition of continuous variables
* VARIX(K,L,I,J) -estimated covariance matrices for each group
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
CHARACTER*16 infile, datafile
PARAMETER (PIE=3.141592653589792, iob=2000, ip15=15, ik6=6,
: im10=10, iter=200)
DIMENSION EMU(ik6,ip15,ip15),VAR(ik6,ip15,ip15,ip15),
: Z(iob,ik6), PI(ik6), DENS(ik6,ip15), VARIN(ik6,ip15,ip15,ip15),
: ZSUM(ik6), XSUM(ik6,ip15), ADET(ik6,ip15), CLOGLI(iter),
: VARIX(ik6,ip15,ip15,ip15), APRODENS(ik6), IP(ip15), IPC(ip15),
: ISV(ip15), IEV(ip15), ITYPE(ip15), EMUL(ik6,ip15,ip15,im10),
: THETA(ik6,ip15,0:im10), PROB(ik6,iob),INTYPE(ip15),NCAT(ip15),
: IM(ip15), IGP(iob), NUM(ik6), XSUM2(ik6,ip15,ip15),ZM(ik6,ip15),
: IGRP(iob), JP(ip15), IX(iob,ip15), X(iob,ip15)
PRINT *, ' MIXTURE ESTIMATION BY EM'
PRINT *, '-------------------------------'
PRINT *, 'Data file: '
READ (*,10) datafile
10 FORMAT (A16)
PRINT *, 'Parameter file: '
READ (*,10) infile
OPEN (7, FILE='GENERAL.OUT', STATUS='NEW')
OPEN (8, FILE=datafile, STATUS='OLD')
OPEN (9, FILE=infile, STATUS='OLD')
OPEN(12, FILE='GROUPS.OUT',STATUS='NEW')
READ (9,*) NG, NOBS, NVAR, NPAR,ISPEC
READ (9,*) (JP(J),J=1,NVAR)
READ (9,*) (IP(L),L=1,NPAR)
READ (9,*) (IPC(L), L=1,NPAR)
READ (9,*) (ISV(L),L=1,NPAR)
READ (9,*) (IEV(L),L=1,NPAR)
READ (9,*) (ITYPE(L),L=1,NPAR)
READ (9,*) (INTYPE(J),J=1,NVAR)
READ (9,*) (NCAT(J),J=1,NVAR)
* read in estimates of the parameters if grouping not specified
IF(ISPEC.EQ.1) THEN
READ(9,*) (PI(K),K=1,NG)
DO 12 K=1,NG
DO 12 L=1,NPAR
IF (ITYPE(L).EQ.1) THEN
DO 13 J=ISV(L),IEV(L)
READ(9,*) (THETA(K,J,M),M=1,NCAT(J))
13 CONTINUE
ELSE IF(ITYPE(L).EQ.2) THEN
READ(9,*)(EMU(K,L,J),J=1,IPC(L))
ELSE IF(ITYPE(L).EQ.3) THEN
DO 14 J=ISV(L),IEV(L)
IF(INTYPE(J).EQ.3) THEN
READ(9,*)(THETA(K,J,M),M=1,NCAT(J))
IM(L)=NCAT(J)
END IF
14 CONTINUE
J1=0
DO 15 J=ISV(L),IEV(L)
IF(INTYPE(J).EQ.4) THEN
J1=J1+1
READ(9,*)
: (EMUL(K,L,J1,M),M=1,IM(L))
END IF
15 CONTINUE
END IF
12 CONTINUE
DO 16 K=1,NG
DO 16 L=1,NPAR
IF(ITYPE(L).NE.1)
: READ(9,*)((VARIX(K,L,I,J),J=1,IPC(L)),I=1,IPC(L))
16 CONTINUE
ELSE
READ(9,*) (IGRP(I),I=1,NOBS)
DO 18 I=1,NOBS
DO 18 K=1,NG
Z(I,K)=0.0
18 CONTINUE
DO 31 I=1,NOBS
IK=IGRP(I)
Z(I,IK)=1.0
31 CONTINUE
DO 33 L=1,NPAR
IF(ITYPE(L).EQ.3) THEN
DO 32 J=ISV(L),IEV(L)
IF (INTYPE(J).EQ.3) IM(L)=NCAT(J)
32 CONTINUE
END IF
33 CONTINUE
END IF
DO 17 I=1,NOBS
READ(8,* ) (X(I,JP(J)),J=1,NVAR)
17 CONTINUE
* Check the categorical variable to see if 0 is a category.
