TinyLVR:A utility for viewing single predictor multivariate models in terms of a two factor latent vector model

Tapp, Henri S., Penfold, Robert and Kemsley, E. Kate ORCID: https://orcid.org/0000-0003-0669-3883 (2011) TinyLVR:A utility for viewing single predictor multivariate models in terms of a two factor latent vector model. Chemometrics and Intelligent Laboratory Systems, 105 (1). pp. 19-26. ISSN 0169-7439

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This paper describes an adaptation of Ergon's 2PLS approach (Compression into two-component PLS factorizations. J. Chemom. 2003: 17: 303-312.) to represent a single predictor regression model in terms of a two-factor latent vector model. The purpose of this reduction is to aid model interpretation and diagnostics. Non-orthogonal score vectors are produced from two orthonormal loading vectors: one identical to the first PLS loading vector, and a second built from the regression vector. Using an invertible matrix, the factorization can be alternatively represented by two orthogonal score vectors, one of which is proportional to centred predictions. An auxiliary set of loadings is also calculated, which captures a different model space, but is provided since its associated residuals have useful properties. Identities connecting the two model spaces are provided. The latent vector regression coefficients are not always least-squares estimates but can be represented as the solution to a two-term generalized ridge regression. Consequences of this are addressed. The utility of TinyLVR is demonstrated with example models built using stepwise variate selection and ridge regression. (c) 2010 Elsevier B.V. All rights reserved.

Item Type: Article
Uncontrolled Keywords: bi-plots,opls,target projection,regression model interpretation,multivariate,near-infrared spectroscopy,pls plus st,regression,projections,calibration,selection,plots,net
Faculty \ School: Faculty of Science > School of Mathematics
Faculty of Science > School of Chemistry
Depositing User: Pure Connector
Date Deposited: 24 Sep 2016 00:55
Last Modified: 21 Mar 2024 01:28
URI: https://ueaeprints.uea.ac.uk/id/eprint/60288
DOI: 10.1016/j.chemolab.2010.10.006

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