z_B4._Information_criterion_: Information criterion of the estimated model from 'scp'...

In scpm: An R Package for Spatial Smoothing

Description

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

Usage

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

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 ω_{μ_*,V} where ω_{μ_*,V} = ω_{μ_*} + ω_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 ω_{μ_*,V}.

Note that μ_* depends on the criterion being used so it can be μ_* = μ_m or μ_* = μ. See scp.

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.

Author(s)

Mario A. Martinez Araya, [e-mail]

References

• Mueller, Samuel; Scealy, J. L. and Welsh, A. H. (2013) Model Selection in Linear Mixed Models. Statist. Sci. 28, no. 2, 135–167. doi:10.1214/12-STS410. http://projecteuclid.org/euclid.ss/1369147909.

scpm documentation built on Feb. 17, 2020, 5:08 p.m.