* Add 1 to the variables if it is so that Xij=0 is taken as
* level 1, Xij=1 is level 2 etc.
DO 80 J=1,NVAR
IF ((INTYPE(J).EQ.1).OR.(INTYPE(J).EQ.3)) THEN
IMIN=NINT(X(1,J))
DO 81 I=2,NOBS
INEXT=NINT(X(I,J))
IF(INEXT.LT.IMIN) IMIN=INEXT
81 CONTINUE
IF (IMIN.EQ.0) THEN
DO 82 I=1,NOBS
IX(I,J)=NINT(X(I,J)) + 1
82 CONTINUE
ELSE
DO 83 I=1,NOBS
IX(I,J)=NINT(X(I,J))
83 CONTINUE
END IF
END IF
80 CONTINUE
* print the input values
WRITE(7,50)NG,NOBS,NVAR,NPAR
50 FORMAT(/,' NO OF GROUPS IS ',I3,/,' NO OF OBSERVATIONS IS ',
: I5,/,' NO OF VARIABLES ',I3,/,' NO OF PARTITIONS', I3)
WRITE(7,51)(IP(L),L=1,NPAR)
51 FORMAT(/,' THE NO OF VARIABLES IN EACH PARTITION IS',/,10I3)
* Send to the M step if ISPEC = 2 (groups specified)
IF(ISPEC.EQ.2) GO TO 100
* otherwise, print the parameter estimates
WRITE(7,52)
52 FORMAT(/,' MIXING PROPORTIONS')
WRITE(7,53)(PI(K),K=1,NG)
53 FORMAT(/,10F6.3)
DO 56 K=1,NG
DO 56 L=1,NPAR
IF(ITYPE(L).EQ.1) THEN
WRITE(7,54) K
54 FORMAT(/,2X,' THETA(K,J,M) FOR GROUP ',I2)
DO 64 J=ISV(L),IEV(L)
WRITE(7,55)(THETA(K,J,M),M=1,NCAT(J))
55 FORMAT(10F8.4)
64 CONTINUE
ELSE IF(ITYPE(L).EQ.2) THEN
WRITE(7,57) K,L
57 FORMAT(/,' FOR GROUP ',I2,' AND PARTITION',I2,
: ' THE MEAN IS')
WRITE(7,58)(EMU(K,L,J),J=1,IPC(L))
58 FORMAT(10F12.6)
ELSE
WRITE(7,57) K,L
WRITE(7,58)((EMUL(K,L,J,M),M=1,IM(L)),J=1,IPC(L))
DO 62 J=ISV(L),IEV(L)
IF (INTYPE(J).EQ.3) THEN
WRITE(7,54)
WRITE(7,55)(THETA(K,J,M),M=1,NCAT(J))
END IF
62 CONTINUE
END IF
56 CONTINUE
DO 59 K=1,NG
DO 59 L=1,NPAR
IF (ITYPE(L).NE.1) THEN
WRITE(7,60) L,K
60 FORMAT(/,2X,'VARIANCE FOR PARTITION',I2,' AND GROUP',I2)
DO 63 I=1,IPC(L)
WRITE(7,61)(VARIX(K,L,I,J),J=1,IPC(L))
61 FORMAT(10F13.6)
63 CONTINUE
END IF
59 CONTINUE
DO 74 L=1,NPAR
IF (ITYPE(L).EQ.1) THEN
WRITE(7,75) L,IP(L),ITYPE(L)
75 FORMAT(' PARTITION',I3,' HAS',I2,' VARIABLES',/,' ITYPE',
: ' IS',I2,' HENCE A CATEGORICAL MODEL FOR THIS PARTITION')
ELSE IF (ITYPE(L).EQ.2) THEN
WRITE(7,76) L,IP(L),ITYPE(L)
76 FORMAT(' PARTITION',I3,' HAS',I2,' VARIABLES',/,' ITYPE',
: ' IS',I2,' HENCE A MVN MODEL FOR THIS PARTITION')
ELSE
WRITE(7,77) L,IP(L),ITYPE(L)
77 FORMAT(' PARTITION',I3,' HAS',I2,'VARIABLES',/,' ITYPE',
: ' IS',I2,' HENCE A LOCATION MODEL FOR THIS PARTITION')
END IF
74 CONTINUE
* E step of the EM algorithm.
