mstep                 package:mclust                 R Documentation

_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:

     M-step for estimating parameters given conditional probabilities
     in a MVN mixture model with possibly one Poisson noise term.

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

     mstep(data, modelid, z, ...)

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

    data: matrix of observations. 

 modelid: An integer specifying a parameterization of the MVN
          covariance matrix defined  by volume, shape and orientation
          charactertistics of the underlying clusters.  The allowed
          values for `modelid' and their interpretation are as follows:
          `"EI"' : uniform spherical, `"VI"' : spherical, `"EEE"' :
          uniform variance, `"VVV"' : unconstrained variance, `"EEV"' :
          uniform shape and volume, `"VEV"' : uniform shape. 

       z: matrix of conditional probabilities. `z' should have a row
          for each observation in `data', and a column for each
          component of the mixture. 

     ...: additional arguments, as follows: 

     eps: Tolerance for determining singularity in the covariance
          matrix. The precise  definition of `eps' varies the
          parameterization, each of which has a default. 

   equal: Logical variable indicating whether or not to assume equal
          proportions in the mixture. Default : `F'. 

   noise: Logical variable indicating whether or not to include a
          Poisson noise term in the model. Default : `F'. 

    Vinv: An estimate of the inverse hypervolume of the data region
          (needed only if `noise = T'). Default : determined by
          function `hypvol' 

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

     A list whose components are the parameter estimates corresponding
     to `z':

      mu: matrix whose columns are the Gaussian group means. 

   sigma: group variance matrix. 

    prob: probabilities (mixing proportions) for each group (present
          only when `equal = T'). The loglikelihood is returned as an
          attribute. 

_N_O_T_E:

     The reciprocal condition estimate returned as an attribute ranges
     in value between 0 and 1. The closer this estimate is to zero, the
     more likely it is that the corresponding EM result (and BIC) are
     contaminated by roundoff error.

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

     G. Celeux and G. Govaert, Gaussian parsimonious clustering models,
     Pattern Recognition, 28:781-793 (1995).

     A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum Likelihood
     from Incomplete Data via the EM Algorithm, Journal of the Royal
     Statistical Society, Series B, 39:1-22 (1977).

     G. J. MacLachlan and K. E. Basford, The EM Algorithm and
     Extensions, Wiley, (1997).

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

     `me', `estep'

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

     data(iris)
     cl <- mhclass(mhtree(iris[,1:4], modelid = "VVV"),3)
     z <- me( iris[,1:4], modelid = "VVV", ctoz(cl))
     pars <- mstep(iris[,1:4], modelid="VVV", z)

