  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.
