Evaluation of nonlinear regression with extended least squares: simulation study.
A new approach to nonlinear least-squares regression analysis using extended least squares (ELS) was compared with three conventional methods: ordinary least squares (OLS); weighted least squares 1/C (WLS-1) and weighted least squares 1/C2 (WLS-2). With Monte Carlo simulation techniques, 3 X 200 data sets were constructed with constant proportional error (5, 10, and 15% error) and 3 X 200 with constant additive error (0.05, 0.10, and 0.15 g/mL) from an initial (perfect) data set based on known parameters. Two sampling strategies were employed: one with 17 time points and one with 10 time points. All data sets were fitted by each of the four methods, and parameter estimation bias was assessed by comparing the mean parameter estimate with the known value. The relative precision of each method was investigated by examination of the absolute deviations of each individual parameter estimate from the known value. ELS performed as well as the appropriate weighting scheme (WLS-2 for constant proportional error sets and OLS for constant additive error sets) and was superior with regard to both bias and precision to less appropriate methods.
D007700:Kinetics; D008962:Models, Theoretical; D009010:Monte Carlo Method; D012044:Regression Analysis