simE                 package:mclust                 R Documentation

_S_i_m_u_l_a_t_e _f_r_o_m _a _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

_D_e_s_c_r_i_p_t_i_o_n:

     Simulate data from a parameterized MVN mixture model.

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

     simE(mu, sigmasq, pro, ..., seed = 0)
     simV(mu, sigmasq, pro, ..., seed = 0)
     simEII(mu, sigmasq, pro, ..., seed = 0)
     simVII(mu, sigmasq, pro, ..., seed = 0)
     simEEI(mu, decomp, pro, ..., seed = 0)
     simVEI(mu, decomp, pro, ..., seed = 0)
     simEVI(mu, decomp, pro, ..., seed = 0)
     simVVI(mu, decomp, pro, ..., seed = 0)
     simEEE(mu, pro, ..., seed = 0)
     simEEV(mu, decomp, pro, ..., seed = 0)
     simVEV(mu, decomp, pro, ..., seed = 0)
     simVVV(mu, pro, ..., seed = 0)

_A_r_g_u_m_e_n_t_s:

      mu: The mean for each component. If there is more than one
          component, 'mu' is a matrix whose columns are the means of
          the components. 

 sigmasq: for the one-dimensional models ("E", "V") and spherical
          models ("EII", "VII"). This is either a vector whose _k_th
          component is the variance for the _k_th component in the
          mixture model ("V" and "VII"), or a scalar giving the common
          variance for all components in the mixture model ("E" and
          "EII").  

  decomp: for the diagonal models ("EEI", "VEI", "EVI", "VVI") and some
          ellipsoidal models ("EEV", "VEV"). This is a list described
          in 'cdens'. 

     pro: Component mixing proportions. If missing, equal proportions
          are assumed. 

          *  Other terms describing variance:

          _S_i_g_m_a for the equal variance model "EEE". A _d_ by _d_ matrix
               giving the common covariance for all components of the
               mixture model.

          _s_i_g_m_a for the unconstrained variance model "VVV". A _d_ by
               _d_ by _G_ matrix array whose  '[,,k]'th entry is the
               covariance matrix for the _k_th component of the mixture
               model.

               The form of the variance specification is the same as
               for the output for the 'em', 'me', or 'mstep' methods
               for the specified mixture model.  

     _n An integer specifying the number of data points to be simulated.

    seed: A integer between 0 and 1000, inclusive, for specifying a
          seed for  random class assignment. The default value is 0. 

_D_e_t_a_i_l_s:

     This function can be used with an indirect or list call using
     'do.call', allowing the output of e.g. 'mstep', 'em' 'me', or
     'EMclust', to be passed directly without the need to specify
     individual parameters as arguments.

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

     A data set consisting of 'n' points simulated from  the specified
     MVN mixture model.

_R_e_f_e_r_e_n_c_e_s:

     C. Fraley and A. E. Raftery (2002a). Model-based clustering,
     discriminant analysis, and density estimation. _Journal of the
     American Statistical Association 97:611-631_.  See <URL:
     http://www.stat.washington.edu/mclust>. 

     C. Fraley and A. E. Raftery (2002b). MCLUST:Software for
     model-based clustering, density estimation and  discriminant
     analysis.  Technical Report, Department of Statistics, University
     of Washington. See <URL: http://www.stat.washington.edu/mclust>.

_S_e_e _A_l_s_o:

     'sim', 'EMclust', 'mstepE', 'do.call'

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

     d <- 2
     G <- 2
     scale <- 1
     shape <- c(1, 9)

     O1 <- diag(2)
     O2 <- diag(2)[,c(2,1)]
     O <- array(cbind(O1,O2), c(2, 2, 2))
     O

     decomp <- list(d= d, G = G, scale = scale, shape = shape, orientation = O)
     mu <- matrix(0, d, G) ## center at the origin
     simdat <- simEEV(n=200, mu=mu, decomp=decomp, pro = c(1,1))

     cl <- attr(simdat, "classification")
     sigma <- array(apply(O, 3, function(x,y) crossprod(x*y), 
                      y = sqrt(scale*shape)), c(2,2,2))
     paramList <- list(mu = mu, sigma = sigma)
     coordProj( simdat, paramList = paramList, classification = cl)

