Partial regression-based models

Apart from pharmacophore-based approaches, a variety of methods were applied to decipher important ligand features of PXR activation. VolSurf descriptor-based partial least squares (PLS) regression-based models pointed toward amide responsive regions that implicated good acceptor abilities as key variables [33]. 

Endeavors have been made to find a link between two data sets (sensory versus instrumental data). The common goal of these tools is to discover the components or parameters whose variation explains the variation of sensory characteristics. The most useful statistical methods used for such purpose are partial least squares regression and generalized procrustes analysis. From a practical point of view, the models can be used to complement sensory assessment in routine quality control or in product and process development work. Regression-based statistical techniques are often used in conjunction with GC to distinguish well-known brands of alcoholic beverages from less expensive ones to detect counterfeit products. 

Experience in this laboratory has shown that even with careful attention to detail, determination of coal mineralogy by classical least-squares analysis of FTIR data may have several limitations. Factor analysis and related techniques have the potential to remove or lessen some of these limitations. Calibration models based on partial least-squares or principal component regression may allow prediction of useful properties or empirical behavior directly from FTIR spectra of low-temperature ashes. Wider application of these techniques to coal mineralogical studies is recommended. 

Based on the computed AHf, ELUMO values, and the kinetic rates, linear tree-energy relationships (LFERs) for the dechlorination rate constants were developed by using a partial least squares (PLS) regression. Using this model, the reaction rate constants can be expressed as ... 

On the surface it might appear that partial control does not require a first-principles model for its implementation. After all, M is a regression model and controller tuning is based on relay-feedback information. For simple systems this may be correct. However, for most industrially relevant systems it is not intuitively obvious what constitutes the dominant variables in the system and how to identify appropriate manipulators to control the dominant variables. This requires nonlinear, first-principles models. The models are run off-line and need only contain enough information to predict the correct trends and relations in the system. The purpose is not to predict outputs from inputs precisely and accurately, but to identify dominant variables and their relations to possible manipulators. 

In most cases, the MFTA models are built using the Partial Least Squares Regression (PLSR) technique that is suitable for the stable modeling based on the excessive and/or correlated descriptors (under-defined data sets). However, the MFTA approach is not limited to the PLSR models and can successfully employ other statistical learning techniques such as the Artificial Neural Networks (ANN) supporting the detection of the nonlinear structure-activity relationships. ... 

The simplest definition of model complexity is based on the number of terms in the model or, in other words, the model complexity is made up by the number of model variables from Ordinary Least Squares regression cpx = p), the number M of significant principal components from Principal Component Regression (cpx = M), and the number of significant latent variables from Partial Least Squares regression (cpx = M)... 

The kinetics of partial oxidation, ATR, and dry reforming of liquid hydrocarbons have also been reported recently.103,155 Pacheco et al.155 developed and validated a pseudo-homogeneous mathematical model for the ATR of isooctane and the subsequent WGS reaction, based on the reaction kinetics and intraparticle mass transfer resistance. They regressed the kinetic expressions from the literature for partial oxidation and steam reforming reactions to determine the kinetics parameters for the ATR of isooctane on Pt/ceria catalyst. The rate expressions used in the reformer modeling and the parameters of these rate expressions are given in Tables 2.19 and 2.20, respectively. 

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