Regressions and partial correlations implied by a precision matrix

beta_jk = -theta_jk / theta_jj, residual variance 1 / theta_jj and partial correlation -theta_jk / sqrt(theta_jj theta_kk) (ESL eqs 17.6-17.9).

Usage

morie_esl_precision_regression(Theta)

Arguments

Theta

Precision matrix.

Value

Named list: coefficients, residual_variance, partial_correlation.

References

Hastie, Tibshirani & Friedman (2009), sec. 17.3.

Examples

morie_esl_precision_regression(solve(matrix(c(2, 0.5, 0.5, 1), 2)))$partial_correlation
#>           [,1]      [,2]
#> [1,] 1.0000000 0.3535534
#> [2,] 0.3535534 1.0000000