Residuals indicating which observations are misclassified.


The residuals for the multinomial model are defined as

argmax(y_i) \neq argmax(p_i)

where argmax(y_i) is the index of the category for the endogenous variable and argmax(p_i) is the index of the predicted probabilities for each category. That is, the residual is a binary indicator that is 0 if the category with the highest predicted probability is the same as that of the observed variable and 1 otherwise.