Although the starting parameter list P may be specified directly,
Note also that any matrices specified must be positive definite.
This function calculates an initial P from D and a starting
value for Z.
initParamList(D, Z)an object of class multimixSettings---see
data_organise for details.
an \(n \times q\) matrix, where \(n\) is the number
of rows of dframe and \(q\) is the number of components in the
mixture. During the fitting \(Z_{ij}\) holds the currently estimated
probability that observation \(i\) belongs to component \(j\).
Often Z is initialized to a matrix of indicator columns for a
partition of the data. It is also common to initialize Z to be the
final Z from the fitting of a simpler model.
an object of class multimixParamList which is a list
with the following elements:
dstat -- list of matrices for each discrete variable
not included in a location model. The matrix for each discrete variable
is made up of a column of length \(q\) for each level (value) of the
variable giving the expected proportion of each level (column) for each
mixture component (row). Rows sum to 1.
ldstat -- list of matrices for each discrete
variable within a location model. The matrix for each discrete variable is
made up of a column of length \(q\) for each level (value) of the
variable giving the expected proportion of each level (column) for each
mixture component (row). Rows sum to 1.
ostat -- matrix with a column for each continuous
variable outside any location mode whose \(q\) rows give the current
estimated mean for each mixture component.
ostat2 -- matrix with a column for each continuous
variable outside any location mode whose \(q\)rows give the current
estimated mean square for each mixture component.
osvar -- matrix with a column for each continuous
variable outside any location mode whose \(q\) rows give the current
estimated variance for each mixture component.
cstat -- list with a member for each nontrivial,
fully continuous, partition cell, that is not including discrete cells or
cells listed in lcdep, each member being a matrix with a column for each
continuous variable in that cell, whose \(q\) rows give the current
estimated mean for each mixture component.
cstat2 -- list with a member for each nontrivial,
fully continuous, partition cell, each member being a matrix with a column
for each continuous variable in that cell, whose \(q\) rows give the
current estimated mean square for each mixture component.
cvar -- list with a member for each nontrivial,
fully continuous, partition cell, each member being a matrix with a column
for each continuous variable in that cell, whose \(q\) rows give the
current estimated variance for each mixture component.
cpstat -- list with a member for each nontrivial,
fully continuous, partition cell, each member being the matrix with rows
for each of the \(q\) mixture components and columns for each pair of
continuous variables in that cell, as ordered by pair.index.
The matrix
elements are the currently expected products of the variable pairs
arranged by component and pair.
ccov -- list with a member for each nontrivial,
fully continuous, partition cell, each member being the matrix with rows
for each of the \(q\) mixture components and columns for each pair of
continuous variables in that cell, as ordered by pair.index. The matrix
elements are the currently expected covariances of the variable pairs
arranged by component and pair.
MVMV -- list with a member for each nontrivial,
fully continuous, partition cell, each member being a list with members
for each of the \(q\) mixture components whose values are the
covariance matrix estimates for that cell and component.
lcstat -- list with a member for location partition
cell, each member being a matrix with a column for each continuous
variable in that cell, whose \(q\) rows give the current estimated
mean for each mixture component.
lcstat2 -- list with a member for location partition
cell, each member being a matrix with a column for each continuous
variable in that cell, whose \(q\) rows give the current estimated
mean square for each mixture component.
lcpstat -- list with a member for each location
cell, each member being the matrix with rows for each of the
\(q\) mixture components and columns for each pair of continuous
variables in that cell, as ordered by pair.index. The matrix
elements are the currently expected products of the variable pairs
arranged by component and pair.
lccov -- list with a member for each location cell,
each member being the matrix with rows for each of the \(q\) mixture
components and columns for each pair of continuous variables in that cell,
as ordered by pair.index. The matrix elements are the
currently estimated covariances of the variable pairs arranged by
component and pair.
ldxcstat -- list with a member for each location
partition cell, each member being a list with a member for each level of
the cell's discrete variable that member being a matrix of mean values of
the continuous variables for each level-class combination.
pistat -- vector containing estimates of population
proportion in each cluster; column means of \(Z\) matrix.
W -- matrix of weights of observation \(i\) in
cluster \(j\); the columns of the \(Z\) matrix are each
multiplied by constant to give \(W\) columns summing to 1.