Different Methods for Determining the Dimensionality of Multivariate Models

A tricky aspect in the use of all multivariate analysis methods is the choice of the number of Latent Variables to use in the model, whether in the case of exploratory methods such as Principal Components Analysis (PCA) or predictive methods such as Principal Components Regression (PCR), Partial Least Squares regression (PLS). For exploratory methods, we want to know which Latent Variables deserve to be selected for interpretation and which contain only noise. For predictive methods, we want to ensure that we include all the variability of interest for the prediction, without introducing variability that would lead to a reduction in the quality of the predictions for samples other than those used to create the multivariate model.