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, ...)

_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. The precise  definition of
          `eps' varies the parameterization, each of which has a
          default. 

          Furthermore `z', a 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').

          Next argument: `equal', a logical variable indicating whether
          or not the mixing proportions are equal in the model. The
          default is to assume they are unequal.

          The `noise' logical variable indicates whether or not to
          include a Poisson noise term in the model. Default : `F'. 

          Finally, `Vinv' gives 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)

