me                  package:mclust                  R Documentation

_E_M _a_l_g_o_r_i_t_h_m _s_t_a_r_t_i_n_g _w_i_t_h _M-_s_t_e_p _f_o_r _p_a_r_a_m_e_t_e_r_i_z_e_d _M_V_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:

     Implements the EM algorithm for parameterized MVN mixture models,
     starting with the maximization step.

_U_s_a_g_e:

     me(modelName, data, z, ...)

_A_r_g_u_m_e_n_t_s:

modelName: A character string indicating the model: 
           "E": equal variance  (one-dimensional) 
           "V": variable variance (one-dimensional)
            "EII": spherical, equal volume 
           "VII": spherical, unequal volume 
           "EEI": diagonal, equal volume and shape
            "VEI": diagonal, varying volume, equal shape
            "EVI": diagonal, equal volume, varying shape 
           "VVI": diagonal, varying volume and shape 
           "EEE": ellipsoidal, equal volume, shape, and orientation 
           "EEV": ellipsoidal, equal volume and equal shape
           "VEV": ellipsoidal, equal shape 
           "VVV": ellipsoidal, varying volume, shape, and orientation  

    data: A numeric vector, matrix, or data frame of observations.
          Categorical variables are not allowed. If a matrix or data
          frame, rows correspond to observations and columns correspond
          to variables. 

       z: A matrix whose '[i,k]'th entry is the conditional probability
          of the ith observation belonging to the _k_th component of
          the mixture.   

     ...: Any number of the following:

        _e_p_s A scalar tolerance for deciding when to terminate
             computations due to computational singularity in
             covariances. Smaller values of 'eps' allow computations to
             proceed nearer to singularity. The default is
             '.Mclust\$eps'. 

             For those models with iterative M-step ("VEI", "VEV"), two
             values can be entered for 'eps', in which case the second
             value is used for determining singularity in the M-step. 

        _t_o_l A scalar tolerance for relative convergence of the
             loglikelihood. The default is '.Mclust\$tol'.

             For those models with iterative M-step ("VEI", "VEV"), two
             values can be entered for 'tol', in which case the second
             value governs parameter convergence in the M-step.  

        _i_t_m_a_x An integer limit on the number of EM iterations. The
             default is '.Mclust\$itmax'. For those models with
             iterative M-step ("VEI", "VEV"), two values can be entered
             for 'itmax', in which case the second value is an upper
             limit on the number of iterations in the M-step. 

        _e_q_u_a_l_P_r_o Logical variable indicating whether or not the mixing
             proportions are equal in the model. The default is
             '.Mclust\$equalPro'.

        _w_a_r_n_S_i_n_g_u_l_a_r A logical value indicating whether or not a
             warning should be issued whenever a singularity is
             encountered. The default is '.Mclust\$warnSingular'.

        _n_o_i_s_e A logical value indicating whether or not the model
             includes a Poisson noise component. The default assumes
             there is no noise component. 

        _V_i_n_v An estimate of the reciprocal hypervolume of the data
             region. The default is determined by applying function
             'hypvol' to the data. Used only when 'noise = TRUE'. 

_V_a_l_u_e:

     A list including the following components:  

      mu: A matrix whose kth column is the mean of the _k_th component
          of the mixture model.  

   sigma: For multidimensional models, a three dimensional array  in
          which the '[,,k]'th entry gives the the covariance for the
          _k_th group in the best model. <br> For one-dimensional
          models, either a scalar giving a common variance for the
          groups or a vector whose entries are the variances for each
          group in the best model. 

     pro: A vector whose _k_th component is the mixing proportion for
          the _k_th component of the mixture model. 

       z: A matrix whose '[i,k]'th entry is the conditional probability
          of the _i_th observation belonging to the _k_th component of
          the mixture.   

  loglik: The logliklihood for the data in the mixture model.  

modelName: A character string identifying the model (same as the input
          argument). 

        "_i_n_f_o" Information on the iteration.

        "_w_a_r_n" An appropriate warning if problems are encountered in
             the computations.

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

     C. Fraley and A. E. Raftery (2002a). Model-based clustering,
     discriminant analysis, and density estimation. _Journal of the
     American Statistical Association 97:611-631_. See <URL:
     http://www.stat.washington.edu/mclust>. 

     C. Fraley and A. E. Raftery (2002b). MCLUST:Software for
     model-based clustering, density estimation and  discriminant
     analysis.  Technical Report, Department of Statistics, University
     of Washington. See <URL: http://www.stat.washington.edu/mclust>.

_S_e_e _A_l_s_o:

     'meE',..., 'meVVV', 'em', 'mstep', 'estep', 'mclustOptions'

_E_x_a_m_p_l_e_s:

     data(iris)
     irisMatrix <- as.matrix(iris[,1:4])
     irisClass <- iris[,5]
      
     me(modelName = "VVV", data = irisMatrix, z = unmap(irisClass))

