[R] Collinearity in nls problem

[Simon Frost]

Dear R-Help list,

I have a nonlinear least squares problem, which involves a changepoint;
at the beginning, the outcome y is constant, and after a delay, t0, y
follows a biexponential decay. I log-transform the data, to stabilize
the error variance. At time t < t0, my model is

log(y_i)=log(exp(a0)+exp(b0))

at time t >= t0, the model is

log(y_i)=log(exp(a0-a1*(t_i - t0))+exp(b0=b1*(t_i - t0)))

I thought that I would have identifiability issues, but this model seems
to work fine except that the parameters t0 (the delay) is highly
correlated with the initial decay slope a0 (which makes sense, as the
longer the delay, the more rapid the drop has to be, conditional on the
data).

To get over this problem, I could reparameterize the problem, but it
isn't clear to me how to do this for the above model. I also thought
about using a penalized least square approach, to shrink t0 and a1
towards 0. I haven't seen much on penalized least squares in a nonlinear
least squares setting; is this a good way to go? Can I justifiably
penalize only a0 and a1, or should I also penalize the other parameters?

Thanks for any help!
Simon
-- 
Simon D.W. Frost, D.Phil.
Assistant Adjunct Professor of Pathology
University of California, San Diego
Mailcode 8208
UCSD Antiviral Research Center
150 W. Washington St.
San Diego, CA 92103
Tel: +1 619 543 8898
Fax: +1 619 543 5094
Email: sdfrost at ucsd.edu