mclustVariance            package:mclust            R Documentation

_T_e_m_p_l_a_t_e _f_o_r _v_a_r_i_a_n_c_e _s_p_e_c_i_f_i_c_a_t_i_o_n _f_o_r _p_a_r_a_m_e_t_e_r_i_z_e_d 
_G_a_u_s_s_i_a_n _m_i_x_t_u_r_e _m_o_d_e_l_s.

_D_e_s_c_r_i_p_t_i_o_n:

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

_D_e_t_a_i_l_s:

        *  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:

        _m_o_d_e_l_N_a_m_e A character string indicating the model.

        _d The dimension of the data.

        _G The number of components in the mixture model.

        _s_i_g_m_a_s_q 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").

        _S_i_g_m_a 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.

        _c_h_o_l_S_i_g_m_a 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.

        _s_i_g_m_a 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. 

        _c_h_o_l_s_i_g_m_a For the unconstrained covaraince 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. 

        _s_c_a_l_e 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.

        _s_h_a_p_e 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.

        _o_r_i_e_n_t_a_t_i_o_n For the constant-shape models "EEV" and "VEV".
             Either a _d_ by _d_ by _G_ array whose '[,,k]'th entry is
             the orthonomal matrix of 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.

_R_e_f_e_r_e_n_c_e_s:

     C. Fraley and A. E. Raftery (2002). Model-based clustering,
     discriminant analysis, and density estimation. _Journal of the
     American Statistical Association 97:611:631_.

     C. Fraley and A. E. Raftery (2006). MCLUST Version 3 for R: Normal
     Mixture Modeling and Model-Based Clustering,  Technical Report no.
     504, Department of Statistics, University of Washington.

