Hierarchical Variable Selection in Polynomial Regression Models |
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Authors: | Julio L. Peixoto |
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Affiliation: | Department of Decision and Information Sciences , University of Houston , Houston , Texas , 77089 , USA |
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Abstract: | 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. |
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Keywords: | Well-formulated model Hierarchically inferior predictor Hierarchical ordering All-possible-subset regression Linear transformation Coding |
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