Partial least squares multiple responses

Other chemometrics methods to improve caUbration have been advanced. The method of partial least squares has been usehil in multicomponent cahbration (48—51). In this approach the concentrations are related to latent variables in the block of observed instmment responses. Thus PLS regression can solve the colinearity problem and provide all of the advantages discussed earlier. Principal components analysis coupled with multiple regression, often called Principal Component Regression (PCR), is another cahbration approach that has been compared and contrasted to PLS (52—54). Cahbration problems can also be approached using the Kalman filter as discussed (43). 

For inttoductory purposes multiple linear regression (MLR) is used to relate the experimental response to the conditions, as is common to most texts in this area, but it is important to realise that odter regression methods such as partial least squares (PLS) are applicable in many cases, as discussed in Chapter 5. Certain designs, such as dtose of Section 2.3.4, have direct relevance to multivariate calibration. In some cases multivariate methods such as PLS can be modified by inclusion of squared and interaction terms as described below for MLR. It is important to remember, however, diat in many areas of chemistry a lot of information is available about a dataset, and conceptually simple approaches based on MLR are often adequate. 

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

Partial Least Squares regression (PLS) is usually performed on a - data matrix to search for a correlation between the thousands of CoMFA descriptors and biological response. However, usually after - variable selection, the PLS model is transformed into and presented as a multiple regression equation to allow comparison with classical QSAR models. 

Nowadays, the most favored regression technique is Partial Least Squares Regression (PLS or PLSR). As happens with PCR, PLS is based on components (or latent variables ). The PLS components are computed by taking into account both the x and the y variables, and therefore they are slightly rotated versions of the Principal Components. As a consequence, their ranking order corresponds to the importance in the modeling of the response. A further difference with OLS and PCR is that, while the former must work on each response variable separately, PLS can be applied to multiple responses at the same time. 

In addition to the above-described multiple linear regression method, metal ions can be determined by using other multivariate approaches such as partial least squares (PLS) and neural networks. Neural networks produce their own rules of operation by learning from previously processed examples. The learning process relies on a training rule that alters the weights of the neural connections as a function of the response to previous inputs and their desired responses. In this way, neural software learns from experience. 

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