

bic(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

_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"' : uni-
          form spherical, `"VI"' : spherical, `"EEE"' : uni-
          form variance, `"VVV"' : unconstrained variance,
          `"EEV"' : uniform shape and volume, `"VEV"' : uni-
          form 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 Infor-
     mation Criterion for the given mixture model and given
     conditional probabilites. The model parameters and
     reciprocal condition estimate are returned as
     attributes.

_D_E_S_C_R_I_P_T_I_O_N_:

     Bayesian Information Criterion for MVN mixture models
     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_:

     C. Fraley and A. E. Raftery, How many clusters? Which
     clustering method?  Answers via model-based cluster
     analysis. Technical Report No. 329, Dept. of Statis-
     tics, 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)

