multmixEM: EM Algorithm for Mixtures of Multinomials

In mixtools: Tools for Analyzing Finite Mixture Models

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	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.

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.

See Also

compCDF, makemultdata, multmixmodel.sel

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)
em.out[1:4]

mixtools documentation built on April 12, 2025, 2:31 a.m.