Sensible parameters for univariate and multivariate splines
Roger B. Newson
National Heart and Lung Institute
Imperial College London
London, UK
[email protected]
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Abstract. The package bspline, downloadable from Statistical Software Components,
now has three commands. The first, bspline, generates a basis of
Schoenberg B-splines. The second, frencurv, generates a basis of
reference splines whose parameters in the regression model are simply values
of the spline at reference points on the X axis. The recent addition,
flexcurv, is an easy-to-use version of frencurv that generates
reference splines with automatically generated, sensibly spaced knots.
frencurv and flexcurv now have the additional option of
generating an incomplete basis of reference splines, with the reference spline
for a baseline reference point omitted or set to 0. This incomplete basis can
be completed by adding the standard unit vector to the design matrix and can
then be used to estimate differences between values of the spline at the
remaining reference points and the value of the spline at the baseline
reference point. Reference splines therefore model continuous factor
variables as indicator variables (or “dummies”) model discrete
factor variables. The method can be extended in a similar way to define
factor-product bases, allowing the user to estimate factor-combination means,
subset-specific effects, or even factor interactions involving multiple
continuous or discrete factors.
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Roger B. Newson
View all articles with these keywords:
bspline, flexcurv, frencurv, polynomial, spline, B-spline, interpolation, linear, quadratic, cubic, multivariate, factor, interaction
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