normalmixEM: EM Algorithm for Mixtures of Univariate Normals

Description

Return EM algorithm output for mixtures of normal distributions.

Usage

normalmixEM(x, lambda = NULL, mu = NULL, sigma = NULL, k = 2,
            arbmean = TRUE, arbvar = TRUE, epsilon = 1e-08, 
            maxit = 1000, maxrestarts=20, verb = FALSE, fast=FALSE)

Arguments

A vector of length n consisting of the data.

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 mu.

A k-vector of initial values for the mean parameters. If NULL, then the vector is generated from a normal distribution according to a binning method done on the data. If both lambda and mu are NULL, then number of com

sigma

A k-vector of initial values for the standard deviation parameters. If NULL, then 1/sigma$^2$ has random exponential entries according to a binning method done on the data. If lambda, mu, and sigm

Number of components. Ignored unless lambda, mu, and sigma are all NULL.

arbmean

If TRUE, then the component densities are allowed to have different mus. If FALSE, then a scale mixture will be fit.

arbvar

If TRUE, then the component densities are allowed to have different sigmas. If FALSE, then a location mixture will be fit.

epsilon

The convergence criterion. Convergence is declared when the change in the observed data log-likelihood increases by less than epsilon.

maxit

The maximum number of iterations.

maxrestarts

The maximum number of restarts allowed in case of a problem with the particular starting values chosen (each restart uses randomly chosen starting values).

verb

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

fast

If TRUE and k==2 and arbmean==TRUE, then use normalmixEM2comp, which is a much faster version of the EM algorithm for this case. This version is less protected against certain kinds of u

Value

normalmixEM returns a list of class mixEM with items:
xThe raw data.
lambdaThe final mixing proportions.
muThe final mean parameters.
sigmaThe final standard deviations. If arbmean = FALSE, then only the smallest standard deviation is returned. See scale below.
scaleIf arbmean = FALSE, then the scale factor for the component standard deviations is returned. Otherwise, this is omitted from the output.
loglikThe final log-likelihood.
posteriorAn nxk matrix of posterior probabilities for observations.
all.loglikA vector of each iteration's log-likelihood. This vector includes both the initial and the final values; thus, the number of iterations is one less than its length.
restartsThe number of times the algorithm restarted due to unacceptable choice of initial values.
ftA character vector giving the name of the function.

References

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

Examples

Run this code

##Analyzing the Old Faithful geyser data with a 2-component mixture of normals.

data(faithful)
attach(faithful)
system.time(out<-normalmixEM(waiting, arbvar = FALSE, epsilon = 1e-03))
out
system.time(out2<-normalmixEM(waiting, arbvar = FALSE, epsilon = 1e-03, fast=TRUE))
out2 # same thing but much faster