rnormDag: Random sample from a decomposable Gaussian model

In ggm: Graphical Markov Models with Mixed Graphs

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)

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.

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.

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)).

Author(s)

Giovanni M. Marchetti

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

ggm documentation built on May 29, 2024, 7:27 a.m.