* Estimate the complete data sufficient statistics given the
* data, & current values of means,variances and mixing proportions.
* call DETINV to calculate the determinants and inverses for each
* covariance matrix. This subroutine uses NAG to calculate
* the determinants and inverses.
ICNT=1
99999 DO 19 L=1,NPAR
IF (ITYPE(L).NE.1) THEN
ITYPE_CURR=ITYPE(L)
IPC_CURR=IPC(L)
L_CURR=L
CALL DETINV(NG,L_CURR,IPC_CURR,ADET,VARIX,VARIN)
END IF
19 CONTINUE
ALL=0.0
DO 20 II = 1,NOBS
SDENS = 0.0
DO 21 K=1,NG
PROB(K,II)=1.0
APRODENS(K)=1.0
* evaluate the discrete variables contribution to the densities
DO 22 J=1,NVAR
IF((INTYPE(J).EQ.1).OR.(INTYPE(J).EQ.3))
: PROB(K,II) = THETA(K,J,IX(II,J))*PROB(K,II)
22 CONTINUE
* evaluate the continuous variables contribution to the densities
DO 23 L=1,NPAR
IF (ITYPE(L).NE.1) THEN
DENS(K,L)=0.0
I1=0
* (i) evaluate the MVN contribution
IF(ITYPE(L).EQ.2) THEN
DO 24 I=ISV(L),IEV(L)
J1=0
I1=I1+1
DO 24 J=ISV(L),IEV(L)
J1=J1+1
DENS(K,L) = DENS(K,L)
: + (X(II,I)-EMU(K,L,I1))*VARIN(K,L,I1,J1)*(X(II,J)-EMU(K,L,J1))
24 CONTINUE
* (ii) evaluate the continuous location variables contribution
ELSE IF(ITYPE(L).EQ.3) THEN
DO 25 I=ISV(L),IEV(L)
IF(INTYPE(I).EQ.3) M=IX(II,I)
25 CONTINUE
DO 26 I=ISV(L),IEV(L)
IF (INTYPE(I).EQ.4) THEN
J1=0
I1=I1+1
DO 30 J=ISV(L),IEV(L)
IF (INTYPE(J).EQ.4) THEN
J1=J1+1
DENS(K,L)=DENS(K,L) + (X(II,I)-EMUL(K,L,I1,M))
: *VARIN(K,L,I1,J1)*(X(II,J)-EMUL(K,L,J1,M))
END IF
30 CONTINUE
END IF
26 CONTINUE
END IF
DENS(K,L) = DEXP(-0.5*DENS(K,L))
A=0.5*FLOAT(IPC(L))
DENS(K,L)=DENS(K,L)/((2.0*PIE)**(A)*DSQRT(ADET(K,L)))
APRODENS(K)=APRODENS(K)*DENS(K,L)
END IF
23 CONTINUE
APRODENS(K)=APRODENS(K)*PROB(K,II)*PI(K)
SDENS=SDENS+APRODENS(K)
21 CONTINUE
IF (SDENS.NE.0.0) THEN
DO 27 K=1,NG
Z(II,K)=APRODENS(K)/SDENS
27 CONTINUE
ALL=ALL+DLOG(SDENS)
ELSE
DO 28 K=1,NG
Z(II,K)=0.01
28 CONTINUE
WRITE(7,29)II
29 FORMAT(//'SUM OF DENSITY FUNCTIONS IS ZERO',
: 'FOR OBSERVATION',I4)
END IF
20 CONTINUE
* Check on convergence - look at the likelihood function
* If the absolute value of the difference in 2 likelihoods is
* less than a tolerance value the estimates are written out.
* A check is made on the number of iterations (200 max).
