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An Easy-to-Implement Hierarchical Standardization for Variable Selection Under Strong Heredity Constraint

For many practical problems, the regression models follow the strong heredity property (also known as the marginality), which means they include parent main effects when a second-order effect is present. Existing methods rely mostly on special penalty functions or algorithms to enforce the strong heredity in variable selection. We propose a novel hierarchical standardization procedure to maintain strong heredity in variable selection. Our method is effortless to implement and is applicable to any variable selection method for any type of regression. The performance of the hierarchical standardization is comparable to that of the regular standardization. We also provide robustness checks and real data analysis to illustrate the merits of our method.