IDEAS home Printed from
   My bibliography  Save this paper

Sensible parameters for polynomials and other splines


  • Roger Newson

    () (National Heart and Lung Institute, Imperial College London)


Splines, including polynomials, are traditionally used to model nonlinear relationships involving continuous predictors. However, when they are included in linear models (or generalized linear models), the estimated parameters for polynomials are not easy for nonmathematicians to understand, and the estimated parameters for other splines are often not easy even for mathematicians to understand. It would be easier if the parameters were differences or ratios between the values of the spline at the reference points and the value of the spline at a base reference point or if the parameters were values of the polynomial or spline at reference points on the x-axis, or The bspline package can be downloaded from Statistical Software Components, and generates spline bases for inclusion in the design matrices of linear models, based on Schoenberg B-splines. The package now has a recently added module flexcurv, which inputs a sequence of reference points on the x-axis and outputs a spline basis, based on equally spaced knots generated automatically, whose parameters are the values of the spline at the reference points. This spline basis can be modified by excluding the spline vector at a base reference point and including the unit vector. If this is done, then the parameter corresponding to the unit vector will be the value of the spline at the base reference point, and the parameters corresponding to the remaining reference spline vectors will be differences between the values of the spline at the corresponding reference points and the value of the spline at the base reference point. The spline bases are therefore extensions, to continuous factors, of the bases of unit vectors and/or indicator functions used to model discrete factors. It is possible to combine these bases for different continuous and/or discrete factors in the same way, using product bases in a design matrix to estimate factor-value combination means and/or factor-value effects and/or factor interactions.

Suggested Citation

  • Roger Newson, 2011. "Sensible parameters for polynomials and other splines," United Kingdom Stata Users' Group Meetings 2011 01, Stata Users Group.
  • Handle: RePEc:boc:usug11:01

    Download full text from publisher

    File URL:
    File Function: presentation materials
    Download Restriction: no

    File URL:
    File Function: sample do-files
    Download Restriction: no

    References listed on IDEAS

    1. Roger Newson, 2001. "Splines with parameters that can be explained in words to non-mathematicians," United Kingdom Stata Users' Group Meetings 2001 11, Stata Users Group.
    2. Roger Newson, 2001. "B-splines and splines parameterized by their values at reference points on the x-axis," Stata Technical Bulletin, StataCorp LP, vol. 10(57).
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Roger B. Newson, 2012. "Sensible parameters for univariate and multivariate splines," Stata Journal, StataCorp LP, vol. 12(3), pages 479-504, September.
    2. Roger Newson, 2014. "Easy-to-use packages for estimating rank and spline parameters," United Kingdom Stata Users' Group Meetings 2014 01, Stata Users Group.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boc:usug11:01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F Baum). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.