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scpm (version 2.0.0)

B4. Information criterion: Information criterion of the estimated model from scp object.

Description

Return the information criterion of the estimated model from a scp object.

Usage

# S4 method for sssFit
AIC(object, k, only.criterion)
# S4 method for sssFit
BIC(object, only.criterion)
# S4 method for sssFit
AICm(object, k, only.criterion)
# S4 method for sssFit
AICc(object, k, only.criterion)
# S4 method for sssFit
BICc(object, only.criterion)
# S4 method for sssFit
BICj(object, k, tol, only.criterion)
# S4 method for sssFit
GIC(object, k, only.criterion)
# S4 method for sssFit
GIChq(object, k, only.criterion)
# S4 method for sssFit
GICpn(object, only.criterion)
# S4 method for sssFit
GICb(object, only.criterion)

Arguments

object

sssFit object from scp.

k

numeric. Factor multiplying the number of parameters in each criterion. Default to k=2.

tol

numeric. Value for the tolerance in some computation of inverse matrices. By default is set to .Machine$double.neg.eps.

only.criterion

logical. If TRUE (the default) returns only the value of the criterion.

Value

If only.criterion=TRUE returns the value of the criterion. If only.criterion=FALSE returns a list with the following elements:

logLik

numeric. The log-likelihood or conditional log-likelihood (given \(r\)) of the model depending of the criterion used.

criterion

numeric. The value of the information criterion.

ka0

numeric. Factors \(ka_0\) multiplying the number of parameters. Depends on the criterion selected.

numpar

numeric. The (effective) number of parameters. Depends on the criterion selected.

penalty

numeric. The value of the penalty.

Details

The information criterion for a mixed model is defined as $$IC = -2\ell + penalty$$ where \(\ell\) is the log-likelihood \(\ell(\vartheta)\) or conditional log-likelihood \(\ell(\vartheta|r)\) (see scp). The penalty is expressed as \(k\times a_0\times \omega_{\mu_*,V}\) where \(\omega_{\mu_*,V} = \omega_{\mu_*} + \omega_V\) is the (effective) number of parameters in the mean and variance and \(k\) and \(a_0\) are factors that depend on the criterion used. Thus the information criterion can be written as $$IC = -2\ell + k\times a_0\times \omega_{\mu_*,V}.$$ Note that \(\mu_*\) depends on the criterion being used so it can be \(\mu_* = \mu_m\) or \(\mu_* = \mu\). See scp.

References