How to define deviance residuals in multinomial regression.

This work is devoted to the study of diagnostic tools for categorical data models with an emphasis on the presence of continuous covariates. In particular, the aim is to define a new class of residuals from the parametric multinomial family of models and to study their asymptotics properties. In logistic regression (as in generalized linear models), there are a few different kinds of residuals; we propose a generalization of deviance residuals as defined in logistic regression to the multinomial case and propose their use in order to identify inadequacies in a multinomial model.