[R-sig-ME] Piecewise linear regression using lme()

[Goulven SALIC]

Hi everyone,

I'm trying to fit a of piecewise regression model on a time series. The 
idea is to divide the series into segments and then to apply linear 
regression models on each segment but in a "global way" and considering 
heteroskedasticity between the segments. For example, I build a time 
series y with 3 segments:

segment1=1:20+rnorm(20,0,2)
segment2=20-2*1:30+rnorm(30,0,5)
segment3=-40+0.5*1:15+rnorm(15,0,1)

group=c(rep(1,20),rep(2,30),rep(3,15))
y=c(segment1,segment2,segment3)

Data=data.frame(y,t=1:65,group=as.factor(group))

the model I'd like to fit is:

y_t= 
(beta_01+beta_11*t+error_1)*(group==1)+(beta_02+beta_12*t+error_2)*(group==2)+(beta_03+beta_13*t+error_3)*(group==3)

It looks like a mixed effects model were the fixed effect are the 
piecewise linear regression parts (beta_0i+beta_1i*t) and the random 
effects are the variance components error_i.

The problem is that I can't find the way the write this model correctly 
using the lme() function of the package nlme. I can't remove the global 
intercept and the global variance component. Here's what I tried:

#1 Using a prior piecewise linear regression

lm.list=lmList(y~t|group,Data)

model.lme=lme(lm.list,weights=varIdent(form=~1|group))

#2 Trying to estimate the whole model directly and considering the 
different lines as random effects

model.lme=lme(y~1,random=~t|group,data=Data)

but the intercept remains...

I read a lot of R-help messages before posting this one (my first!) and 
I'm not getting any closer. It looks like no one tried to estimate the 
exact same model. I'll be very grateful if someone could help me on this.

Thanks

Goulven 
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