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Structural equation models (SEM) are powerful tools for estimating the value of a set of unobserved or latent variables. These latent variables represent concepts that can be inferred from blocks of variables measured in the same collection of individuals. The nature of the association between latent and manifest variables –formative or reflective, composites or factors—determines the mathematical model for estimating the variables and the relationship between them. Several methods exist for learning SEM, with sequential multiblock component methods widely applied in practice. A general framework is provided by Regularized Generalized Canonical Correlation Analysis (RGCCA). The machinery involves the construction of a set of block components in such a way to maximize a function of the covariances between linear combinations of the block of variables. Special cases of RGCCA are the classic methods of canonical correlation analysis and redundancy analysis, as well as SUMCOR, SSQCOR, and SABSCOR. In this work, I review the main definitions related to RGCCA, including its origins, theoretical foundations, optimization problems, and algorithms.

Structural equation models, RGCCA, multiblock learning