akaike.weights: Calculation of Akaike weights/relative likelihoods/delta-AICs

Description

Calculates Akaike weights from a vector of AIC values.

Usage

akaike.weights(x)

Arguments

a vector containing the AIC values.

Value

A list containing the following items:

deltaAIC

the $\Delta(AIC)$ values.

rel.LL

the relative likelihoods.

weights

the Akaike weights.

Details

Although Akaike's Information Criterion is recognized as a major measure for selecting models, it has one major drawback: The AIC values lack intuitivity despite higher values meaning less goodness-of-fit. For this purpose, Akaike weights come to hand for calculating the weights in a regime of several models. Additional measures can be derived, such as $\Delta(AIC)$ and relative likelihoods that demonstrate the probability of one model being in favor over the other. This is done by using the following formulas:

delta AICs: $$\Delta_i(AIC) = AIC_i - min(AIC)$$

relative likelihood: $$L \propto exp\left(-\frac{1}{2}\Delta_i(AIC)\right)$$

Akaike weights: $$w_i(AIC) = \frac{exp\left(-\frac{1}{2}\Delta_i(AIC)\right)}{\sum_{k=1}^K exp\left(-\frac{1}{2}\Delta_k(AIC)\right)}$$

References

Classical literature: Akaike Information Criterion Statistics. Sakamoto Y, Ishiguro M and Kitagawa G. D. Reidel Publishing Company (1986).

Model selection and inference: a practical information-theoretic approach. Burnham KP & Anderson DR. Springer Verlag, New York, USA (2002).

A good summary: AIC model selection using Akaike weights. Wagenmakers EJ & Farrell S. Psychonomic Bull Review (2004), 11: 192-196.

Examples

Run this code

# NOT RUN {
## Apply a list of different sigmoidal models to data
## and analyze GOF statistics with Akaike weights
## on 8 different sigmoidal models.
modList <- list(l7, l6, l5, l4, b7, b6, b5, b4)
aics <- sapply(modList, function(x) AIC(pcrfit(reps, 1, 2, x))) 
akaike.weights(aics)$weights 
# }

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