Thomson A H, Kelman A W, Whiting B
J Pharm Sci. 1985 Dec;74(12):1327-30. doi: 10.1002/jps.2600741215.
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.
一种使用扩展最小二乘法（ELS）进行非线性最小二乘回归分析的新方法，与三种传统方法进行了比较：普通最小二乘法（OLS）；加权最小二乘法1/C（WLS-1）和加权最小二乘法1/C2（WLS-2）。利用蒙特卡罗模拟技术，基于已知参数，从初始（完美）数据集中构建了3×200个具有恒定比例误差（5%、10%和15%误差）的数据集以及3×200个具有恒定加性误差（0.05、0.10和0.15 g/mL）的数据集。采用了两种采样策略：一种有17个时间点，另一种有10个时间点。所有数据集都用这四种方法进行拟合，并通过将平均参数估计值与已知值进行比较来评估参数估计偏差。通过检查每个单独参数估计值与已知值的绝对偏差，研究了每种方法的相对精度。ELS的表现与适当的加权方案（对于恒定比例误差集为WLS-2，对于恒定加性误差集为OLS）相当，并且在偏差和精度方面都优于不太合适的方法。