* statement 100 - the M step
* statement 500 - print out the current estimates (algorithm
* has converged)
* statement 501 - algorithm hasn't converged, current estimates
* are printed out.
CLOGLI(ICNT) = ALL
WRITE(7,888) ICNT,CLOGLI(ICNT)
888 FORMAT(1X,'FOR LOOP',I5,' LOGLIKELIHOOD IS',F16.8)
IF (ICNT.LE.10) GO TO 100
C=1.D-06
TOL=ABS(CLOGLI(ICNT) - CLOGLI(ICNT-10))
IF(TOL.LE.C) GO TO 500
IF(ICNT.GE.iter) GO TO 501
* M step of the EM algorithm
* Calculate an updated estimate of the parameters
* means and covariances.
* (i) the mixing proportions,
100 DO 101 K=1,NG
ZSUM(K)=0.0
DO 102 II=1,NOBS
ZSUM(K)=ZSUM(K) + Z(II,K)
102 CONTINUE
PI(K) = ZSUM(K)/NOBS
101 CONTINUE
* (ii) the conditional probabilities
DO 103 K=1,NG
DO 103 L=1,NPAR
IF(ITYPE(L).EQ.1) THEN
DO 104 J=ISV(L),IEV(L)
DO 104 M=1,NCAT(J)
THETA(K,J,M) = 0.0
DO 105 II=1,NOBS
IF (IX(II,J).EQ.M) THETA(K,J,M)
: = THETA(K,J,M) + Z(II,K)
105 CONTINUE
THETA(K,J,M)=THETA(K,J,M)/ZSUM(K)
104 CONTINUE
ELSE IF(ITYPE(L).EQ.2) THEN
* (iii) the means (EMU(K,L,J))
J1=0
DO 106 J=ISV(L),IEV(L)
J1=J1+1
XSUM(K,J1)=0.0
DO 107 II=1,NOBS
XSUM(K,J1)=XSUM(K,J1) + X(II,J)*Z(II,K)
107 CONTINUE
EMU(K,L,J1)=XSUM(K,J1)/ZSUM(K)
106 CONTINUE
* (iv) the location model parameters
* (i)the discrete variable
ELSE IF(ITYPE(L).EQ.3) THEN
DO 108 J=ISV(L),IEV(L)
IF(INTYPE(J).EQ.3) THEN
DO 109 M=1,NCAT(J)
THETA(K,J,M)=0.0
DO 110 II=1,NOBS
IF(IX(II,J).EQ.M) THETA(K,J,M)
: = THETA(K,J,M) + Z(II,K)
110 CONTINUE
THETA(K,J,M)=THETA(K,J,M)/ZSUM(K)
109 CONTINUE
END IF
108 CONTINUE
* (ii) the continuous variables the means EMUL(K,L,J,M)
DO 111 J=ISV(L),IEV(L)
IF (INTYPE(J).EQ.3) THEN
DO 112 M=1,IM(L)
J1=0
DO 112 JJ=ISV(L),IEV(L)
IF (INTYPE(JJ).EQ.4) THEN
J1=J1+1
XSUM2(K,J1,M)=0.0
ZM(K,M)=0.0
DO 113 II=1,NOBS
IF(IX(II,J).EQ.M) THEN
XSUM2(K,J1,M)=XSUM2(K,J1,M) +
: X(II,JJ)*Z(II,K)
ZM(K,M)=ZM(K,M)+Z(II,K)
END IF
113 CONTINUE
EMUL(K,L,J1,M)=XSUM2(K,J1,M)/ZM(K,M)
END IF
112 CONTINUE
END IF
111 CONTINUE
WRITE(7,601)K,((EMUL(K,L,J1,M),M=1,IM(L)),J1=1,IPC(L))
