Statalist


[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

Re: st: Re: spline regression (Kit Baum)


From   "Sergiy Radyakin" <serjradyakin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: spline regression (Kit Baum)
Date   Sun, 23 Mar 2008 11:52:36 -0400

This page has a nice applet illustrating the concept of one-sided derivatives:
http://www.ies.co.jp/math/java/calc/limrl/limrl.html


On 3/23/08, Mohammed El Faramawi <melfaram@yahoo.com> wrote:
> Hi Kit,
> Thank you very much. Pardon me, I am not good in MAth.
> i will be very grateful if you explain more what you
> mean by  "the derivative (slope) of the function is
> equal on either side of each knot point, but the
> curvature on either side may differ" and "The first
> and  second derivatives of the function are equal on
> either side of each  knot point." Thanks again Kit
>
>
> --- Kit Baum <baum@bc.edu> wrote:
>
> > Mohammed said
> >
> > I have a question about cubic spline regression and
> > linear spline regressionv. I would like to know what
> > are the differences between them?
> >
> >  From a mathematical standpoint a linear spline,
> > defined over a
> > number of 'knot points' (or join points) is
> > continuous but not
> > differentiable. It is the equivalent of a dot-to-dot
> > drawing from
> > kindergarten.
> >
> > A quadratic spline is continuous and once
> > differentiable. That is,
> > the derivative (slope) of the function is equal on
> > either side of
> > each knot point, but the curvature on either side
> > may differ.
> >
> > A cubic spline is continuous and twice
> > differentiable. The first and
> > second derivatives of the function are equal on
> > either side of each
> > knot point.
> >
> > A polynomial spline of order k is differentiable
> > (k-1) times.
> >
> > There are different kinds of splines; e.g. b-splines
> > that have
> > similar properties, but are defined using different
> > mathematics than
> > polynomial splines.
> >
> > Linear splines are discussed in my book, referenced
> > below.
> >
> > Kit
> >
> > Kit Baum, Boston College Economics and DIW Berlin
> > http://ideas.repec.org/e/pba1.html
> > An Introduction to Modern Econometrics Using Stata:
> > http://www.stata-press.com/books/imeus.html
> >
> >
> > *
> > *   For searches and help try:
> > *
> > http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> >
>
>
>
>      ____________________________________________________________________________________
> Never miss a thing.  Make Yahoo your home page.
> http://www.yahoo.com/r/hs
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



© Copyright 1996–2014 StataCorp LP   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index