[R] Collinearity in nls problem

From: Simon Frost <sdfrost_at_ucsd.edu>
Date: Tue 28 Feb 2006 - 11:34:19 EST


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@ucsd.edu

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Received on Tue Feb 28 12:20:26 2006

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