Revision 1c995ef374a8438306839bffe3c09b7c524aebdd authored by Derek Young on 28 April 2009, 07:56:28 UTC, committed by cran-robot on 28 April 2009, 07:56:28 UTC
1 parent cda9e55
mvnormalmixEM.Rd
\name{mvnormalmixEM}
\title{EM Algorithm for Mixtures of Multivariate Normals}
\alias{mvnormalmixEM}
\usage{
mvnormalmixEM(x, lambda = NULL, mu = NULL, sigma = NULL, k = 2,
arbmean = TRUE, arbvar = TRUE, epsilon = 1e-08,
maxit = 10000, verb = FALSE)
}
\description{
Return EM algorithm output for mixtures of multivariate normal distributions.
}
\arguments{
\item{x}{A matrix of size nxp consisting of the data.}
\item{lambda}{Initial value of mixing proportions. Entries should sum to
1. This determines number of components. If NULL, then \code{lambda} is
random from uniform Dirichlet and number of
components is determined by \code{mu}.}
\item{mu}{A list of size k consisting of initial values for the p-vector mean parameters.
If NULL, then the vectors are generated from a normal distribution with
mean and standard deviation according to a binning method done on the data.
If both \code{lambda} and \code{mu} are NULL, then number of components is determined by \code{sigma}.}
\item{sigma}{A list of size k consisting of initial values for the pxp variance-covariance matrices.
If NULL, then \code{sigma} is generated using the data.
If \code{lambda}, \code{mu}, and \code{sigma} are
NULL, then number of components is determined by \code{k}.}
\item{k}{Number of components. Ignored unless \code{lambda}, \code{mu}, and \code{sigma}
are all NULL.}
\item{arbmean}{If TRUE, then the component densities are allowed to have different \code{mu}s. If FALSE, then
a scale mixture will be fit.}
\item{arbvar}{If TRUE, then the component densities are allowed to have different \code{sigma}s. If FALSE, then
a location mixture will be fit.}
\item{epsilon}{The convergence criterion.}
\item{maxit}{The maximum number of iterations.}
\item{verb}{If TRUE, then various updates are printed during each iteration of the algorithm.}
}
\value{
\code{normalmixEM} returns a list of class \code{mixEM} with items:
\item{x}{The raw data.}
\item{lambda}{The final mixing proportions.}
\item{mu}{A list of with the final mean vectors.}
\item{sigma}{A list with the final variance-covariance matrices.}
\item{loglik}{The final log-likelihood.}
\item{posterior}{An nxk matrix of posterior probabilities for
observations.}
\item{all.loglik}{A vector of each iteration's log-likelihood.}
\item{restarts}{The number of times the algorithm restarted due to unacceptable choice of initial values.}
\item{ft}{A character vector giving the name of the function.}
}
\seealso{
\code{\link{normalmixEM}}
}
\references{
McLachlan, G. J. and Peel, D. (2000) \emph{Finite Mixture Models}, John Wiley \& Sons, Inc.
}
\examples{
##Fitting randomly generated data with a 2-component location mixture of bivariate normals.
x.1<-rmvnorm(40, c(0, 0))
x.2<-rmvnorm(60, c(3, 4))
X.1<-rbind(x.1, x.2)
mu<-list(c(0, 0), c(3, 4))
out.1<-mvnormalmixEM(X.1, arbvar = FALSE, mu = mu,
epsilon = 1e-02)
out.1[2:5]
##Fitting randomly generated data with a 2-component scale mixture of bivariate normals.
x.3<-rmvnorm(40, c(0, 0), sigma =
matrix(c(200, 1, 1, 150), 2, 2))
x.4<-rmvnorm(60, c(0, 0))
X.2<-rbind(x.3, x.4)
lambda<-c(0.40, 0.60)
sigma<-list(diag(1, 2), matrix(c(200, 1, 1, 150), 2, 2))
out.2<-mvnormalmixEM(X.2, arbmean = FALSE,
sigma = sigma, lambda = lambda,
epsilon = 1e-02)
out.2[2:5]
}
\keyword{file}
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