qpcR (version 1.4-1)

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

x

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.

See Also

AIC, logLik.

Examples

# 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 
# }