Traditional factor analysis provides an important tool to investigate standard two-way data regarding the measurements of a collection of manifest variables (e.g., various anxiety scales registered by a psychologist) on a set of individuals (e.g., patients). However, it may occur that, for getting more information on the analyzed phenomena, such measurements are repeated in different (time) occasions (e.g., by a number of psychologists, and/or in different stressful conditions, and/or yearly). In these cases, the observed data acquire a multi-way structure, and they can be stored in a multi-way array or tensor (standard matrices can be seen as two-way arrays or tensors). Multi-way data are inherently complex, making conventional factor analysis inadequate. While posing several challenges from a theoretical point of view, such a data complexity has also a positive by-product in the richness of data features that are observed and made available to deepen the knowledge on the phenomena of interest. In this talk, limiting the attention to the three-way framework, I will show how to generalize traditional factor analysis to three-way data with a particular focus on the so-called Tucker3 and PARAllel FACtor (PARAFAC) models. Tucker3 and PARAFAC will be introduced, and their recent advances, developed to fully exploit the rich information given by such a complex and unconventional data structure, will be discussed. These advances include novel penalized estimation methods, as well as new modeling strategies.
about the speaker
Paolo Giordani is Full Professor of Statistics at Sapienza University of Rome, where he obtained his PhD in Statistical Methodology in 2005. His research focus is on dimension reduction, mainly principal component techniques, factor analysis and clustering methods for two- and multi-way data. Paolo has published in a variety of high-quality peer-review journals such as Psychometrika, the British Journal of Mathematical and Statistical Psychology and the Journal of Multivariate Analysis, among other outlets. He is author of four R packages (ThreeWay, fclust, dclust, datasetsICR) and of a Springer monography on applied research in clustering with the R software. Paolo currently serves as Executive Editor for Metron and as an Associate Editor for Advances in Data Analysis and Classification. He is currently a member of the Scientific Committee of the Classification and Data Analysis Group of the Italian Statistical Society.