Brooks I, Watts D G, Soneson K K, Hensley P
Department of Macromolecular Sciences, SmithKline Beecham Pharmaceuticals, King of Prussia, Pennsylvania 19406.
Methods Enzymol. 1994;240:459-78. doi: 10.1016/s0076-6879(94)40060-1.
In the above discussion, we have introduced the profiling approach of Bates and Watts. It is an easy to implement, empirical approach to the determination of confidence intervals for parameters in nonlinear models. We have applied the approach to the analysis of equilibrium sedimentation data and have demonstrated that, although models for analyzing such data are formally nonlinear they are functionally linear. As such, linear approximation confidence intervals for the parameters are adequate for these models and data sets. Further, we have been able to examine the effect of implementing a multiple independent variable approach (in this case, using multiple rotor speeds) on the precision of the analysis. We found that the standard errors of the parameters were reduced and that this is accounted for by either the increase in the number of data points or the decreases in parameter correlation. In this case, profiling helped to visualize the effect on the sum of squares surface of reducing parameter correlation, making the effect of the small decreases in the correlation of some parameters more evident. Using profiling, it should be easy to explore other methods for the improvement of the analysis of ultracentrifugation data and to be able to quantitate the improvement. With the above discussion as an example, it is likely that the profiling approach should be quite useful and broadly applicable in the analysis of data in terms of nonlinear models.
在上述讨论中，我们介绍了贝茨和瓦茨的剖析方法。它是一种易于实施的实证方法，用于确定非线性模型中参数的置信区间。我们已将该方法应用于平衡沉降数据的分析，并证明，尽管用于分析此类数据的模型形式上是非线性的，但在功能上是线性的。因此，这些模型和数据集的参数的线性近似置信区间就足够了。此外，我们能够研究采用多自变量方法（在这种情况下，使用多个转子速度）对分析精度的影响。我们发现参数的标准误差降低了，这是由数据点数量的增加或参数相关性的降低所导致的。在这种情况下，剖析有助于直观显示降低参数相关性对平方和曲面的影响，使某些参数相关性的小幅降低的影响更加明显。使用剖析方法，应该很容易探索其他改进超速离心数据分析的方法，并能够对改进程度进行量化。以上述讨论为例，剖析方法在基于非线性模型的数据分析中可能非常有用且具有广泛的适用性。
