The amounts of data collected from each sample of e.g. chemical or biological materials have increased by orders of magnitude since the beginning of the 20th century. Furthermore, the number of ways to collect data from observations is also increasing. Such configurations with several massive data sets increase the demands on the methods used to analyse them. Methods that handle such data are called multiblock methods and they are the topic of this thesis. Data collected from advanced analytical instruments often contain variation from diverse mutually independent sources, which may confound observed patterns and hinder interpretation of latent variable models. For this reason, new methods have been developed that decompose the data matrices, placing variation from different sources of variation into separate parts. Such procedures are no longer merely pre-processing filters, as they initially were, but have become integral elements of model building and interpretation. One strain of such methods, called OPLS, has been particularly successful since it is easy to use, understand and interpret. This thesis describes the development of a new multiblock data analysis method called OnPLS, which extends the OPLS framework to the analysis of multiblock and path models with very general relationships between blocks in both rows and columns. OnPLS utilises OPLS to decompose sets of matrices, dividing each matrix into a globally joint part (a part shared with all the matrices it is connected to), several locally joint parts (parts shared with some, but not all, of the connected matrices) and a unique part that no other matrix shares. The OnPLS method was applied to several synthetic data sets and data sets of “real” measurements. For the synthetic data sets, where the results could be compared to known, true parameters, the method generated global multiblock (and path) models that were more similar to the true underlying structures compared to models without such decompositions. I.e. the globally joint, locally joint and unique models more closely resembled the corresponding true data. When applied to the real data sets, the OnPLS models revealed chemically or biologically relevant information in all kinds of variation, effectively increasing the interpretability since different kinds of variation are distinguished and separately analysed. OnPLS thus improves the quality of the models and facilitates better understanding of the data since it separates and separately analyses different kinds of variation. Each kind of variation is purer and less tainted by other kinds. OnPLS is therefore highly recommended to anyone engaged in multiblock or path model data analysis.

Multivariate and multiblock data analysis involves useful methodologies for analyzing large data sets in chemistry, biology, psychology, economics, sensory science, and industrial processes; among these methodologies, partial least squares (PLS) and orthogonal projections to latent structures (OPLS®) have become popular. Due to the increasingly computerized instrumentation, a data set can consist of thousands of input variables which contain latent information valuable for research and industrial purposes. When analyzing a large number of data sets (blocks) simultaneously, the number of variables and underlying connections between them grow very much indeed; at this point, reducing the number of variables keeping high interpretability becomes a much needed strategy. The main direction of research in this thesis is the development of a variable selection method, based on variable influence on projection (VIP), in order to improve the model interpretability of OnPLS models in multiblock data analysis. This new method is called multiblock variable influence on orthogonal projections (MB-VIOP), and its novelty lies in the fact that it is the first multiblock variable selection method for OnPLS models. Several milestones needed to be reached in order to successfully create MB-VIOP. The first milestone was the development of a single-block variable selection method able to handle orthogonal latent variables in OPLS models, i.e. VIP for OPLS (denoted as VIPOPLS or OPLS-VIP in Paper I), which proved to increase the interpretability of PLS and OPLS models, and afterwards, was successfully extended to multivariate time series analysis (MTSA) aiming at process control (Paper II). The second milestone was to develop the first multiblock VIP approach for enhancement of O2PLS® models, i.e. VIPO2PLS for two-block multivariate data analysis (Paper III). And finally, the third milestone and main goal of this thesis, the development of the MB-VIOP algorithm for the improvement of OnPLS model interpretability when analyzing a large number of data sets simultaneously (Paper IV). The results of this thesis, and their enclosed papers, showed that VIPOPLS, VIPO2PLS, and MB-VIOP methods successfully assess the most relevant variables for model interpretation in PLS, OPLS, O2PLS, and OnPLS models. In addition, predictability, robustness, dimensionality reduction, and other variable selection purposes, can be potentially improved/achieved by using these methods.