601 FORMAT(/2X,'FOR GROUP',I2,' EMUL',10F10.4)
END IF
103 CONTINUE
* Calculate updated estimates of the variances
* (i) the multivariate normal data
DO 115 K=1,NG
DO 116 L=1,NPAR
IF (ITYPE(L).NE.1) THEN
DO 117 J=1,IPC(L)
DO 117 I=1,J
VAR(K,L,I,J)=0.0
117 CONTINUE
END IF
116 CONTINUE
DO 118 II=1,NOBS
DO 118 L=1,NPAR
IF (ITYPE(L).EQ.2) THEN
J1=0
DO 119 J=ISV(L),IEV(L)
I1=0
J1=J1+1
DO 119 I=ISV(L),ISV(L)+J1
I1=I1+1
VAR(K,L,I1,J1) = VAR(K,L,I1,J1) + (X(II,J)
: -EMU(K,L,J1))*(X(II,I)-EMU(K,L,I1))*Z(II,K)
119 CONTINUE
END IF
118 CONTINUE
* (ii) the continuous location data
DO 120 L=1,NPAR
IF (ITYPE(L).EQ.3) THEN
DO 121 J=ISV(L),IEV(L)
IF (INTYPE(J).EQ.3) THEN
DO 122 II=1,NOBS
DO 122 M=1,IM(L)
IF(IX(II,J).EQ.M) THEN
J1=0
DO 123 JJ=ISV(L),IEV(L)
IF (INTYPE(JJ).EQ.4) THEN
I1=0
J1=J1+1
DO 124 I=ISV(L),ISV(L)+J1
IF (INTYPE(I).EQ.4) THEN
I1=I1+1
VAR(K,L,I1,J1) = VAR(K,L,I1,J1)+(X(II,JJ)
: -EMUL(K,L,J1,M))*(X(II,I)-EMUL(K,L,I1,M))
: *Z(II,K)
END IF
124 CONTINUE
END IF
123 CONTINUE
END IF
122 CONTINUE
END IF
121 CONTINUE
END IF
120 CONTINUE
DO 126 L=1,NPAR
IF (ITYPE(L).NE.1) THEN
DO 125 J=1,IPC(L)
DO 125 I=1,J
VAR(K,L,I,J)=VAR(K,L,I,J)/ZSUM(K)
VAR(K,L,J,I)=VAR(K,L,I,J)
125 CONTINUE
END IF
126 CONTINUE
115 CONTINUE
* Make a copy of the covariance matrix before we use NAG
DO 130 K=1,NG
DO 130 L=1,NPAR
IF(ITYPE(L).NE.1) THEN
DO 131 J=1,IPC(L)
DO 131 I=1,IPC(L)
VARIX(K,L,I,J)=VAR(K,L,I,J)
131 CONTINUE
END IF
130 CONTINUE
ICNT=ICNT+1
* send back to the E step
GO TO 99999
* Write out the current estimates of the parameters.
* (1) If the algorithm has not converged:-
501 WRITE(7,502)
502 FORMAT(//'----------------------------------------------------')
WRITE(7,503) iter
503 FORMAT(//' THE EM ALGORITHM HAS NOT CONVERGED AFTER ',I3,
: /,'ITERATIONS BUT THE CURRENT ESTIMATES OF THE PARAMETERS ',
:/,'WILL BE PRINTED OUT.')
WRITE(7,502)
* The parameters are to be written to 'EMPARAMEST.DAT' to be
* used as input for the PROGRAM MULTIMIX. ISPEC is set to 1.
