Multivariate regression spline model

The model for a multivariate regression spline is based on linear combinations of univariate spUne functions of the general form [10]... 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

Xu, Q. S., Massart, D. L., Liang, Y. Z., Fang, K. T. J. Chromatogr. A 998, 2003, 155-167. Two-step multivariate adaptive regression splines for modeling a quantitative relationship between gas chromatographic retention indices and molecular descriptors. 

Exploration of the linear modeling techniques and their combination with multivariate adaptive regression splines to predict gastrointestinal absorption of drugs... 

In this section, on the one hand, methods that are used to estimate intrinsically nonlinear parameters by means of nonlinear regression (NLR) analysis will be introduced. On the other hand, we will learn about methods that are based on nonpara-metric, nonlinear modeling. Among those are nonlinear partial least squares (NPLS), the method of alternating conditional expectations (ACE), and multivariate adaptive regression splines (MARS). 

If gas selectivity cannot be achieved by improving the sensor setup itself, it is possible to use several nonselective sensors and predict the concentration by model based, such as multilinear regression (MLR), principle component analysis (PCA), principle component regression (PCR), partial least squares (PLS), and multivariate adaptive regression splines (MARS), or data-based algorithms, such as cluster analysis (CA) and artificial neural networks (ANN) (for details see Reference 10) (Figure 22.5). For common applications of pattern recognition and multi component analysis of gas mixtures, arrays of sensors are usually chosen... 

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