The joint distribution exists only where the precision matrix is
positive definite. The book states the bound through the eigenvalues
of W (eq 6.48): for Q = I - rho W the range is
(1/theta_min, 1/theta_max); for Q = D - rho W the same condition
applies to the eigenvalues of D^-1/2 W D^-1/2.
Usage
car_rho_bounds(W, parameterization = "weighted")
Arguments
- W
Symmetric adjacency weights (n by n).
- parameterization
"weighted" (Q = D - rho W) or "identity"
(Q = I - rho W).
Value
Numeric length-2 vector, the open interval (lo, hi).
References
Schabenberger & Gotway (2005), eq (6.48), p. 340.
Examples
car_rho_bounds(W = 5L)
#> [1] -Inf 1
