AICweights.R

# models from p. 146 of
# http://www.uni-tuebingen.de//uni/sii/pw/heller/statistics_III_ws14/stat5www.pdf

# c(model1, model2, model3)
aic <- c(8128.519, 8249.935, 8163.826)
llh <- c(-4039.260, -4118.967, -4074.913)
params <- c(25, 6, 7)

# compute the relative distance of each model AIC to the
# model with the minimum AIC
rel <- sapply(aic, function(i) i - min(aic))

fn <- function(r) exp(-r / 2)
normalizer <- sum(sapply(rel, fn))

# compute the AIC weights for each model
weights <- sapply(rel, function(r) fn(r) / normalizer)

# evidence ratio of model 1 compared to model 3 is
comp1 <- weights[1] / weights[3]

# direct computation of the evidence ratio of AIC weights
# comparison of model 1 and 3
comp2 <- exp(llh[1] - llh[3] + params[3] - params[1])

# this is a little contrived, since model 1 is just sooo much better than model 3
# in general, AIC weights provide a continuous measure of strength of evidence!
# for more, see http://ejwagenmakers.com/2004/aic.pdf and
# http://www.ejwagenmakers.com/inpress/VandekerckhoveEtAlinpress.pdf