smaa.entropy {smaa} | R Documentation |
Calculate decision entropy from the sampled SMAA rankings. For both ranking and choice problematics.
smaa.entropy.ranking(ranks, p0 = 1) smaa.entropy.choice(ra, p0 = 1)
ranks |
Object of class |
ra |
Object of class |
p0 |
Baseline probability for the entropy calculation. |
Calculates the entropy for the given problematic, quantifying either the uncertainty in the ranking of the alternatives (where the outcome space Y consists of the m! possible rankings) or in the choice of the best alternative (where the outcome space Y consists of the m alternatives). The entropy is given by:
H(Y|W) = -sum [over y in Y] [ p0 p(y|W) log p0 p(y|W) ]
where W is the space of feasible weights. Since the SMAA analysis samples from the outcome space, the p(y|W) can be estimated directly from the given sample.
The entropy (a single numeric value).
The number of samples needed to accurately estimate H(Y|W) for the ranking problematic is currently unknown.
Gert van Valkenhoef
G. van Valkenhoef and T. Tervonen, Optimal weight constraint elicitation for additive multi-attribute utility models, presentation at EURO 2013, July 2013, Rome, Italy.
N <- 1E4; m <- 2; n <- 3 meas <- dget(system.file("extdata/thrombo-meas.txt.gz", package="smaa")) pref <- dget(system.file("extdata/thrombo-weights-nopref.txt.gz", package="smaa")) # Calculate ranks values <- smaa.values(meas, pref) ranks <- smaa.ranks(values) # Calculate ranking entropy smaa.entropy.ranking(ranks) # Calculate choice entropy # (equal to ranking entropy because there are only two alternatives) smaa.entropy.choice(ranks) smaa.entropy.choice(smaa.ra(ranks))