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EM Algorithm for Mixtures of Multinomials

multmixEM.Rd

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

Either An nxp matrix of data (multinomial counts), where n is the sample size and p is the number of multinomial bins, or the output of the makemultdata function. It is not necessary that all of the rows contain the same number of multinomial trials (i.e., the row sums of y need not be identical).

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 Dirichlet. If both lambda and theta are NULL, then number of components is determined by k.

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.

restarts

The number of times the algorithm restarted due to unacceptable choice of initial values.

ft

A character vector giving the name of the function.

See also

compCDF, makemultdata, multmixmodel.sel

References

  • McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley and Sons, Inc.

  • Elmore, R. T., Hettmansperger, T. P. and Xuan, F. (2004) The Sign Statistic, One-Way Layouts and Mixture Models, Statistical Science 19(4), 579–587.

Examples

## The sulfur content of the coal seams in Texas

set.seed(100)
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)
#> number of iterations= 29 
em.out[1:4]
#> $y
#>      [,1] [,2]
#> [1,]    2    5
#> [2,]    4    4
#> [3,]    1    8
#> [4,]    6    2
#> [5,]    8    2
#> 
#> $lambda
#> [1] 0.4259325 0.5740675
#> 
#> $theta
#>          theta.1   theta.2
#> comp.1 0.2192859 0.7807141
#> comp.2 0.6936807 0.3063193
#> 
#> $loglik
#> [1] -10.16364
#>