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

In qpcR: Modelling and Analysis of Real-Time PCR Data

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 Δ(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:

Δ_i(AIC) = AIC_i - min(AIC)

relative likelihood:

L \propto exp≤ft(-\frac{1}{2}Δ_i(AIC)\right)

Akaike weights:

w_i(AIC) = \frac{exp≤ft(-\frac{1}{2}Δ_i(AIC)\right)}{∑_{k=1}^K exp≤ft(-\frac{1}{2}Δ_k(AIC)\right)}

Value

A list containing the following items:

deltaAIC	the Δ(AIC) values.
rel.LL	the relative likelihoods.
weights	the Akaike weights.

Author(s)

Andrej-Nikolai Spiess

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

## 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 

Example output

Loading required package: MASS
Loading required package: minpack.lm
Loading required package: rgl
Loading required package: robustbase
Loading required package: Matrix
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found 
[1] 9.992057e-01 7.862460e-09 6.649082e-09 3.118704e-11 7.942767e-04
[6] 5.829852e-10 1.076385e-09 1.269969e-09

qpcR documentation built on May 2, 2019, 5:17 a.m.