Métodos multivariantes para evaluar patrones de estabilidad y cambio desde una perspectiva biplot

Laburpena

The main part of this research consists on the study of several three-way methods, stressing technical aspects on which comparisons between the methods can be based. The two most common methods are TRIADIC and TUCKER3 analyses. In the first one, data are compared over occasions by a principal component analysis of the matrices strung out into column vectors (considered as variables), belonging to different occasions (inter-analysis). TUCKER summarizes the data by components for all three modes, and for the entities pertaining to each mode they yield components loadings; in addition, a so-called core array is given which relates the components for all three modes to each other and gives equal attention to inter and intra relations. As a result of detailed study of these techniques, the main purpose of this work, among others, is to propose a new method, the CO-TUCKER, that solves the problem of describing not only the stable part of relations between variables (in different occurrences, such as multiple times/sites), but also to extract hidden structures, capture the underlying correlations and differences between variables in a multi-array. Unlike other related models, CO-TUCKER model proves to have some intrinsic and unique properties due to its relationship with the STATICO and the Tucker3 model. Thus, because of parsimony and correspondence between the nature of the data and the model, results of high structural quality, as well as more interpretable, were achieved. In addition, through the core matrix and the joint biplots, these results capture better and / or more real predictions. It also highlights information about the differences between data tables and provides a better understanding of the patterns of variability associated with temporal and spatial changes of complex data sets. To improve the interpretation of the results, a significant number of methodological problems will be presented.