Multiblock methods make it possible to relate a set of blocks of variables and to identify meaningful relationships among them. All variables are measured on the same observations, but each block represents one dimension of the problem to be addressed. This makes multiblock methods multidimensional data analysis methods, as they allow the modeling of a problem by incorporating multiple dimensions. The variable blocks are linked through a set of components. These components are linear combinations of the variables. The weights of these combinations are obtained by solving an optimization problem. Multiblock methods maximize a function of the covariance or the correlations between components or blocks of variables, subject to a set of equality constraints. The constraints may be imposed either on the components or on the weights. There are several strategies for solving the optimization problem, with the sequential approach being the most common one. A search algorithm provides a means for obtaining a set of weights and components for each block. Multiblock methods have been widely used in marketing, psychometrics, and the natural and life sciences. In this work, I will review the main formulations of the optimization problems and search algorithms, their benefits, risks, and limitations, as well as the practical consequences of adopting these models to address real-world problems.
