mixtools (version 0.1.0)

multmixEM: EM Algorithm for Mixtures of Multinomials

Description

Return EM algorithm output for mixtures of multinomial distributions.

Usage

multmixEM(y, lambda = NULL, theta = NULL, k = 2,
          maxit = 10000, epsilon = 1e-08, verb = FALSE)

Arguments

y

An nxp matrix of data (multinomial counts), where n is the sample size and p is the number of multinomial bins.

lambda

Initial value of mixing proportions. Entries should sum to 1. This determines number of components. If NULL, then lambda is random from uniform Dirichlet and number of components is determined by theta.

theta

Initial value of theta parameters. Should be a kxp matrix, where p is the number of columns of y and k is number of components. Each row of theta should sum to 1. If NULL, then each row is random from uniform Diri

k

Number of components. Ignored unless lambda and theta are NULL.

epsilon

The convergence criterion.

maxit

The maximum number of iterations.

verb

If TRUE, then various updates are printed during each iteration of the algorithm.

Value

• multmixEM returns a list of class mixEM with items:
• y
  The raw data.
• lambda
  The final mixing proportions.
• theta
  The final multinomial parameters.
• loglik
  The final log-likelihood.
• posterior
  An nxk matrix of posterior probabilities for observations.
• all.loglik
  A vector of each iteration's log-likelihood.
• ft
  A character vector giving the name of the function.

References

McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley & Sons, Inc. Elmore, R. T., Hettmansperger, T. H. and Xuan, F. (2004) The Sign Statistic, One-Way Layouts and Mixture Models, Statistical Science 19(4), 579--587.

See Also

compCDF, makemultdata, multmixmodel.sel

Examples

## The sulfur content of the coal seams in Texas

A<-c(1.51, 1.92, 1.08, 2.04, 2.14, 1.76, 1.17)
B<-c(1.69, 0.64, .9, 1.41, 1.01, .84, 1.28, 1.59) 
C<-c(1.56, 1.22, 1.32, 1.39, 1.33, 1.54, 1.04, 2.25, 1.49) 
D<-c(1.3, .75, 1.26, .69, .62, .9, 1.2, .32) 
E<-c(.73, .8, .9, 1.24, .82, .72, .57, 1.18, .54, 1.3)

dis.coal<-makemultdata(A, B, C, D, E, 
                       cuts = median(c(A, B, C, D, E)))
em.out<-multmixEM(dis.coal$y, lambda = dis.coal$lambda, 
                  theta = dis.coal$theta)
em.out[1:4]