RE: Log-transformation

From:"Kowalski, Ken" Subject:RE: [NMusers] Log-transformation Date:Fri, 4 Apr 2003 12:10:09 -0500 Hi Luann, Another option is the following log-transformed model that introduces an additional theta to account for systematic bias at very low concentrations to resolve the log(0) problem. This approach is suggested by Beal, JPP 2001;28:481-504. M = THETA(n) Y = LOG(F+M) + (F/(F+M))*EPS(1) + (M/(F+M))*EPS(2) When F>>M the model collapses to the standard log-transformed model with EPS(1) the additive residual error in the log-scale. When M>>F (i.e., as F goes to zero) the prediction goes to log(M) (i.e., the bias) and EPS(2) becomes dominant representing the residual variation at very low concentrations. A reasonable estimate of M should be around the QL (quantification limit) or lower. Ken