qpcR (version 1.1-8)

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.

encoding

latin1

Details

Although Akaike's Information Criterion is recognized as a major measure for selecting models, it has one major drawback: The AIC values are arbitrary, and despite higher values meaning less goodness-of-fit, this is not very intuitive. 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: $$L \propto exp\left{-\frac{1}{2}\Delta_i(AIC)\right}$$ 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: 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 9 different sigmoidal models 
modList <- list(l5(), l4(), l3(), b5(), b4(), b3(), w4(), w3(), baro5())
aics <- sapply(modList, function(x) AIC(drmfit(F1.1 ~ Cycles, data = reps, fct = x))) 
akaike.weights(aics)$weights