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\name{mclustVariance}
\alias{mclustVariance}
\title{
Template for variance specification for parameterized Gaussian mixture models
}
\description{
Specification of variance parameters for the various types
of Gaussian mixture models.
}
\usage{
mclustVariance(modelName, d = NULL, G = 2)
}
\arguments{
\item{modelName}{A character string specifying the model.}
\item{d}{A integer specifying the dimension of the data.}
\item{G}{An integer specifying the number of components in the mixture model.}
}
\details{The \code{variance} component in the \code{parameters} list from the
output to e.g. \code{me} or \code{mstep} or input to e.g. \code{estep} may contain one or more of the following arguments, depending on the model:
\describe{
\item{\code{modelName}}{
A character string indicating the model.
}
\item{\code{d}}{
The dimension of the data.
}
\item{\code{G}}{
The number of components in the mixture model.
}
\item{\code{sigmasq}}{
for the one-dimensional models (\code{"E"}, \code{"V"}) and spherical
models (\code{"EII"}, \code{"VII"}). This is either a vector whose
\emph{k}th component is the variance for the \emph{k}th component in
the mixture model (\code{"V"} and \code{"VII"}), or a scalar giving
the common variance for all components in the mixture model (\code{"E"}
and \code{"EII"}).
}
\item{\code{Sigma}}{
For the equal variance models \code{"EII"}, \code{"EEI"}, and
\code{"EEE"}.
A \emph{d} by \emph{d} matrix giving the common covariance for all
components of the mixture model.
}
\item{\code{cholSigma}}{
For the equal variance model \code{"EEE"}.
A \emph{d} by \emph{d} upper triangular matrix giving the
Cholesky factor of the common covariance for all
components of the mixture model.
}
\item{\code{sigma}}{
For all multidimensional mixture models. A
\emph{d} by \emph{d} by \emph{G} matrix array whose
\code{[,,k]}th entry is the covariance matrix for
the \emph{k}th component of the mixture model.
}
\item{\code{cholsigma}}{
For the unconstrained covariance mixture model \code{"VVV"}.
A \emph{d} by \emph{d} by \emph{G} matrix array whose
\code{[,,k]}th entry is the upper triangular Cholesky factor
of the covariance matrix for the \emph{k}th component of the
mixture model.
}
\item{\code{scale}}{
For diagonal models \code{"EEI"}, \code{"EVI"}, \code{"VEI"},
\code{"VVI"} and constant-shape models \code{"EEV"} and \code{"VEV"}.
Either a \emph{G}-vector giving the scale of the covariance (the
\emph{d}th root of its determinant) for each component in the
mixture model, or a single numeric value if the scale is the
same for each component.
}
\item{\code{shape}}{
For diagonal models \code{"EEI"}, \code{"EVI"}, \code{"VEI"},
\code{"VVI"} and constant-shape models \code{"EEV"} and \code{"VEV"}.
Either a \emph{G} by \emph{d} matrix in which the \emph{k}th
column is the shape of the covariance matrix (normalized to have
determinant 1) for the \emph{k}th component, or a
\emph{d}-vector giving a common shape for all components.
}
\item{\code{orientation}}{
For the constant-shape models \code{"EEV"} and \code{"VEV"}.
Either a \emph{d} by \emph{d} by \emph{G} array whose
\code{[,,k]}th entry is the orthonomal matrix whose
columns are the eigenvectors of the covariance matrix of
the \emph{k}th component, or a \emph{d} by \emph{d}
orthonormal matrix if the mixture components have a
common orientation. The \code{orientation} component
is not needed in spherical and diagonal models, since
the principal components are parallel to the coordinate axes
so that the orientation matrix is the identity.
}
}
In all cases, the value
\code{-1} is used as a placeholder for unknown nonzero entries.
}
\keyword{cluster}
|
