akaike.weights {qpcR}R Documentation

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.

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's and relative likelihoods that demonstrate the probability of one model being in favor over the other. This is done by using the following formulae:

delta AICs:

Delta_i(AIC) = AIC_i - min(AIC)

relative likelihood:

L propto exp<=ft{-frac{1}{2}Delta_i(AIC)right}

Akaike weights:

w_i(AIC) = frac{exp<=ft{-frac{1}{2}Delta_i(AIC)right}}{sum_{k=1}^K exp<=ft{-frac{1}{2}Delta_k(AIC)right}}

Value

A list containing the following items:

deltaAIC the delta-AIC values.
rel.LL the relative likelihoods.
weights the Akaike weights.

Author(s)

Andrej-Nikolai Spiess

References

Classical literature:
Sakamoto Y, Ishiguro M, and Kitagawa G (1986). Akaike Information Criterion Statistics. D. Reidel Publishing Company.
Burnham KP, Anderson DR. Model selection and inference: a practical information-theoretic approach (2002). Springer Verlag, New York, USA

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

See Also

AIC, logLik.

Examples

## apply a list of different sigmoidal models to data
## and analyze GOF statistics with Akaike weights
## on 6 different sigmoidal models 
modList <- list(l5, l4, l3, b5, b4, b3)
aics <- sapply(modList, function(x) AIC(pcrfit(reps, 1, 2, x))) 
akaike.weights(aics)$weights 

[Package qpcR version 1.2-4 Index]