Hierarchical Variable Selection in Polynomial Regression Models

Significance tests on coefficients of lower-order terms in polynomial regression models are affected by linear transformations.For this reason, a polynomial regression model that excludes hierarchically inferior predictors (i.e., lower-order terms) is considered to be not well formulated.Existing variable-selection algorithms do not take into account the hierarchy of predictors and often select as .best. a model that is not hierarchically well formulated.This article proposes a theory of the hierarchical ordering of the predictors of an arbitrary polynomial regression model in m variables, where m is any arbitrary positive integer.Ways of modifying existing algorithms to restrict their search to well-formulated models are suggested.An algorithm that generates all possible well-formulated models is presented.