mclust (version 1.1-7)

estep: E-step for parameterized MVN mixture models

Description

E-step for estimating conditional probabilities from parameter estimates in an MVN mixture model having possibly one Poisson noise term.

Usage

estep(data, modelid, mu, ...)

Arguments

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"

mu

matrix whose columns are the Gaussian group means.

...

additional arguments, as follows:

sigmasq

sigma

group variances (sigmasq - spherical models) or covariances (sigma - elliposidal models)

prob

mixing proportions (probabilities) for each group. If prob is missing, the number of groups is assumed to be the number of columns in mu (no noise). A Poisson noise term will appear in the conditional probabilities if leng

eps

Tolerance for determining singularity in the covariance matrix. The precise definition of eps varies the parameterization, each of which has a default.

Vinv

An estimate of the inverse hypervolume of the data region (needed only if prob indicates a noise term). Default : determined by function hypvol

Value

• the conditional probablilities corresponding to the parameter estimates. The loglikelihood is returned as an attribute.

NOTE

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.

References

G. Celeux and G. Govaert, Gaussian parsimonious clustering models, Pattern Recognition,28:781-793 (1995).

A. P. Dempster, N. M. Laird and D. B. Rubin, Maximum Likelihood from Incomplete Data via the EM Algorithm, Journal of the Royal Statistical Society, Series B,39:1-22 (1977).

G. J. MacLachlan and K. E. Basford, The EM Algorithm and Extensions, Wiley (1997).

See Also

me, mstep

Examples

Run this code

data(iris)
cl <- mhclass(mhtree(iris[,1:4], modelid="VI"), 3)
z <- me( iris[,1:4], ctoz(cl), modelid = "VI")
pars <- mstep( iris[,1:4], modelid = "VI", z)
estep(iris[,1:4], modelid = "VI", pars$mu, pars$sigma, pars$prob)

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