Error models for log-transformed data

Dear NMusers, I am working on a PK model using log-transformed data. I have read previous discussions on NMusers regarding this, and they are really helpful, but I am still a little bit confused about the following questions. I would greatly appreciate it if someone could make it clear: 1. Dr. Mats Karlsson suggested Y=LOG(F)+SQRT(THETA(x)**2+THETA(y)**2/F**2)*ERR(1) with $SIGMA 1 FIX as an equivalent error structure to the additive+proportional error model on the normal scale. What is the rationale of fixing $SIGMA 1? 2. Dr. Stu Beal and Dr. William Bachman suggested the "double exponential error model": Y = LOG(F+M) + (F/(F+M))*ERR(1) + (M/(F+M))*ERR(2) without fixing $SIGMA. The Goodness-of-Fit plot looks slightly better using this error model in my study. What an error structure on the normal scale is this "double exponential error model" equivalent to? 3. Compared to the simplest error model Y=LOG(F)+ERR(1), the two error models mentioned above contain additional THETA's. Are these additional THETA's accounted for in the calculation of the objective function value? This especially bothers me because the "double exponential error model" leads to a lower OFV compared to Y=LOG(F)+ERR(1) (also slightly better Goodness-of-Fit plot) in my study. Sorry for the length. Would anyone please give me some explanations or references? Thanks a lot! Kelong Han PhD Candidate