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st: re: linear and cubic spline regression


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: linear and cubic spline regression
Date   Sun, 23 Mar 2008 09:27:44 -0400

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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