Generates a $p \times p$ intraclass covariance matrix

This function generates a $p \times p$ intraclass covariance matrix with correlation rho. The variance sigma2 is constant for each feature and defaulted to 1.

cov_intraclass(p, rho, sigma2 = 1)

Arguments

p	the size of the covariance matrix
rho	the value of the off-diagonal elements
sigma2	the variance of each feature

Value

intraclass covariance matrix

Details

The intraclass covariance matrix is defined as: $\sigma^2 * (\rho * J_p + (1 - \rho) * I_p),$ where $J_p$ is the $p \times p$ matrix of ones and $I_p$ is the $p \times p$ identity matrix.

By default, with sigma2 = 1, the diagonal elements of the intraclass covariance matrix are all 1, while the off-diagonal elements of the matrix are all rho.

The value of rho must be between $1 / (1 - p)$ and 1, exclusively, to ensure that the covariance matrix is positive definite.

Generates a p×pp \times p intraclass covariance matrix

Arguments

Value

Details