sglasso (version 1.2.6)

loglik: Extract Log-Likelihood

Description

This function extracts the log-likelihood for the sequence of weighted l1-penalized RCON(V, E) models estimated by sglasso function.

Usage

loglik(object, N = 2)

Value

loglik returns a vector containing the log-likelihood computed for the sequence of weighted l1-penalized RCON(V, E).

Arguments

object

a fitted sglasso object;

N

sample size. Default value is 2 to remove the constant term in the log-likelihood function. See below for more details.

Author

Luigi Augugliaro
Maintainer: Luigi Augugliaro

Details

Denoted with \(\psi = (\eta',\theta')'\) the parameter vector of the structured concentration matrix \(K(\psi)\), the log-likelihood function of the RCON(V, E) model is equal, up to a constant, to the following expression $$\ell(\psi) = \frac{N}{2}[\log det K(\psi) - tr\{S K(\psi)\}],$$ where \(S = N^{-1}\sum_{i=1}^NX_iX_i^T\), \(N\) is the sample size and \(X_i\) is the \(i\)th observed \(p\)-dimensional vector. Denoted with \(\hat\psi = (\hat\eta',\hat\theta')'\) the sglasso estimates, straightforward algebra shows that $$\ell(\hat\psi) = \frac{N}{2}[\log det K(\hat\psi) - p + \rho\sum_{m=1}^S w_m|\hat\theta_m|],$$ where \(\rho\) is the tuning parameter and \(w_m\) are the weights used to define the weighted l1-norm.

See Also

summary.sglasso method and sglasso function.

Examples

N <- 100
p <- 5
X <- matrix(rnorm(N * p), N, p)
S <- crossprod(X) / N
mask <- outer(1:p, 1:p, function(i, j) 0.5^abs(i-j))
out.sglasso_path <- sglasso(S, mask, nrho = 5, tol = 1.0e-13)
out.sglasso_path
loglik(out.sglasso_path, N = N)
rho <- out.sglasso_path$rho[3]
out.sglasso_single <- sglasso(S, mask, nrho = 1, min_rho = rho, 
   tol = 1.0e-13, algorithm = "ccm")
loglik(out.sglasso_single, N = N)