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