Specification of variance parameters for the various types of Gaussian mixture models.

`mclustVariance(modelName, d = NULL, G = 2)`

- modelName
A character string specifying the model.

- d
A integer specifying the dimension of the data.

- G
An integer specifying the number of components in the mixture model.

The `variance`

component in the parameters list from the
output to e.g. `me`

or `mstep`

or input to e.g. `estep`

may contain one or more of the following arguments, depending on the model:

`modelName`

A character string indicating the model.

`d`

The dimension of the data.

`G`

The number of components in the mixture model.

`sigmasq`

for the one-dimensional models (

`"E"`

,`"V"`

) and spherical models (`"EII"`

,`"VII"`

). This is either a vector whose*k*th component is the variance for the*k*th component in the mixture model (`"V"`

and`"VII"`

), or a scalar giving the common variance for all components in the mixture model (`"E"`

and`"EII"`

).`Sigma`

For the equal variance models

`"EII"`

,`"EEI"`

, and`"EEE"`

. A*d*by*d*matrix giving the common covariance for all components of the mixture model.`cholSigma`

For the equal variance model "EEE". A

*d*by*d*upper triangular matrix giving the Cholesky factor of the common covariance for all components of the mixture model.`sigma`

For all multidimensional mixture models. A

*d*by*d*by*G*matrix array whose`[,,k]`

th entry is the covariance matrix for the*k*th component of the mixture model.`cholsigma`

For the unconstrained covariance mixture model

`"VVV"`

. A*d*by*d*by*G*matrix array whose`[,,k]`

th entry is the upper triangular Cholesky factor of the covariance matrix for the*k*th component of the mixture model.`scale`

For diagonal models

`"EEI"`

,`"EVI"`

,`"VEI"`

,`"VVI"`

and constant-shape models`"EEV"`

and`"VEV"`

. Either a*G*-vector giving the scale of the covariance (the*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.`shape`

For diagonal models

`"EEI"`

,`"EVI"`

,`"VEI"`

,`"VVI"`

and constant-shape models`"EEV"`

and`"VEV"`

. Either a*G*by*d*matrix in which the*k*th column is the shape of the covariance matrix (normalized to have determinant 1) for the*k*th component, or a*d*-vector giving a common shape for all components.`orientation`

For the constant-shape models

`"EEV"`

and`"VEV"`

. Either a*d*by*d*by*G*array whose`[,,k]`

th entry is the orthonomal matrix whose columns are the eigenvectors of the covariance matrix of the*k*th component, or a*d*by*d*orthonormal matrix if the mixture components have a common orientation. The`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
`-1`

is used as a placeholder for unknown nonzero entries.