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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: broken stick (piecewise linear) regression |

Date |
Thu, 31 Jan 2008 21:05:58 +0000 (GMT) |

--- Raphael Fraser <raphael.fraser@gmail.com> wrote: > I saw a thread with the above subject line concerning > piecewise linear regression posted in 2005 on Statalist. > I am facing the same problem now; that of estimating the unknown > change point. Mention was made of using -nl- but it uses > least squares method. The only way to solve this problem > is numerical optimization. The problem can be solved > quite easily in SAS using NLIN PROC. > Is there a Stata solution? Purely looking at the name my guess would be that both -nl- and NLIN PROC use the same or a very similar algorithm: nonlinear least squares, which is not the same as least squares. It is the most common way I have seen to estimate these kinds of models, though you could also us -ml- but that would be a bit (but not much) more work. Notice that this is a tough maximization problem so it really helps to have good starting values. I would recommend starting with a scatter plot, and find the likely location for the knot, use that knot to create a spline and estimate a regression. Use those parameters as starting values when you use -nl- like in the example below to finally estimate your parameters. *--------------- begin example ----------------- sysuse auto, clear // first take a look twoway scatter price mpg // 20 seems a nice starting value for // the knot location mkspline mpg1 20 mpg2 = mpg, marginal reg price mpg1 mpg2 local cons = _b[_cons] local b1 = _b[mpg1] local b2 = _b[mpg2] predict initial // use -nl- to find the knot nl (price = {cons=`cons'} + {b1=`b1'}*mpg + /// {b2=`b2'}*max(mpg -{k1=20},0)) predict nl // look at the results twoway scatter price mpg || /// line initial nl mpg, sort /// legend(order( 2 "first guess" /// 3 "estimated")) *---------------- end example ------------------- (For more on how to use examples I sent to the Statalist, see http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html ) Hope this helps, Maarten ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- __________________________________________________________ Sent from Yahoo! Mail - a smarter inbox http://uk.mail.yahoo.com * * 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/

**References**:**st: broken stick (piecewise linear) regression***From:*"Raphael Fraser" <raphael.fraser@gmail.com>

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