Re: [R] Robustness of Segmented Regression Contributed by Muggeo

From: Achim Zeileis <Achim.Zeileis_at_wu-wien.ac.at>
Date: Wed 08 Jun 2005 - 22:55:43 EST

On Wed, 8 Jun 2005 08:25:16 -0400 Park, Kyong H Mr. RDECOM wrote:

> Hello, R users,
> I applied segmented regression method contributed by Muggeo and got
> different slope estimates depending on the initial break points. The
> results are listed below and I'd like to know what is a reasonable
> approach handling this kinds of problem. I think applying various
> initial break points is certainly not a efficient approach. Is there
> any other methods to deal with segmented regression? From a graph, v
> shapes are more clear at 1.2 and 1.5 break points than 1.5 and 1.7.
> Appreciate your help.

When you keep the number of break points fixed, then there is a unique solution to the problem of fitting a segmented regression: the solution which maximizes the likelihood (or for linear models equivalently minimizes the RSS). Vito's segmented package gives an iterative method which can be shown to converge to this unique solution. If empirically you find different solutions with different starting values, you can always compare them using the RSS or log-likelihood and choose the one which fits better (because the other one can't be the optimal solution).

The function breakpoints() in package strucchange computes (as opposed to approximates) the unique solution for a fully segmented model instead of a broken line trend.

Another nonparametric solution using quantreg was already pointed out by Roger.

hth,
Z  

> Result1:
> Initial break points are 1.2 and 1.5. The estimated break points and
> slopes:
>
> Estimated Break-Point(s):
> Est. St.Err
> Mean.Vel 1.285 0.05258
> 1.652 0.01247
>
> Est. St.Err. t value
> CI(95%).l
> CI(95%).u
> slope1 0.4248705 0.3027957 1.403159 -0.1685982
> 1.018339 slope2 2.3281445 0.3079903 7.559149 1.7244946
> 2.931794
> slope3 9.5425516 0.7554035 12.632390 8.0619879
> 11.023115 Adjusted R-squared: 0.9924.
>
> Result2:
> Initial break points are 1.5 and 1.7. The estimated break points and
> slopes:
>
> Estimated Break-Point(s):
> Est. St.Err
> Mean.Vel 1.412 0.02195
> 1.699 0.01001
>
> Est. St.Err. t value
> CI(95%).l
> CI(95%).u
> slope1 0.7300483 0.1381587 5.284129 0.4592623
> 1.000834 slope2 3.4479466 0.2442530 14.116289 2.9692194
> 3.926674
> slope3 12.5000000 1.7783840 7.028853 9.0144314
> 15.985569
>
> Adjusted R-squared: 0.995.
>
>
>
>
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>
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R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Jun 08 23:03:31 2005

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