[R] Piecewise regression using lme()

[goulvenS]

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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