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st: Re: spline regression (Kit Baum)


From   Mohammed El Faramawi <melfaram@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: spline regression (Kit Baum)
Date   Sun, 23 Mar 2008 07:15:07 -0700 (PDT)

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
> 
> 
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