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From |
Kit Baum <[email protected]> |

To |
[email protected] |

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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**Follow-Ups**:**st: Re: spline regression (Kit Baum)***From:*Mohammed El Faramawi <[email protected]>

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