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NAME

       multimix, multimix-prep - automatically discover classes in data

SYNOPSIS

       multimix

       multimix-prep

DESCRIPTION

       multimix  fits  a  mixture  of  multivariate  distributions to a set of
       observations using the EM algorithm. The data  file  may  contain  both
       categorical and continuous variables.

       multimix prompts for the names of the data and parameter files.

       The  assignment  of  the  observations  to  groups  and  the  posterior
       probabilities  are  written  to   GROUPS.OUT.    Parameter   estimates,
       convergence information, and group assignment probabilities are written
       to GENERAL.OUT.

       If multimix does not converge after ITER=200 iterations, the  estimates
       of the parameters will be written to EMPARAMEST.OUT. This file can then
       be used as the parameter input file for multimix if desired.

       multimix is limited to a maximum of
              1500 observations (IOB=1500)
              6 groups (IK6=6)
              15 attributes and partition cells (IP15=15)
              10 levels of categories (IM10=10)
              200 iterations to convergence (ITER=200)
       Recompilation is required to change these parameters.

DATA FILE

       The data file has one line for each observation.   Each  line  has  one
       entry  for each variable.  Only the first NVAR entries on each line are
       read.

PARAMETER FILE

       The parameter file contains free field values which describe  the  data
       and  the  fitting  models.  multimix-prep will ask the user a series of
       questions and write a suitable parameter file.  If the  starting  point
       for  the  fit  is given by specifying initial group assignments for the
       observations,  then  the  user  should  prepare  the  file   of   group
       assignments  before starting multimix-prep.  The file format is simple:
       the Ith line of the file contains an integer between 1  and  NG  giving
       the  group  number of the Ith observation.  (The experienced user finds
       it faster to edit old parameter files into new ones.)

       multimix 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.

       The first five values are

       NG     The number of groups (distributions) in the finite mixture to be
              fitted.

       NOBS   The number of observations.

       NVAR   The number of attributes.

       NPAR   The  number  of  partition  cells (sets of attributes associated
              within each distribution).

       ISPEC  Flag indicating how the starting point is specified for the fit:
                     1   Initial parameter estimates are specified.

                     2   Observations are assigned to groups.
       Next come eight arrays of data:

       JP     JP(J)  is  the  column  of  the  data  array  into which the Jth
              attribute of the data file will be stored, where J varies from 1
              to  NVAR.   For  example, suppose we want the third attribute in
              the first column, attribute 4 in the second column, attribute  7
              in  the  3rd  column,  and then attributes 1, 2, 5, and 6.  Then
              JP(J) = 4 5 1 2 6 7 3, for J=1,...,7.

       IP     IP(L) is the number of attributes in  the  Lth  partition  cell,
              L=1,...,NPAR.

       IPC    IPC(L)  is  the  number  of  continuous  attributes  in  the Lth
              partition cell.

       ISV    ISV(L) gives the index J of the start of partition cell L.  E.g.
              if attributes 6, 7, and 8 are in the same partition cell L, then
              ISV(L)=6 and IEV(L)=8.

       IEV    IEV(L) gives the index J of the end of partition cell L.

       IPARTYPE
              IPARTYPE(L) is  an  indicator  giving  the  type  of  model  for
              partition L:
                     1   for a categorical model.

                     2   for a multivariate normal model.

                     3   for a location model.

       IVARTYPE
              IVARTYPE(J) is an indicator for the type of attribute J:
                     1   for a categorical attribute.

                     2   for a multivariate normal attribute;

                     3   for a categorical attribute in a location model;

                     4    for  a  multivariate  normal attribute in a location
              model.

       NCAT   NCAT(J) is the number of  categories  for  the  Jth  categorical
              attribute.  For continuous attributes, NCAT(J) should be 0.

       If   observations   are   assigned  to  groups  (ISPEC=2),  then  those
       assignments are next:

       IGRP   IGRP(I) is the index of the group that observation I is in.

       If observations are not assigned to groups (ISPEC=1), then estimates of
       the parameters are next:

       PI     PI(K)   is   the   estimated   mixing  proportion  for  group  K
              (K=1,...,NG).

       The parameters for each group depend on the type of attribute:

       THETA  THETA(K,J,M)  is  the  estimated  probability   that   the   Jth
              categorical  attribute  is  at  level  M, given that in group K.
              Repeat  for  each   attribute,   J=ISV(L),IEV(L).    categorical
              attributes only

       EMU    EMU(K,L,J)  is  the estimated mean vector for group K, partition
              cell L and attribute J.  multivariate normal model only

       THETA  THETA(K,J,M)  is  the  estimated  probability   that   the   Jth
              categorical attribute in the location model is at level M, given
              that in group K.  categorical attributes only

       EMUL   EMUL(K,L,J,M)  is  the  estimated  mean  vector  for  group   K,
              partition  cell  L  and  attribute  J,  at  the Mth level of the
              categorical  attribute  in  the  location  model.   multivariate
              normal model only

       VARIX  ((VARIX(K,L,I,J),J=1,IPC(L)),  I=1,IPC(L))  An entry in VARIX is
              the estimated covariance between attributes I and J for group K,
              partition cell L, where I=1,...,IPC(L), and J=1,...,IPC(L).

       The   required   parameters  are  read  in  for  each  partition  cell,
       L=1,...,NPAR.  For example, if the attributes within the partition cell
       are  all  categorical,  that  is,  ITYPE(L)=1,  then  THETA(K,J,M), for
       M=1,...,NCAT(J) is required for the attribute in that partition cell.

       If  the  attributes  within  the   partition   cell   are   continuous,
       multivariate  normal  attributes, that is ITYPE(L)=2, then estimates of
       EMU(K,L,J) are required for each attribute.

       If the attributes within the partition cell follow the location  model,
       that  is, ITYPE(L)=3, then THETA(K,J,M),M=1,...,NCAT(J) is required for
       the categorical attribute, and EMUL(K,L,J,M),M=1,...,IM(L) is  required
       for each continuous multivariate normal attribute.  (Note that IM(L) is
       the number of categories of the categorical attribute  associated  with
       the location model.)

       The estimates are read in first for group 1, then for group 2, etc.

EXAMPLES

       See /usr/share/doc/multimix/examples.

FILES

       GROUPS.OUT  multimix  output:  the  assignment  of  the observations to
       groups and the posterior probabilities.  If observations were initially
       assigned to groups (ISPEC=2), these assignments may be different.  Some
       are likely to be different if the fitting distributions overlap.

       GENERAL.OUT   multimix   output:   parameter   estimates,   convergence
       information, and group assignment probabilities.

       EMPARAMEST.OUT   multimix   output  on  failure  to  converge:  current
       parameter estimates.  This file can then be used as the parameter input
       file for multimix if desired.

AUTHORS

       Lynette    A.    Hunt    <lah@waikato.ac.nz>   and   Murray   Jorgensen
       <maj@waikato.ac.nz>.

SEE ALSO

       /usr/share/doc/multimix/paper.ps.gz
       /usr/share/doc/multimix/talk.ps.gz
       /usr/share/doc/multimix/notes.ps.gz
       /usr/share/doc/multimix/PPAPER.ps.gz
       /usr/share/doc/multimix/alltables.ps.gz
       autoclass(1).

                               December 10, 2001                   MULTIMIX(1)