estep                 package:mclust                 R Documentation

_E-_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 expectation step of EM algorithm for parameterized
     MVN mixture models.

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

     estep(modelName, data, mu, ...)

_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.  

      mu: The mean for each component. If there is more than one
          component, 'mu' is a matrix whose columns are the means of
          the components.  

     ...: Arguments for model-specific functions. Specifically:

             *  An argument describing the variance (depends on the
                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").

             _d_e_c_o_m_p for the diagonal models ("EEI", "VEI", "EVI",
                  "VVI") and some ellipsoidal models ("EEV", "VEV").
                  This is a list described in 'cdens'.

             _S_i_g_m_a for the equal variance model "EEE". A _d_ by _d_
                  matrix giving the common covariance for all
                  components of the mixture model.

             _s_i_g_m_a for the unconstrained variance model "VVV". 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. 

                  The form of the variance specification is the same as
                  for the output for the 'em', 'me', or 'mstep' methods
                  for the specified mixture model. 

        _p_r_o Mixing proportions for the components of the mixture. There
             should one more mixing proportion than the number of MVN
             components if the mixture model includes a Poisson noise
             term. 

        _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'. 

        _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'.  

        _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 'pro' includes an
             additional mixing proportion for a noise component.

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

     This function can be used with an indirect or list call using
     'do.call', allowing the output of e.g. 'mstep' to be passed
     without the need to specify individual parameters as arguments.

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

     A list including the following components:  

       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). 

             *  '"warn"': 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:

     'estepE', ..., 'estepVVV', 'em', 'mstep', 'do.call',
     'mclustOptions'

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

     data(iris)
     irisMatrix <- as.matrix(iris[,1:4])
     irisClass <- iris[,5]

     msEst <- mstep(modelName = "EII", data = irisMatrix, 
                    z = unmap(irisClass))
     names(msEst)

     estep(modelName = msEst$modelName, data = irisMatrix,
           mu = msEst$mu, sigmasq = msEst$sigmasq, pro = msEst$pro)           
     ## Not run: 
     do.call("estep", c(list(data = irisMatrix), msEst))   ## alternative call
     ## End(Not run)