OPEN(11, FILE='EMPARAMEST.OUT',STATUS='NEW')
ISPEC=1
WRITE(11,504) NG, NOBS, NVAR, NPAR, ISPEC
504 FORMAT(1X,5I6)
WRITE(11,505) (IP(L),L=1,NPAR)
WRITE(11,505) (IPC(L),L=1,NPAR)
WRITE(11,505) (ISV(L),L=1,NPAR)
WRITE(11,505) (IEV(L),L=1,NPAR)
WRITE(11,505) (ITYPE(L),L=1,NPAR)
WRITE(11,505) (INTYPE(J),J=1,NVAR)
WRITE(11,505) (NCAT(J),J=1,NVAR)
505 FORMAT(10I4)
WRITE(11,506) (PI(K),K=1,NG)
506 FORMAT(10F10.6)
DO 507 K=1,NG
DO 507 L=1,NPAR
IF (ITYPE(L).EQ.1) THEN
DO 508 J=ISV(L),IEV(L)
WRITE(11,509)(THETA(K,J,M),M=1,NCAT(J))
509 FORMAT(10F10.6)
508 CONTINUE
ELSE IF(ITYPE(L).EQ.2) THEN
WRITE(11,510) (EMU(K,L,J),J=1,1,IPC(L))
510 FORMAT(10F13.6)
ELSE
DO 511 J=ISV(L),IEV(L)
IF (INTYPE(J).EQ.3) THEN
WRITE(11,509)(THETA(K,J,M),M=1,NCAT(J))
END IF
511 CONTINUE
DO 512 J=1,IPC(L)
WRITE(11,510) (EMUL(K,L,J,M),M=1,IM(L))
512 CONTINUE
END IF
507 CONTINUE
DO 513 K=1,NG
DO 513 L=1,NPAR
IF (ITYPE(L).NE.1) THEN
DO 514 I=1,IPC(L)
WRITE(11,515)(VARIX(K,L,I,J),J=1,IPC(L))
515 FORMAT(10F13.6)
514 CONTINUE
END IF
513 CONTINUE
* (2) the current estimates of the parameters are printed out
* Estimates of the proportions in each group and loglikelihood
500 WRITE(7,888) ICNT,CLOGLI(ICNT)
DO 540 K=1,NG
WRITE(7,541) K,PI(K)
541 FORMAT(//'THE ESTIMATE OF THE MIXING PROPORTION IN GROUP ',I3,
: ' IS ', F10.8)
540 CONTINUE
* estimates of the probabilities for each group
DO 525 K=1,NG
DO 525 L=1,NPAR
WRITE(7,524)K,L
524 FORMAT(//,'THE CURRENT ESTIMATES FOR GROUP',I3,' AND'
: ,' PARTITION ',I3, ' ARE ')
IF (ITYPE(L).EQ.1) THEN
DO 528 J=ISV(L),IEV(L)
WRITE(7,529)J
529 FORMAT(/,' FOR VARIABLE ',I3,' THETA(K,J,M) IS')
WRITE(7,530) (THETA(K,J,M),M=1,NCAT(J))
530 FORMAT(10F10.6)
528 CONTINUE
ELSE IF(ITYPE(L).EQ.2) THEN
* Estimate of the means for each group.
WRITE(7,531) (EMU(K,L,J),J=1,IPC(L))
531 FORMAT(/,' THE MEAN FOR THIS PARTITION IS ',/,10F13.6)
* estimates of the location model parameters
ELSE IF(ITYPE(L).EQ.3) THEN
DO 533 J=ISV(L),IEV(L)
IF (INTYPE(J).EQ.3) THEN
WRITE(7,534)J,(THETA(K,J,M),M=1,NCAT(J))
534 FORMAT(/,' FOR VARIABLE',I3,' THETA(K,J,M)'
:,' IS',10F10.6)
END IF
533 CONTINUE
J1=0
DO 535 J=ISV(L),IEV(L)
IF(INTYPE(J).EQ.4) THEN
J1=J1+1
WRITE(7,536) (EMUL(K,L,J1,M),M=1,IM(L))
536 FORMAT(/,1X,'THE MEAN FOR THE CONTINUOUS LOCATION'
:,' VARIABLES IS',/,10F13.6)
END IF
535 CONTINUE
END IF
525 CONTINUE
* Estimates of the variances for each group.
