Covariance matrix of Synthetic example

Covariance matrix of Synethetic example consisting of 9 variables with 3 hidden factors.

Usage

data(syn)

Details

This \(9 \times 9\) matrix is the covariance matrix of 9 variables, $$\xi_i = \eta_1 + \epsilon_i, ~ i=1,2,3,$$ $$\xi_i = \eta_2 + \epsilon_i, ~ i=4,5,6,$$ $$\xi_i = \eta_3 + \epsilon_i, ~ i=7,8,9,$$ where \(\epsilon_i, ~ i=1,\ldots,9\) are independent and \(\eta_i, ~ i=1,2,3\) are three hidden factors such that $$\eta_1 \sim N(0,290), ~ \eta_2 \sim N(0,300), ~ \eta_3 = 0.3 \eta_1 + 0.98 \eta_2 + \epsilon,$$ where \(\epsilon \sim N(0,1)\) and \(\eta_1\), \(\eta_2\), and \(\epsilon\) are independent.

Examples

# load the covariance matrix
data(syn)

# the dimension of the covariance matrix
dim(syn)
#> [1] 9 9