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From |
Maarten buis <[email protected]> |

To |
[email protected] |

Subject |
RE: st: SPLINE commands |

Date |
Fri, 4 Feb 2011 16:42:12 +0000 (GMT) |

--- On Fri, 4/2/11, Ronald McDowell wrote: > I'm not familiar with the concept of splines, and am > looking for a gentle introduction to the area, in > order to move beyond using quadratic and cubic etc > terms in my models. You could look at Marsh, Lawrence C. and David R. Cormier (2002) "Spline Regression Models". Quantitative Applications in the Social Sciences, nr. 137. Thousand Oacks: Sage. I am actually moving back towards linear splines (from more smooth restricted cubic, B-splines, etc.), as I find linear splines to have a nicer balance between interpretability of the parameters and flexibility of the curve. Anyone who can interpret regular regression parameters can also interpret the parameters of a linear spline terms. Consider the example below: *--------------- begin example -------------------- sysuse auto, clear mkspline mpg1 20 mpg2 = mpg reg price mpg1 mpg2 foreign // use adjust to predict price while keeping foreign at 0 adjust foreign = 1, by(mpg) generate(yhat) // graph the predicted price against mpg twoway line yhat mpg, sort *---------------- end example ---------------------- The graph illustrates what happend, we basically have two linear regression: one for cars with an mpg < 20 and one for cars with an mpg >20, and the regression lines meet at mpg == 20. Moreover, the standard parameterization, as implemented by -mkspline-, lets you interpret the coefficients of these splines as regular regression coefficients. So, for cars with mpg < 20 and additional mile per gallon leads to a drop in price of 845 dollars, while for cars with mpg > 20 the drop in price is a insignificant 70 dollars per mile per gallon. As always there is a price that needs to be paid for such convenient interpretability, and for linear splines it is that sudded change in direction at the knot and the linearity between the knots. Some people find this not smooth enough or not realistic enough. However, I am willing to sacrifice a lot of "realism" of my model if that helps me to get across what I have done to my data in order to arrive at my conclussions. With linear splines one often must view models as a useful summary/simplification of reality, but isn't that what a model is supposed to be anyhow? Having said all that, work has been done on making the coefficients of other types of splines more interpretable, but linear splines seems to me a logical place to start before entering into more complicated variations of it (and don't be afraid to move back to linear splines once you have looked at those variations). Hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: SPLINE commands***From:*Roger Newson <[email protected]>

**References**:**RE: st: SPLINE commands***From:*Ronald McDowell <[email protected]>

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