Functional marginality and response-surface fitting

J. A. Nelder

Journal of Applied Statistics, 2000, vol. 27, issue 1, 109-112

Abstract: Well-formed polynomials contain the marginal terms of all terms; for example, they contain both x 1 and x 2 if x 1 x 2 is present. Such models have a goodness of fit that is invariant to linear transformations of the x variables. Recently, selection procedures have been proposed which may not give well-formed polynomials. Analysis of two data sets for which non-well-formed polynomials have been selected shows that conversion to well-formed polynomials is beneficial in terms of goodness of fit, as well as giving fits invariant to linear transformation of the x variables. It is concluded that selection procedures should search among well-formed polynomials only.

Date: 2000
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DOI: 10.1080/02664760021862

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