  This paper studies posterior contraction rates in multi-category logit models
with priors incorporating group sparse structures. We consider a general class
of logit models that includes the well-known multinomial logit models as a
special case. Group sparsity is useful when predictor variables are naturally
clustered and particularly useful for variable selection in the multinomial
logit models. We provide a unified platform for posterior contraction rates of
group-sparse logit models that include binary logistic regression under
individual sparsity. No size restriction is directly imposed on the true signal
in this study. In addition to establishing the first-ever contraction
properties for multi-category logit models under group sparsity, this work also
refines recent findings on the Bayesian theory of binary logistic regression.
