akaike.weights {qpcR} | R Documentation |
Calculates Akaike weights from a vector of AIC values.
akaike.weights(x)
x |
a vector containing the AIC values. |
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<=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}}
A list containing the following items:
deltaAIC |
the delta-AIC values. |
rel.LL |
the relative likelihoods. |
weights |
the Akaike weights. |
Andrej-Nikolai Spiess
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.
### 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