Complex Nonlinear Least-Squares Analysis

ABORTIVE COMPLEX Nonlinear kinetics of drug bioavailability, PHARMACOKINETICS NONLINEAR LEAST SQUARES ANALYSIS Nonmetal oxides,... 

J. R. Macdonald, J. Schoonman, and A. P. Lehnen, "The Applicability and Power of Complex Nonlinear Least Squares for the Analysis of Impedance and Immittance Data," Journal of Electroanalytical Chemistry, 131 (1982) 77-95. 

It is valuable to notice a difference in the method of data analysis for the modified Stem-Volmer plots (Section 8.8.A) and for the quenching-resi vedeiiussion spectra. In analyzing a modified Stem-Volmer plot, one assumes that a fraction of the fluorescence is totally inaccessible to quenchers. This may not be completely true because one component can be more weakly quenched, but still quenched to some extent. If possible, it is preferable to analyze the Stem-Volmer plots by nonlinear least-squares analysis when the/ and K/ values are variable. With this approach, one allows each component to contribute to the data according to its fractional accessibility, instead of forcing one component to be an inaccessible fraction. Of course, such an analysis is more complex, and the data may not be adequate to recover the values of fi and Kj at each wavelength. 

Presently, the most often used analysis is based on the complex nonlinear least-squares approximation of the impedance data acquired at a constant potential. The total impedance may be separated into the real and imaginary parts and fitted to the Randles model ... 

Y.-T. Tsai and D. W. Whitmore [1982] Nonlinear Least-Squares Analysis of Complex Impedance and Admittance Data, Solid State Ionics 1, 129-139. 

Principal component analysis and partial least squares analysis are chemometric tools for extracting and rationalizing the information from any multivariate description of a biological system. Complexity reduction and data simplification are two of the most important features of such tools. PCA and PLS condense the overall information into two smaller matrices, namely the score plot (which shows the pattern of compounds) and the loading plot (which shows the pattern of descriptors). Because the chemical interpretation of score and loading plots is simple and straightforward, PCA and PLS are usually preferred to other nonlinear methods, especially when the noise is relatively high. ... 

Complex chemical systems are composed of one or more components in a mixture with a significant degree of spectral interference, or of several components with a large amount of mutual physical and/or chemical interaction. In these cases, quantitative analysis is best performed by statistical methods such as principal component regression (PCR) or partial least squares (PLS) [36] these are offered in the software packages of instrument manufacturers and software suppliers. Artificial neural networks (ANNs) should be primarily used when a data set is nonlinear [37]. 

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