# Calculating the Brier score for multinomial models

I was wondering whether it is possible to calculate the Brier score for multinomial models in R?

For example:

library(nnet)
data(iris)
mlogit <- multinom(Species ~ ., data = iris)


and given the definition of the Brier score for multinomial model on Wikipedia. I do not believe I can compute the Brier score, because I lack the class probabilities of the non-realized classes for each observation right? Or am I missing something?

doi:10.1002/sim.5321 may give you some ideas. I don't think an overall Brier score for polytomous outcomes has been fully worked out. But at least you could report $$k-1$$ Brier scores for predicting the probability of $$k-1$$ out of the $$k$$ levels of $$Y$$.