# 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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ## 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, r@marioma.me

## References

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