[R] Piecewise Lasso Regression

[Vito Muggeo (UniPa)]

dear Lucas,
If you are interested in selecting the number of breakpoints here a 
possible remedy:

1. Fit a segmented model with a large number of breakpoints via the 
arguments psi=NA and stop.if.error=FALSE in seg.control() (see the 
example below)

2. extract the "model matrix" relevant to the variables of the breakpoints

3. Use lars with the extracted model matrix

Notice that there are at least two issues that I did not mention:
a) The criterion to be used to select the variables (i.e the breakpoints)
b) When you remove variables (i.e. breakpoints) you are assuming that 
the ML estimate of the remaining breakpoints is the same (and this is 
not the case here, as point estimates of the breakpoints depend on the 
number of breakpoints themselves..)


vito

###Here a simple example
      n=100
      xx<-1:n/n
      psi0<-seq(.2,.8,by=.2)
      X<-sapply(c(0,psi0), function(x)pmax(xx-x,0))
      b<-c(-.6,.7,.4,-1,.5)
      mu<-drop(X%*%b)
      yy<-mu+rnorm(n)*.01
      plot(xx,mu);lines(xx, mu)



library(segmented)
o<-lm(yy~xx)
os<-segmented(o,seg.Z=~xx,psi=NA,control=seg.control(stop.if.error=FALSE,K=30, 
n.boot=0))
plot(os, add=T, col=2) #have a look to results

#extract the new model matrix
new.X<-model.matrix(os)[,os$nameUV$U]

#finally use lars on y~new.X

Hope this helps you,
vito

Il 06/06/2012 15.48, Lucas Santana dos Santos ha scritto:
> Hi Vito,
>
> I am more interested in selecting the number of breakpoints. My data has some structure and I believe that fitting a piecewise regression would be of great benefit.
>
> Thanks,
>
> Lucas
>
> On Jun 6, 2012, at 4:54 AM, Vito Muggeo (UniPa) wrote:
>
>> dear lucas,
>> yes you are right, segmented does not handle 'lars' objects.
>>
>> Out of curisity, are you interested in selecting the number of breakpoints or in selecting additional covariates with linear parameters?
>>
>> vito
>>
>>
>> Il 06/06/2012 0.01, Lucas Santana dos Santos ha scritto:
>>> Hi All,
>>>
>>>
>>> I am trying to fit a piecewise lasso regression, but package Segmented does not work with Lars objects.
>>> Does any know of any package or implementation of piecewise lasso regression?
>>>
>>> Thanks,
>>>
>>> Lucas
>>> ______________________________________________
>>> R-help at r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>
>> --
>> ====================================
>> Vito M.R. Muggeo
>> Dip.to Sc Statist e Matem `Vianelli'
>> Università di Palermo
>> viale delle Scienze, edificio 13
>> 90128 Palermo - ITALY
>> tel: 091 23895240
>> fax: 091 485726
>> http://dssm.unipa.it/vmuggeo
>> ====================================
>
>

-- 
====================================
Vito M.R. Muggeo
Dip.to Sc Statist e Matem `Vianelli'
Università di Palermo
viale delle Scienze, edificio 13
90128 Palermo - ITALY
tel: 091 23895240
fax: 091 485726
http://dssm.unipa.it/vmuggeo