Partial Least Squares case study

Savolainen et al. investigated the role of Raman spectroscopy for monitoring amorphous content and compared the performance with that of NIR spectroscopy [41], Partial least squares (PLS) models in combination with several data pre-processing methods were employed. The prediction error for an independent test set was in the range of 2-3% for both NIR and Raman spectroscopy for amorphous and crystalline a-lactose monohydrate. The authors concluded that both techniques are useful for quantifying amorphous content however, the performance depends on process unit operation. Rantanen et al. performed a similar study of anhydrate/hydrate powder mixtures of nitrofurantoin, theophyllin, caffeine and carbamazepine [42], They found that both NIR and Raman performed well and that multivariate evaluation not always improves the evaluation in the case of Raman data. Santesson et al. demonstrated in situ Raman monitoring of crystallisation in acoustically levitated nanolitre drops [43]. Indomethazine and benzamide were used as model... 

The kinds of calculations described above are done for all the molecules under investigation and then all the data (combinations of 3-point pharmacophores) are stored in an X-matrix of descriptors suitable to be submitted for statistical analysis. In theory, every kind of statistical analysis and regression tool could be applied, however in this study we decided to focus on the linear regression model using principal component analysis (PCA) and partial least squares (PLS) (Fig. 4.9). PCA and PLS actually work very well in all those cases in which there are data with strongly collinear, noisy and numerous X-variables (Fig. 4.9). 

In the first case, attention is paid to excluding variables carrying low or redundant information, in the second, to excluding variables which are not functionally related to the studied response. In the latter, besides the exclusion of specific variables, one can condense the information from all the original variables into a few significant latent variables (linear combinations) by methods such as Principal Component Regression and Partial Least Squares regression. 

As with ordinary ATR spectroscopy, ATR-FT-IR imaging results can be analyzed quantitatively, some recent examples including the study of tablet dissolution in water. In this case, the concentration profiles of hydroxylpropylmethylcellulose (HPMC) and niacinamide, at different stages of the dissolution process, were utilized to provide an understanding of the drug release mechanism [54]. Using this technique, it could be shown that the concentration profiles of different components could be obtained with the partial least squares (PLS) method. Here, with... 

Several studies have employed chemometric designs in CZE method development. In most cases, central composite designs were selected with background electrolyte pH and concentration as well as buffer additives such as methanol as experimental factors and separation selectivity or peak resolution of one or more critical analyte pairs as responses. For example, method development and optimization employing a three-factor central composite design was performed for the analysis of related compounds of the tetracychne antibiotics doxycycline (17) and metacychne (18). The separation selectivity between three critical pairs of analytes were selected as responses in the case of doxycycline while four critical pairs served as responses in the case of metacychne. In both studies, the data were htted to a partial least square (PLS) model. The factors buffer pH and methanol concentration proved to affect the separation selectivity of the respective critical pairs differently so that the overall optimized methods represented a compromise for each individual response. Both methods were subsequently validated and applied to commercial samples. 

Partial least squares (PLS) were used to predict the mass fraction of the standards based on mean-centered and MSC-corrected spectra. More than 600 spectra were obtained for use in the study. The models developed were linear with intercepts near zero in all cases. The correlation coefficient (R ) for the models exceeded. 999, and reproduced the calibration sets to within 0.03 oxygen percent mass fraction. 

As far as the quantitative evaluation of vibrational spectra is concerned, IR and NIR spectroscopy follow Beer s law, whereas the Raman intensity JRaman is directly proportional to the concentration of the compound to be determined (Figure i),i iS Si To compensate laser fluctuations, in many cases, quantitative Raman spectroscopy is performed with an internal reference signal in the vicinity of the analytical band. For Raman and IR spectroscopy, quantitative analysis can be performed by either univariate evaluation of band heights/ areas or multivariate evaluation (e.g., partial least-squares (PLS) regression) of large spectral regions. Due to the overlap of many absorption bands for the quantitative analysis of NIR spectra, predominantly multivariate chemometric procedures are applied. For an in-depth study of the precautions, pitfalls, and limitations, which have to be observed or may be encountered in the measurement of vibrational spectra, the reader is referred to the pertinent literature. " ... 

In a case study of marine clay in Lianyungang, when the partial stress is equal to 31.9 kPa, we use the least square method to parameter fitting and obtain ... 

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