--- Mohammed El Faramawi <[email protected]> wrote:
> I have a question about cubic spline regression and
> linear spline regressionv. I would like to know what
> are the differences between them? I will be very
> grateful if someone explains the difference between
> them particularly when I should use linear spline
> regression and when should i use cubic spline
> regression? If someone has online materials about this
> subject, this will be great.
In Stata 10 -mkspline- has the ability of creating a restricted cubic
spline. This is not the same as a cubic spline: it restricts the line
to be linear before the first knot and after the last knot, between the
first and the last knot, the curve is a cubic spline. This has the
advantage of being more stable.
The difference between the restricted cubic spline and the linear
spline is best explained using a graph:
*--------------- begin example -------------------
sysuse auto, clear
mkspline lin1 18 lin2 =mpg
reg price lin1 lin2
predict yhatlin
mkspline cub=mpg, cubic knots(15 18 30)
reg price cub1 cub2
predict yhatcub
twoway scatter price mpg || ///
line yhatlin yhatcub mpg, sort ///
legend(order( 1 ///
2 "linear spline" ///
3 "restricted" ///
"cubic spline"))
*------------- 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 )
The cubic spline is more smooth, while the linear spline changes very
abrubtly at the knot (mpg=18). The linear spline looks a bit awkward,
but it has the advantage of being able to easily read the effect of
price in the regression table: before mpg=18 a unit change in mpg led
to a decrease in price approx. 1200 dollars, while after mpg=18 a unit
increase in mpg led to a decrease in price of approx. 60 dollars.
I am working on a program that shows the effect of mpg in a restricted
cubic spline. If you are interested I am willing to sent a pre-release
to you privately.
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/
-----------------------------------------
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