Multiple linear regression multivariate approaches

In many chemical studies, the measured properties of the system can be regarded as the linear sum of the fundamental effects or factors in that system. The most common example is multivariate calibration. In environmental studies, this approach, frequently called receptor modeling, was first applied in air quality studies. The aim of PCA with multiple linear regression analysis (PCA-MLRA), as of all bilinear models, is to solve the factor analysis problem stated below ... 

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. 

PLSR nowadays is a reference method for multivariate calibration and its utilization has overcome limitations in the use of multiple linear regressions. In the PLSR approach, the full spectrum is used to establish a linear regression model, where the significant information contained in the near-infrared spectra is concentrated in a few latent variables that are optimized to produce the best correlation with the desired property to be determined. 

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. 

A table of correlations between the variables from the instrumental set and variables from the sensory set may reveal some strong one-to-one relations. However, with a battery of sensory attributes on the one hand and a set of instrumental variables on the other hand it is better to adopt a multivariate approach, i.e. to look at many variables at the same time taking their intercorrelations into account. An intermediate approach is to develop separate multiple regression models for each sensory attribute as a linear function of the physical/chemical predictor variables. 

Linear or nonlinear multiple regression analysis is used as a statistical tool to derive quantitative models, to check the significance of these models and of each individual term in the regression equation. Other statistical methods, such as discriminant analysis, principal component analysis (PCA), or partial least squares (PLS) analysis (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry) are alternatives to regression analysis (see Che mo me tries Multivariate View on Chemical Problems)Newer approaches compare the similarity of molecules with respect to different physicochemical or other properties with their biological activities. 

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