mixAK (version 2.2)

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 class 'NMixEM':
print(x, \dots)

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 $n$

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

## 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)