st: re: linear and cubic spline regression

[Kit Baum <baum@bc.edu>]

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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