Defined as: 1 - (1/n) sum_i sum_j (y_ij - p_ij)^2, where y_ij = 1 if observation i has class j (else 0), and p_ij is the predicted probablity of observation i for class j. This scoring rule is the same as 1 - multiclass.brier. See: Bickel, J. E. (2007). Some comparisons among quadratic, spherical, and logarithmic scoring rules. Decision Analysis, 4(2), 49-65.
QSR(probabilities, truth)[numeric] vector (or matrix with column names of the classes) of predicted probabilities
vector of true values n = 20 set.seed(122) truth = as.factor(sample(c(1,2,3), n, replace = TRUE)) probabilities = matrix(runif(60), 20, 3) probabilities = probabilities/rowSums(probabilities) colnames(probabilities) = c(1,2,3) QSR(probabilities, truth)