The importance of functional marginality in model building — A case study

Polynomial regression models are often used in cases where non-linearity is present between regressors and response. Functional marginality puts certain constraints on polynomial models in terms of which regressors that need to be present; for example, if the interaction term x1x2 is in the model both x1 and x2 need to be present. This paper focuses on variable selection procedures, which are constrained by functional marginality and how functional marginality affects prediction ability of the models using least squares (LS) regression and partial least squares (PLS) regression. A new variable selection procedure for PLS is presented. Detailed computations are performed on three different data sets. The main conclusion obtained is that the restriction of functional marginality either gives similar results to the unrestricted results or it improves them.