rAverage (version 0.5-8)

AIC: Information Criteria for averaging models

Description

Functions to extract or recalculate the Akaike Information Criterion and the Bayesian Information Criterion of an averaging model fitted by the rav function.

Usage

AIC(object, ..., k = 2)
BIC(object, ...)

Arguments

object

An object of class rav containing an estimated averaging model.

...

Optionally more fitted model objects (see details).

k

Numeric, the penalty per parameter to be used; the default k = 2 is the classical AIC.

Value

A numeric value representing the information criterion of the selected model.

Details

The functions AIC and BIC are used, respectively, to extract the Akaike Information Criterion and the Bayesian Information Criterion of a model fitted by the function rav.

AIC is calculated as:

$$ AIC = n \ln \left( \frac{RSS}{n} \right) + k p $$

where \(n\) is the number of data available, \(k\) is the penalty per parameter ()usually equal to 2), \(p\) is the number of parameters and \(RSS\) is the residual sum of squares.

BIC is calculated as:

$$ BIC = n \ln \left( \frac{RSS}{n} \right) + \ln(n) p $$

As default, when \(n / p < 40\), AIC and BIC are corrected in AICc and BICc:

$$ AICc = AIC + \frac{2 (p+1) p}{n-p-1} $$ $$ BICc = BIC + \frac{\ln(n) (p+1) p}{n-p-1} $$

to avoid the correction, set correct = FALSE. On the contrary, if you want the correction, set correct = TRUE. When the argument correct is not specified, the rule \(n / p < 40\) is applied.

As default, the functions extract the indices of the (first) best model. The optional argument whichModel can be specified to extract the indices of another model. Options are:

1. "null": null model

2. "ESM": equal scale values model

3. "SAM": simple averaging model

4. "EAM": equal-weights averaging model

5. "DAM": differential-weight averaging model

6. "IC": information criteria model

See Also

rav, rAverage-package AIC, BIC

Examples

# NOT RUN {
data(fmdata1)
fm1 <- rav(fmdata1, lev=c(3,3))
AIC(fm1)
BIC(fm1)
# }