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Abstract:
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Pliable lasso model (Tibshirani and Friedman 2019) is a type of the lasso (Tibshirani 1996) that considers sparsity of the interaction effects as well as main effects when high-dimensional data is considered in the linear model. In a hierarchical fashion, the model added a weak hierarchy constraint that the interaction effects are zero only if the main effects are zero. In this paper, we propose an extended pliable lasso that considers grouped covariates in the linear regression. l2 penalties for the grouped variables are added in the objective function for the pliable lasso, and an algorithm to solve the objective function is conducted. We first check the sparsity of the main and interaction effects simultaneously corresponding to a group. If there is at least one nonzero effect in the group, we check the sparsity of the main and interaction effects corresponding to each covariate within the group. To demonstrate the performance of our proposed method, we conduct simulation studies by comparing it with the pliable lasso and the Lasso. In a real data analysis, we use a dataset based on the Irritable Bowel Syndrome (IBS) study which is a functional gut disorder.
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