  Polytomous categorical data are frequent in studies, that can be obtained
with an individual or grouped structure. In both structures, the generalized
logit model is commonly used to relate the covariates on the response variable.
After fitting a model, one of the challenges is the definition of an
appropriate residual and choosing diagnostic techniques. Since the polytomous
variable is multivariate, raw, Pearson, or deviance residuals are vectors and
their asymptotic distribution is generally unknown, which leads to difficulties
in graphical visualization and interpretation. Therefore, the definition of
appropriate residuals and the choice of the correct analysis in diagnostic
tools is important, especially for nominal data, where a restriction of methods
is observed. This paper proposes the use of randomized quantile residuals
associated with individual and grouped nominal data, as well as Euclidean and
Mahalanobis distance measures, as an alternative to reduce the dimension of the
residuals. We developed simulation studies with both data structures
associated. The half-normal plots with simulation envelopes were used to assess
model performance. These studies demonstrated a good performance of the
quantile residuals, and the distance measurements allowed a better
interpretation of the graphical techniques. We illustrate the proposed
procedures with two applications to real data.
