[R] Robustness of Segmented Regression Contributed by Muggeo

[Achim Zeileis]

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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