mixAK (version 5.8)

NMixEM: 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 NMixEM
print(x, ...)

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 \(n\)

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.

Author

Arnošt Komárek

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

if (FALSE) {
## 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)
}