ggm (version 2.5.1)

rnormDag: Random sample from a decomposable Gaussian model

Description

Generates a sample from a mean centered multivariate normal distribution whose covariance matrix has a given triangular decomposition.

Usage

rnormDag(n, A, Delta)

Value

a matrix with n rows and nrow(A) columns, a sample from a multivariate normal distribution with mean zero and covariance matrix

S = solve(A) %*% diag(Delta) %*% t(solve(A)).

Arguments

n

an integer > 0, the sample size.

A

a square, upper triangular matrix with ones along the diagonal. It defines, together with Delta, the concentration matrix (and also the covariance matrix) of the multivariate normal. The order of A is the number of components of the normal.

Delta

a numeric vector of length equal to the number of columns of A.

Author

Giovanni M. Marchetti

Details

The value in position \((i,j)\) of A (with \(i < j\)) is a regression coefficient (with sign changed) in the regression of variable \(i\) on variables \(i+1, \dots, d\).

The value in position \(i\) of Delta is the residual variance in the above regression.

References

Cox, D. R. & Wermuth, N. (1996). Multivariate dependencies. London: Chapman & Hall.

See Also

triDec, fitDag

Examples

## Generate a sample of 100 observation from a multivariate normal
## The matrix of the path coefficients
A <- matrix(
c(1, -2, -3,  0, 0,  0,  0,
  0,  1,  0, -4, 0,  0,  0,
  0,  0,  1,  2, 0,  0,  0,
  0,  0,  0,  1, 1, -5,  0,
  0,  0,  0,  0, 1,  0,  3,
  0,  0,  0,  0, 0,  1, -4,
  0,  0,  0,  0, 0,  0,  1), 7, 7, byrow=TRUE)
D <- rep(1, 7)
X <- rnormDag(100, A, D)

## The true covariance matrix
solve(A) %*% diag(D) %*% t(solve(A))

## Triangular decomposition of the sample covariance matrix
triDec(cov(X))$A