

mstep(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

_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"' : uni-
          form spherical, `"VI"' : spherical, `"EEE"' : uni-
          form variance, `"VVV"' : unconstrained variance,
          `"EEV"' : uniform shape and volume, `"VEV"' : uni-
          form 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 loglikeli-
          hood is returned as an attribute.

_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.

_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 clus-
     tering 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)

