NMixEM {mixAK}

EM algorithm for a homoscedastic normal mixture

Description

This function computes ML estimates of the parameters of the p-dimensional K-component normal mixture using the EM algorithm

Usage

NMixEM(y, K, weight, mean, Sigma, toler=1e-5, maxiter=500)

## S3 method for class 'NMixEM'
print(x, ...)

Arguments

y

vector (if p=1) matrix or data frame (if p > 1) with data. Rows correspond to observations, columns correspond to margins.

K

required number of mixture components.

weight

a numeric vector with initial mixture weights.

If not given, initial weights are all equal to 1/K.

mean

vector or matrix of initial mixture means.

For p=1 this should be a vector of length K, for p>1 this should be a K\times p matrix with mixture means in rows.

Sigma

number or p\times p matrix giving the initial variance/covariance matrix.

toler

tolerance to determine convergence.

maxiter

maximum number of iterations of the EM algorithm.

x

an object of class NMixEM.

...

additional arguments passed to the default print method.

Value

An object of class NMixEM which has the following components:

K

number of mixture components

weight

estimated mixture weights

mean

estimated mixture means

Sigma

estimated covariance matrix

loglik

log-likelihood value at fitted values

aic

Akaike information criterion (-2\hat{\ell} + 2\nu), where \hat{\ell} stands for the log-likelihood value at fitted values and \nu for the number of free model parameters

bic

Bayesian (Schwarz) information criterion (-2\hat{\ell} + \log(n)\,\nu), where \hat{\ell} stands for the log-likelihood value at fitted values and \nu for the number of free model parameters, and n for the sample size

iter

number of iterations of the EM algorithm used to get the solution

iter.loglik

values of the log-likelihood at iterations of the EM algorithm

iter.Qfun

values of the EM objective function at iterations of the EM algorithm

dim

dimension p

nobs

number of observations n

Author(s)

Arnošt Komárek [e-mail]

References

Dempster, A. P., Laird, N. M., Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.

Examples

## Not run: 
## Estimates for 3-component mixture in  Anderson's iris data
## ==========================================================
data(iris, package="datasets")
summary(iris)

VARS <- names(iris)[1:4]
fit <- NMixEM(iris[, VARS], K = 3)
print(fit)

apply(subset(iris, Species == "versicolor")[, VARS], 2, mean)
apply(subset(iris, Species == "setosa")[, VARS], 2, mean)
apply(subset(iris, Species == "virginica")[, VARS], 2, mean)

## Estimates of 6-component mixture in Galaxy data
## ==================================================
data(Galaxy, package="mixAK")
summary(Galaxy)

fit2 <- NMixEM(Galaxy, K = 6)
y <- seq(5, 40, length=300)
fy <- dMVNmixture(y, weight=fit2$weight, mean=fit2$mean,
                     Sigma=rep(fit2$Sigma, fit2$K))
hist(Galaxy, prob=TRUE, breaks=seq(5, 40, by=0.5),
     main="", xlab="Velocity (km/sec)", col="sandybrown")
lines(y, fy, col="darkblue", lwd=2)

## End(Not run)