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:

     E-step for estimating conditional probabilities from parameter
     estimates in an MVN mixture model having possibly one Poisson
     noise term.

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

     estep(data, modelid, mu, ...)

_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. 

      mu: matrix whose columns are the Gaussian group means. 

     ...: additional arguments, as follows: 

 sigmasq: 

   sigma: group variances (`sigmasq' - spherical models) or covariances
          (`sigma' - elliposidal models) 

    prob: mixing proportions (probabilities) for each group. If `prob'
          is missing,  the number of groups is assumed to be the number
          of columns in `mu' (no noise). A Poisson noise term will
          appear in the conditional probabilities if `length(prob)' is
          equal to `ncol(mu)+1'. 

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

    Vinv: An estimate of the inverse hypervolume of the data region
          (needed only if `prob' indicates a noise term). Default :
          determined by function `hypvol' 

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

     the conditional probablilities corresponding to the parameter
     estimates. 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', `mstep'

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

     data(iris)
     cl <- mhclass(mhtree(iris[,1:4], modelid="VI"), 3)
     z <- me( iris[,1:4], ctoz(cl), modelid = "VI")
     pars <- mstep( iris[,1:4], modelid = "VI", z)
     estep(iris[,1:4], modelid = "VI", pars$mu, pars$sigma, pars$prob)

