Model Selection for the Conditional Graphical Lasso Estimator

Description

‘select.cglasso’ returns the optimal fitted model selected by a chosen measure of goodness-of-fit.

Usage

select.cglasso(object, GoF = AIC, ...)

Arguments

Details

The function select.cglasso evaluates the goodness-of-fit of the models fitted by cglasso and extracts the selected model.

Model evaluation can be made in two ways. The easiest way is to use a valid goodness-of-fit function, such as AIC.cglasso or BIC.cglasso. In this case, further arguments are passed to these functions by ‘...’. The second way consists on passing the output of a goodness-of-fit function, that is, an R object of class ‘GoF’. Usually, this approach is preferable when the computation of the chosen goodness-of-fit measure is time-consuming, such as when the sample size is small relative to the number of parameters and the AIC or BIC functions are used to evaluate a long sequence of fitted models. In these cases, we suggest the computation of several measures of goodness-of-fit in a preliminary step and then the use of the select.cglasso function in a subsequent step to select the optimal fitted model.

Value

‘select.cglasso’ returns the optimal fitted model.

Author(s)

Gianluca Sottile (gianluca.sottile@unipa.it)

See Also

cglasso, AIC.cglasso and BIC.cglasso.

Examples

set.seed(123)
# Y ~ N(0, Sigma) and probability of left/right censored values equal to 0.05
n <- 100L
p <- 3L
rho <- 0.3
Sigma <- outer(1L:p, 1L:p, function(i, j) rho^abs(i - j))
Z <- rcggm(n = n, Sigma = Sigma, probl = 0.05, probr = 0.05)

out <- cglasso(. ~ ., data = Z)
select.cglasso(out)                                    # models selection by AIC
select.cglasso(out, GoF = BIC)                         # models selection by BIC
select.cglasso(out, GoF = BIC, mle = TRUE, g = 0.5)    # models selection by eBIC

# Y ~ N(b0 + XB, Sigma)  and probability of left/right censored values equal to 0.05
n <- 100L
p <- 3L
q <- 2
b0 <- runif(p)
B <- matrix(runif(q * p), nrow = q, ncol = p)
X <- matrix(rnorm(n * q), nrow = n, ncol = q)
rho <- 0.3
Sigma <- outer(1L:p, 1L:p, function(i, j) rho^abs(i - j))
Z <- rcggm(n = n, b0 = b0, X = X, B = B, Sigma = Sigma, probl = 0.05, probr = 0.05)

out <- cglasso(. ~ ., data = Z, lambda = 0.01)
select.cglasso(out)                                    # models selection by AIC
select.cglasso(out, GoF = BIC)                         # models selection by BIC
select.cglasso(out, GoF = BIC, mle = TRUE, g = 0.5)    # models selection by eBIC

out <- cglasso(. ~ ., data = Z, rho = 0.01)
select.cglasso(out)                                    # models selection by AIC
select.cglasso(out, GoF = BIC)                         # models selection by BIC
select.cglasso(out, GoF = BIC, mle = TRUE, g = 0.5)    # models selection by eBIC

out <- cglasso(. ~ ., data = Z)
select.cglasso(out)                                    # models selection by AIC
select.cglasso(out, GoF = BIC)                         # models selection by BIC
select.cglasso(out, GoF = BIC, mle = TRUE, g = 0.5)    # models selection by eBIC