LAUSR

Methods capable of handling multiple blocks of data have increased in popularity both in industry and academia, namely, in the fields of chemistry, food and beverages, pharmacology, and biology. Among the multiblock methodologies, sequential orthogonalized partial least squares (SO‐PLS) has been attracting great interest, given its interpretation capabilities (eg, the possibility to estimate the relative additional contributions of each block to predict the response and the degree of mutual overlap, ie, the blocks' communalities) associated to desirable modeling features, such as the independence from the relative scaling of the different data blocks and the flexibility to handle blocks with different dimensionalities and pseudo‐ranks. Given the sequential nature of SO‐PLS, it is critically dependent on the order of the blocks used. When a priori knowledge exists about the natural ordering of the blocks (eg, data arising from sequential operations in a production process), this specification is straightforward. However, in the absence of such knowledge or in cases where no order should be preferred a priori (as happens in the case study of this article), SO‐PLS faces the problem of having to find the most adequate one through the exhaustive search of all permutations. This problem is particularly relevant when the number of blocks is larger than 3, getting exponentially worse as this number increases. Situations where the number of natural data blocks is significant are already quite frequent (eg in multistage batch operations) and will tend to occur more often in the future, as Manufacturing 4.0 takes its course and data sources from the entire value chain become more abundant. Therefore, more efficient and systematic approaches are required to retain the benefits of SO‐PLS while coping with the increasing demands for data processing and analysis in Big Data applications. In this article, we introduce Stepwise SO‐PLS as an efficient algorithm for selecting the blocks ordering when performing SO‐PLS, with capabilities of block exclusion (a feature not shared by other current multiblock approaches). A robust statistical comparison framework based on Monte Carlo cross‐validation is employed to compare the proposed stepwise SO‐PLS formulation with the current systematic approach for selecting the block order and its new variant allowing for blocks selection, in their prediction capabilities. A real case study of the prediction of Madeira wine age will be used for establishing the comparison.