.-
help for ^bspline^ and ^frencurv^                                 (STB-57: sg151)
.-

B-splines and splines parameterized by their values at reference points
-----------------------------------------------------------------------

        ^bspline^     [newvarlist] [^if^ exp] [^in^ range] ,^x^var^(^varname^)^ 
			  [^p^ower^(^#^)^ ^k^nots^(^numlist^)^ no^exk^not
                         ^g^enerate^(^varname^)^ ^t^ype^(^type^)^ ^lab^fmt^(%^fmt^)^]


        ^frencurv^    [newvarlist] [^if^ exp] [^in^ range] ,^x^var^(^varname^)^ 
			  [^p^ower^(^#^)^ ^r^efpts^(^numlist^)^ no^exr^ef ^k^nots^(^numlist^)^
                          no^exk^not ^g^enerate^(^varname^)^ ^t^ype^(^type^)^ ^lab^fmt^(%^fmt^)^]

Description
-----------

^bspline^ generates a set of B-splines in the x-variate based on a list
of knots, for use in the design matrix of a regression model. ^frencurv^
generates a set of reference splines, for use in the design matrix of a
regression model, with the property that the parameters fitted will be
values of the spline at a list of reference points. The splines are
either given the names in the newvarlist (if present) or (more usually)
generated as a list of numbered variables, prefixed by the ^generate^ option.

Options for use with ^bspline^ and ^frencurv^
-----------------------------------------

^xvar(^varname^)^ specifies the x-variate on which the splines are based.

^power(^#^)^ (a non-negative integer) specifies the power (or degree) of the
    splines, eg zero for constant, 1 for linear, 2 for quadratic, 3 for
    cubic, 4 for quartic or 5 for quintic. If absent, zero is assumed.

^refpts(^numlist^)^ (only for ^frencurv^) specifies a list of at least 2
    ascending reference points, with the property that, if the splines are
    used in a regression model, then the fitted values will be values of
    the spline at those points. If ^refpts^ is absent, then the list is
    initialized to two points, equal to the minimum and maximum of ^xvar^.

^noexref^ specifies that the original reference list is not to be extended. If
    ^noexref^ is not specified, then the reference list is extended on the left
    and right by int(^power^/2) extra reference points on each side, spaced by
    the distance between the first and last 2 original reference points,
    respectively.

^knots(^numlist^)^ specifies a list of at least 2 ascending knots, on which the
    splines are based. If ^knots^ are absent, then ^bspline^ will initialize the
    list to the minimum and maximum of ^xvar^, and ^frencurv^ will create a list
    of knots equal to the reference points (in the case of odd-degree splines
    such as a linear, cubic or quintic) or midpoints between reference points
    (in the case of even-degree splines such as constant, quadratic or
    quartic).

^noexknot^ specifies that the original knot list is not to be extended. If
    ^noexknot^ is not specified, then the knot list is extended on the left
    and right by ^power^ extra knots on each side, spaced by the distance between
    the first and last 2 original knots, respectively.

^generate(^varname^)^ specifies a prefix for the names of the generated
    splines, which (if there is no newvarlist) will be named as
    varname1...varname`nspline' where nspline is the number of splines.

^type(^type^)^ specifies the storage type of the splines generated (^float^
    or ^double^). If ^type^ is given as anything else (or not given), then
    it is set to ^float^.

^labfmt(%^fmt^)^ specifies the format to be used in the variable labels for the
    generated splines. If absent, then it is set to the format of the ^xvar^.

Remarks
-------

The splines generated are intended for use in the varlist of an estimation
command (eg ^regress^ or ^glm^), typically with a ^noconst^ option. The rules
look complicated, but they are designed to give simple defaults for most users
and also a powerful choice of options for programmers and advanced users. The
principles and definitions of B-splines are given in de Boor (1978) and
Ziegler (1969). ^frencurv^ calculates the reference splines by calling ^bspline^
to calculate B-splines for the reference points and for the ^xvar^ and inverting
the matrix of the B-splines for the reference points to generate a
transformation matrix, which is then used to transform the B-splines for ^xvar^
to reference splines for ^xvar^.

Examples
--------

 . ^frencurv,x(weight) g(sp) r(1760(440)4840) p(3)^
 . ^regress mpg sp* foreign,robust noconst^

 . ^bspline,x(weight) kn(1760(440)4840) power(3) gen(bs)^
 . ^regress mpg bs*,noconst^

 . ^bspline spl1-spl10,x(weight) kn(1760(440)4840) pow(4) ty(double)^
 . ^desc spl*^

Author
------

Roger Newson, Guy's, King's and St Thomas' School of Medicine, London, UK.
Email: ^roger.newson@@kcl.ac.uk^

References
----------

de Boor C. 1978. A practical guide to splines. New York: Springer Verlag.

Ziegler Z. One-Sided L_1-Approximation by Splines of an Arbitrary
Degree. In: Schoenberg I. J. (ed.), 1969. Approximations with Special
Emphasis on Spline Functions. New York: Academic Press.

Also see
--------

Manual:   ^[R] mkspline^
On-line:  help for @mkspline@ or ^spline^