DO 523 K=1,NG
WRITE(7,526)K
526 FORMAT(/,' THE CURRENT ESTIMATE OF THE COVARIANCE MATRIX FOR',
:' GROUP',I3)
DO 523 L=1,NPAR
IF(ITYPE(L).NE.1) THEN
WRITE(7,522)L
522 FORMAT(' AND PARTITION ',I3)
DO 543 I=1,IPC(L)
WRITE(7,527)(VAR(K,L,I,J),J=1,IPC(L))
527 FORMAT(10F15.6)
543 CONTINUE
END IF
523 CONTINUE
* Determine the assignment of the observations to groups
DO 516 I=1,NOBS
IMAX = 1
DO 517 K=2,NG
IF(Z(I,K).GT.Z(I,IMAX)) THEN
IMAX=K
END IF
517 CONTINUE
IGP(I)=IMAX
516 CONTINUE
WRITE(7,542)
542 FORMAT(/,1X,'THE ASSIGNMENT OF OBSERVATIONS TO GROUPS',/)
WRITE(7,518) (IGP(I),I=1,NOBS)
518 FORMAT(10I3)
DO 537 K=1,NG
NUM(K)=0
537 CONTINUE
DO 538 I=1,NOBS
DO 538 K=1,NG
IF(IGP(I).EQ.K) NUM(K)=NUM(K)+1
538 CONTINUE
WRITE(7,539)(NUM(K),K=1,NG)
539 FORMAT(1X,/,' TOTAL NUMBERS IN EACH GROUP',/,10I5)
* have a look at the Zij,s, and write out the assigned groups and
* the Zij's to GROUPS.OUT
WRITE(7,521)
521 FORMAT(//'THE ESTIMATES OF THE POSTERIOR PROBALITIES')
DO 519 I=1,NOBS
WRITE(7,520)I,(Z(I,K),K=1,NG)
520 FORMAT('OBSERVATION',I4,2X,10F10.6)
WRITE(12,532) IGP(I), (Z(I,K),K=1,NG)
532 FORMAT(1X,I2,1X,10F9.6)
519 CONTINUE
END
SUBROUTINE DETINV(NG,L_CURR,IPC_CURR,ADET,VARIX,VARIN)
IMPLICIT DOUBLE PRECISION(A-H,O-Z)
PARAMETER (ik6=6,ip15=15,IIP=ip15+1)
DIMENSION VARIX(ik6,ip15,ip15,ip15),VARIN(ik6,ip15,ip15,ip15),
: ADET(ik6,ip15)
INTEGER IA,IT,NNULL
REAL*8 TEMP(100),WKSPCE(100),B(100),TOL,CMY(100),PROD,RMAX
IA=IIP
IB=IIP
NNULL = 0
DO 201 K=1,NG
IT=0
TOL=0.0
N=IPC_CURR
DO 202 J=1,IPC_CURR
TOL=TOL+SQRT(VARIX(K,L_CURR,J,J))
DO 202 I=1,J
IT=IT+1
TEMP(IT) = VARIX(K,L_CURR,I,J)
202 CONTINUE
TOL=(TOL/FLOAT(IPC_CURR))*0.000001
CALL SYMINV(TEMP,N,B,WKSPCE,NULL,IER,RMAX,CMY,TOL)
IF (IER.NE.0) THEN
WRITE(7,555) K,IER
555 FORMAT (/2X,'Terminal error in SYMINV for matrix',I3,
: ' as IFAULT is ',I3)
RETURN
ELSE
IF (NULL.NE.0) THEN
WRITE (7,556) K,NULL
556 FORMAT (/2X,'Rank deficiency of covariance matrix'
: ,I3,' is',I3)
WRITE (*,556) K,NULL
NNULL=NNULL+1
ENDIF
IT=0
PROD=1.0
DO 220 J=1,IPC_CURR
JJ=J*(J+1)/2
PROD=PROD*CMY(JJ)*CMY(JJ)
DO 220 I=1,J
IT=IT+1
VARIN(K,L_CURR,I,J)=B(IT)
VARIN(K,L_CURR,J,I)=VARIN(K,L_CURR,I,J)
220 CONTINUE
ADET(K,L_CURR)=PROD
ENDIF
201 CONTINUE
NULL=NNULL
RETURN
END
subroutine syminv(a,n,c,w,nullty,ifault,rmax,CMY,TOL)
implicit double precision (a-h,o-z)
c
c algorithm as7, applied statistics, vol.17, 1968.
c
c arguments:-
c a() = input, the symmetric matrix to be inverted, stored in
c lower triangular form
c n = input, order of the matrix
c c() = output, the inverse of a (a generalized inverse if c is
c singular), also stored in lower triangular.
c c and a may occupy the same locations.
c w() = workspace, dimension at least n.
c nullty = output, the rank deficiency of a.
c ifault = output, error indicator
c = 1 if n < 1
c = 2 if a is not +ve semi-definite
c = 0 otherwise
c rmax = output, approximate bound on the accuracy of the diagonal
c elements of c. e.g. if rmax = 1.e-04 then the diagonal
c elements of c will be accurate to about 4 dec. digits.
