rmvnormmix: Simulate from Multivariate (repeated measures) Mixtures of Normals

Description

Simulate from a mixture of multivariate zero-correlation normal distributions

Usage

rmvnormmix(n, lambda=1, mu=0, sigma=1)

Value

rmvnormmix returns an \(n\times r\) matrix in which each row is a sample from one of the components of a mixture of zero-correlation multivariate normals. The mixture structure induces nonzero correlations among the coordinates.

Arguments

n: Number of cases to simulate.
lambda: Vector of mixture probabilities with length equal to \(m\), the desired number of components. This is assumed to sum to 1; if not, it is normalized.
mu: Matrix of means of dimensions \(m\times r\), where \(m\) is the number of components (subpopulations) and \(r\) is the number of coordinates (repeated measurements) per case. Note: mu is automatically coerced to a matrix with \(m\) rows even if it is not given in this form, which can lead to unexpected behavior in some cases.
sigma: Matrix of standard deviations, same dimensions as mu. The coordinates within a case are independent, conditional on the mixture component. (There is marginal correlation among the coordinates, but this is due to the mixture structure only.) Note: sigma is automatically coerced to a matrix with \(m\) rows even if it is not given in this form, which can lead to unexpected behavior in some cases.

Details

It is possible to generate univariate standard normal random variables using the default values (but why bother?). The case of conditionally iid coordinates is covered by the situation in which all columns in mu and sigma are identical.

Examples

Run this code

##Generate data from a 2-component mixture of trivariate normals.

set.seed(100)
n <- 200
lambda <- rep(1, 2)/2
mu <- matrix(2*(1:6), 2, 3)
sigma <- matrix(1,2,3)
mydata<-rmvnormmix(n, lambda, mu, sigma)

## Now check to see if we can estimate mixture densities well:
title <- paste("Does this resemble N(", mu[1,], ",1) and N(", mu[2,],",1)?",
                sep="")
plot(npEM(mydata, 2), title=title)