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In this paper, we study the multinomial logistic regression with interactive effects. Our approach involves the implementation of the pliable lasso penalty which allows for estimating the main effects of the covariates  X  and an interaction effects between the covariates and a set modifiers  Z . The hierarchical penalty helps to avoid over-fitting by excluding the interaction effects when the corresponding main effects are zero. The original log-likelihood model is transformed into an iteratively reweighted least square problem with the pliable lasso penalty and then, the block-wise coordinate descent approach is employed. Our results show that the pliable lasso for multinomial logistic regression has some good qualities and can perform well in multi-classification problems which involve interactive variables.

Pliable lasso for the multinomial logistic regression