PLS-regression: a basic tool of chemometrics
TL;DR: PLS-regression (PLSR) as mentioned in this paper is the PLS approach in its simplest, and in chemistry and technology, most used form (two-block predictive PLS) is a method for relating two data matrices, X and Y, by a linear multivariate model.
About: This article is published in Chemometrics and Intelligent Laboratory Systems.The article was published on 2001-10-28. It has received 7861 citations till now. The article focuses on the topics: Partial least squares regression.
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TL;DR: The authors conclude that PLS-SEM path modeling, if appropriately applied, is indeed a "silver bullet" for estimating causal models in many theoretical models and empirical data situations.
Abstract: Structural equation modeling (SEM) has become a quasi-standard in marketing and management research when it comes to analyzing the cause-effect relations between latent constructs. For most researchers, SEM is equivalent to carrying out covariance-based SEM (CB-SEM). While marketing researchers have a basic understanding of CB-SEM, most of them are only barely familiar with the other useful approach to SEM-partial least squares SEM (PLS-SEM). The current paper reviews PLS-SEM and its algorithm, and provides an overview of when it can be most appropriately applied, indicating its potential and limitations for future research. The authors conclude that PLS-SEM path modeling, if appropriately applied, is indeed a "silver bullet" for estimating causal models in many theoretical models and empirical data situations.
11,624 citations
TL;DR: An overview of NIR spectroscopy for measuring quality attributes of horticultural produce is given in this article, where the problem of calibration transfer from one spectrophotometer to another is introduced as well as techniques for calibration transfer.
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TL;DR: For a reversed-phase LC-MS/MS analysis of nine algal strains, MS-DIAL using an enriched LipidBlast library identified 1,023 lipid compounds, highlighting the chemotaxonomic relationships between theAlgal strains.
Abstract: Data-independent acquisition (DIA) in liquid chromatography (LC) coupled to tandem mass spectrometry (MS/MS) provides comprehensive untargeted acquisition of molecular data. We provide an open-source software pipeline, which we call MS-DIAL, for DIA-based identification and quantification of small molecules by mass spectral deconvolution. For a reversed-phase LC-MS/MS analysis of nine algal strains, MS-DIAL using an enriched LipidBlast library identified 1,023 lipid compounds, highlighting the chemotaxonomic relationships between the algal strains.
1,609 citations
TL;DR: The nature of the VIP method is explored and it is compared with other methods through computer simulation experiments considering four factors–the proportion of the number of relevant predictor, the magnitude of correlations between predictors, the structure of regression coefficients, andThe magnitude of signal to noise.
1,595 citations
TL;DR: Characteristics of the process industry data which are critical for the development of data-driven Soft Sensors are discussed.
1,399 citations
Cites methods from "PLS-regression: a basic tool of che..."
...…to data-driven Soft Sensors are the Principle Component Analysis (Jolliffe, 2002) in a combination with a regression model, Partial Least Squares (Wold et al., 2001), Artificial Neural Networks (Bishop, 1995; Principe et al., 2000; Hastie et al., 2001), Neuro-Fuzzy Systems (Jang et al., 1997;…...
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...One way is by transforming the input variables into a new reduced space with less co-linearity as it is done in the case of the PCA (Jolliffe, 2002) and PLS (Wold et al., 2001; Abdi, 2003)....
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References
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TL;DR: In this article, the authors examined partial least squares and principal components regression from a statistical perspective and compared them with other statistical methods intended for those situations, such as variable subset selection and ridge regression.
Abstract: Chemometrics is a field of chemistry that studies the application of statistical methods to chemical data analysis. In addition to borrowing many techniques from the statistics and engineering literatures, chemometrics itself has given rise to several new data-analytical methods. This article examines two methods commonly used in chemometrics for predictive modeling—partial least squares and principal components regression—from a statistical perspective. The goal is to try to understand their apparent successes and in what situations they can be expected to work well and to compare them with other statistical methods intended for those situations. These methods include ordinary least squares, variable subset selection, and ridge regression.
2,309 citations
TL;DR: In this article, the use of Partial Least Squares (PLS) for handling collinearities among the independent variables X in multiple regression is discussed, and successive estimates are obtained using the residuals from previous rank as a new dependent variable y.
Abstract: The use of partial least squares (PLS) for handling collinearities among the independent variables X in multiple regression is discussed. Consecutive estimates $({\text{rank }}1,2,\cdots )$ are obtained using the residuals from previous rank as a new dependent variable y. The PLS method is equivalent to the conjugate gradient method used in Numerical Analysis for related problems.To estimate the “optimal” rank, cross validation is used. Jackknife estimates of the standard errors are thereby obtained with no extra computation.The PLS method is compared with ridge regression and principal components regression on a chemical example of modelling the relation between the measured biological activity and variables describing the chemical structure of a set of substituted phenethylamines.
2,290 citations
TL;DR: In this paper, the mathematical and statistical structure of PLS regression is developed and the PLS decomposition of the data matrices involved in model building is analyzed. But the PLP regression algorithm can be interpreted in a model building setting.
Abstract: In this paper we develop the mathematical and statistical structure of PLS regression We show the PLS regression algorithm and how it can be interpreted in model building The basic mathematical principles that lie behind two block PLS are depicted We also show the statistical aspects of the PLS method when it is used for model building Finally we show the structure of the PLS decompositions of the data matrices involved
1,778 citations
TL;DR: In this article, the authors show that the inconsistency of the leave-one-out cross-validation can be rectified by using a leave-n v -out crossvalidation with n v, the number of observations reserved for validation, satisfying n v /n → 1 as n → ∞.
Abstract: We consider the problem of selecting a model having the best predictive ability among a class of linear models. The popular leave-one-out cross-validation method, which is asymptotically equivalent to many other model selection methods such as the Akaike information criterion (AIC), the C p , and the bootstrap, is asymptotically inconsistent in the sense that the probability of selecting the model with the best predictive ability does not converge to 1 as the total number of observations n → ∞. We show that the inconsistency of the leave-one-out cross-validation can be rectified by using a leave-n v -out cross-validation with n v , the number of observations reserved for validation, satisfying n v /n → 1 as n → ∞. This is a somewhat shocking discovery, because nv/n → 1 is totally opposite to the popular leave-one-out recipe in cross-validation. Motivations, justifications, and discussions of some practical aspects of the use of the leave-n v -out cross-validation method are provided, and results ...
1,700 citations