bic                  package:mclust                  R Documentation

_B_I_C _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:

     Bayesian Information Criterion for MVN mixture models with
     possibly one  Poisson noise term.

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

     bic(data, modelid, z, eps, tol, itmax, equal = F, noise = F, Vinv)

_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. 

     ...: other arguments, including a quantity `eps' for determining
          singularity in the covariance, and the following: 

       z: matrix of conditional probabilities. `z' should have a row
          for each observation in `data', and a column for each
          component of the mixture. If `z' is missing, a single cluster
          is assumed (all noise if `noise = T'). 

     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 the mixing
          proportions are equal in the model. The default is to assume
          they are unequal. 

   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 the
          function `hypvol' 

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

     An object of class `"bic"' which is the Bayesian Information
     Criterion for the given mixture model and given conditional
     probabilites. The model parameters  and reciprocal condition
     estimate are returned as attributes.

_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:

     C. Fraley and A. E. Raftery, How many clusters? Which clustering
     method? Answers via model-based cluster analysis. Technical Report
     No. 329, Dept. of Statistics, U. of Washington (February 1998).

     R. Kass and A. E. Raftery, Bayes Factors. Journal of the American 
     Statistical Association90:773-795 (1995).

_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 = "VVV"), 3)
     z <- me( iris[,1:4], ctoz(cl), modelid = "VVV")
     bic(iris[,1:4], modelid = "VVV", z = z)