c
c latest revision - 18 april 1981
c
c***************************************************************************
c
dimension a(1),c(1),w(n),CMY(100)
nrow=n
ifault=1
if(nrow.le.0) go to 100
ifault=0
c
c cholesky factorization of a, result in c
c
call chola(a,nrow,c,nullty,ifault,rmax,w,TOL)
if(ifault.ne.0) go to 100
c
c invert c & form the product (cinv)'*cinv, where cinv is the inverse
c of c, row by row starting with the last row.
c irow = the row number, ndiag = location of last element in the row.
c
nn=nrow*(nrow+1)/2
do 200 imy=1,nn
200 cmy(imy)=c(imy)
irow=nrow
ndiag=nn
10 if(c(ndiag).eq.0.0) go to 60
l=ndiag
do 20 i=irow,nrow
w(i)=c(l)
l=l+i
20 continue
icol=nrow
jcol=nn
mdiag=nn
30 l=jcol
x=0.0
if(icol.eq.irow) x=1.0/w(irow)
k=nrow
40 if(k.eq.irow) go to 50
x=x-w(k)*c(l)
k=k-1
l=l-1
if(l.gt.mdiag) l=l-k+1
go to 40
50 c(l)=x/w(irow)
if(icol.eq.irow) go to 80
mdiag=mdiag-icol
icol=icol-1
jcol=jcol-1
go to 30
60 l=ndiag
do 70 j=irow,nrow
c(l)=0.0
l=l+j
70 continue
80 ndiag=ndiag-irow
irow=irow-1
if(irow.ne.0) go to 10
100 return
end
c
c
subroutine chola(a,n,u,nullty,ifault,rmax,r,TOL)
implicit double precision (a-h,o-z)
c
c algorithm as6, applied statistics, vol.17, 1968, with
c modifications by a.j.miller
c
c arguments:-
c a() = input, a +ve definite matrix stored in lower-triangular
c form.
c n = input, the order of a
c u() = output, a lower triangular matrix such that u*u' = a.
c a & u may occupy the same locations.
c nullty = output, the rank deficiency of a.
c ifault = output, error indicator
c = 1 if n < 1
c = 2 if a is not +ve semi-definite
c = 0 otherwise
c rmax = output, an estimate of the relative accuracy of the
c diagonal elements of u.
c r() = output, array containing bounds on the relative accuracy
c of each diagonal element of u.
c
c latest revision - 18 april 1981
c
c***************************************************************************
c
dimension a(1),u(1),r(n)
c
c eta should be set equal to the smallest +ve value such that
c 1.0 + eta is calculated as being greater than 1.0 in the accuracy
c being used.
c
C data eta/1.e-07/
ETA=TOL
ifault=1
if(n.le.0) go to 100
ifault=2
nullty=0
rmax=eta
r(1)=eta
j=1
k=0
c
c factorize column by column, icol = column no.
c
do 80 icol=1,n
l=0
c
c irow = row number within column icol
c
do 40 irow=1,icol
k=k+1
w=a(k)
if(irow.eq.icol) rsq=(w*eta)**2
m=j
do 10 i=1,irow
l=l+1
if(i.eq.irow) go to 20
w=w-u(l)*u(m)
if(irow.eq.icol) rsq=rsq+(u(l)**2*r(i))**2
m=m+1
10 continue
20 if(irow.eq.icol) go to 50
if(u(l).eq.0.0) go to 30
u(k)=w/u(l)
go to 40
30 u(k)=0.0
if(abs(w).gt.abs(rmax*a(k))) go to 100
40 continue
c
c end of row, estimate relative accuracy of diagonal element.
c
50 rsq=sqrt(rsq)
if(abs(w).le.5.*rsq) go to 60
if(w.lt.0.0) go to 100
u(k)=sqrt(w)
r(i)=rsq/w
if(r(i).gt.rmax) rmax=r(i)
go to 70
60 u(k)=0.0
nullty=nullty+1
70 j=j+icol
80 continue
ifault=0.0
100 return
end
|
