Block chemometric methods

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). 

Partial least-squares path modeling with latent variables (PLS), a newer, general method of handling regression problems, is finding wide apphcation in chemometrics. This method allows the relations between many blocks of data ie, data matrices, to be characterized (32—36). Linear and multiple regression techniques can be considered special cases of the PLS method. 

Some of the most interesting theoretical developments in chemometrics over the past few years have been in so-called multiway or multimode data analysis. Many such methods have been available for some years, especially in the area of psychometrics, and a few do have relevance to chemistry. It is important, though, not to get too carried away with the excitement of these novel theoretical approaches. We will restrict the discussion here to trilinear PLS1, involving a three-way x block and a single c variable. If there are several known calibrants, the simplest approach is to perform trilinear PLS1 individually on each variable. 

The problems at the end of each chapter form an important part of the text, the examples being a mixture of simulations (which have an important role in chemometrics) and real case studies from a wide variety of sources. For each problem the relevant sections of the text that provide further information are referenced. However, a few problems build on the existing material and take die reader further a good chemometrician should be able to use the basic building blocks to understand and use new methods. The problems are of various types, so not every reader will want to solve all die problems. Also, instructors can use the datasets to construct workshops or course material that go further than the book. 

Multi-block methods are a rather new area within chemometrics and especially the combination with interval-based selection methods seems to be an interesting avenue for enhancement of predictive performance and understanding of the underlying structure. 

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