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This paper studies posterior contraction rates in multi-category logit modelswith priors incorporating group sparse structures. We consider a general classof logit models that includes the well-known multinomial logit models as aspecial case. Group sparsity is useful when predictor variables are naturallyclustered and particularly useful for variable selection in the multinomiallogit models. We provide a unified platform for posterior contraction rates ofgroup-sparse logit models that include binary logistic regression underindividual sparsity. No size restriction is directly imposed on the true signalin this study. In addition to establishing the first-ever contractionproperties for multi-category logit models under group sparsity, this work alsorefines recent findings on the Bayesian theory of binary logistic regression.

Posterior contraction in group sparse logit models for categorical responses