Weight randomization test for the selection of the number of components in PLS models

Abstract

The selection of the optimal number of components remains a difficult but essential task in partial least squares (PLS). Randomization tests have the advantage of being automatic and they make use of the entire dataset, in contrary with the widely used cross‐validation approaches. Partial least squares modeling may include component(s) with a large amount of irrelevant data variation, and this might affect the model, depending on the assigned y‐loading (which is the regression coefficient in the latent domain). This has recently been indicated by us in the basic sequence framework with respect to the underlying theory of the PLS algorithm and presented to the chemometrics society. We will show in this work that this irrelevant data variation is the root cause of the difficulty in current methods for selecting the optimal number of components. For randomization tests, PLS models with nonsignificant components may result in false positive tests because of the incorrect assumption that “the components enter the model in a natural order”. In this work, we introduce a new randomization test, weight randomization test, selection of the optimal number of components in PLS in light of the underlying theory of the PLS algorithm. In the proposed method the null distribution is well characterized and efficiently determined taking into account a newly defined model quality metric: the number of consecutive non‐significant components (CNC). We illustrate the effectiveness of weight randomization test in optimization of preprocessing as well as in classification models, where results are compared with the double cross‐validation procedure for the latter. This is an important step towards the full automation of PLS model development and routine updates.

Mass Spectrometry Imaging as a Tool to Investigate Region Specific Lipid Alterations in Symptomatic Human Carotid Atherosclerotic Plaques

“…PLS was performed in MATLAB using the plsregress function. The number of the model components for each region was chosen using a weight randomization test [ 63 ]. Characteristic features that discriminated between symptomatic and asymptomatic plaques were defined as the lipid ions with a variable importance in the projection (VIP) greater than one [ 64 ] with a loading on the first PLS axis exceeding the 90th percentile of the positive (increased in symptomatic) or negative (increased in asymptomatic) values.…”

Analysis of Raman spectra for the verification of Australian grass‐ and grain‐fed beef using principal component analysis and partial least square models

“…Researchers have utilised partial least squares discriminant analysis (PLS‐DA) for Raman spectroscopy modelling for many years with great success. [ 16–18 ] In fluorescence spectroscopy, application of PLS‐DA was used to successfully authenticate beef muscles and shows the potential for PLS‐DA to be used in subcutaneous beef fat. Beattie et al [ 19 ] have successfully utilised Raman spectroscopy in combination with PLS‐DA modelling to classify adipose tissue of various species including beef, but no study has utilised these methods to classify the production system of cattle.…”

Variable Selection in Untargeted Metabolomics and the Danger of Sparsity

“…For multivariate analysis, the duplicate measurements were used directly, because multivariate methods may distinguish between variance that explains the response and variance that does not explain the response, e.g., instrumental variability. Multivariate analysis included the following: OPLSDA [ 29 , 30 ] in combination with VIP [ 6 ], weight randomization test for partial least squares (WRT-PLS) [ 31 ] in combination with sMC [ 8 ], CARS-PLS-DA[ 11 ] with two latent variables, and sparse PLS-DA with one latent variable [ 10 ]. Double cross-validation was used to validate the results [ 32 ].…”