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Functional marginality and response-surface fitting

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  • J. A. Nelder

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.

Suggested Citation

  • J. A. Nelder, 2000. "Functional marginality and response-surface fitting," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(1), pages 109-112.
    • Handle: RePEc:taf:japsta:v:27:y:2000:i:1:p:109-112
    DOI: 10.1080/02664760021862
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    Cited by:

    1. Øyvind Langsrud & Kjetil Jørgensen & Ragni Ofstad & Tormod Næs, 2007. "Analyzing Designed Experiments with Multiple Responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(10), pages 1275-1296.
    2. repec:jss:jstsof:34:i12 is not listed on IDEAS
    3. Michael J. Brusco & Douglas Steinley, 2010. "Neighborhood search heuristics for selecting hierarchically well‐formulated subsets in polynomial regression," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(1), pages 33-44, February.

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