rmvnorm {dae}

generates a vector of random values from a multivariate normal distribution

Description

Generates a vector of random values from an n-dimensional multivariate normal distribution whose mean is given by the n-vector mean and variance by the n x n symmetric matrix V. It uses the method described by Ripley (1987, p.98)

Usage

rmvnorm(mean, V, method = 'eigenanalysis')

Arguments

mean

The mean vector of the multivariate normal distribution from which the random values are to be generated.

V

The variance matrix of the multivariate normal distribution from which the random values are to be generated.

method

The method used to decompose the variance matrix in producing a a matrix to transform the iid standard normal values. The two methods available are 'eigenanalysis' and 'choleski', where only the first letter of each option is obligatory. The default method is eigenanalysis, which is slower but is likely to be more stable than Choleski decomposition.

Details

The method is: a) uses either the eigenvalue or Choleski decomposition of the variance matrix, V, to form the matrix that transforms an iid vector of values to a vector with variance V; b) generate a vector of length equal to mean of standard normal values; c) premultiply the vector of standard normal values by the transpose of the upper triangular factor and, to the result, add mean.

Value

A vector of length n, equal to the length of mean.

Author(s)

Chris Brien

References

Ripley, B. D. (1987) Stochastic simulation. Wiley, New York.

See Also

fac.ar1mat, fac.vcmat, in package dae, rnorm, and chol.

Examples

## set up a two-level factor and a three-level factor, both of length 12
A <- factor(rep(1:2, each=6))
B <- factor(rep(1:3, each=2, times=2))

## generate random values from a multivariate normal for which 
#the mean is 20 for all variables and 
#the variance matrix has random effects for factor A, ar1 pattern for B and 
#residual random variation
mean <- rep(20, 12)
V <- fac.vcmat(A, 5) + fac.ar1mat(B, 0.6) + 2*mat.I(12)
y <- rmvnorm(mean, V)