The STATICO method (combination of STATIS and the CIA) between two vertical multi-tables generalizes the co-inertia analysis (CIA) of two tables. In this article, being given the context of STATICO and new methods which recently have been just conceived (canonical correlation analysis and co-inertia analysis between two vertical multi-tables), we propose two methods enable to determine the co-inertia axes associated with each couple of tables. These two methods are conceived starting from the criterion of the sum of squared covariances, thus, extending the traditional co-inertia analysis. The co-inertia axes which are extracted allow to calculate squared coefficients of correlation and projected inertia. At the higher or equal order than two in the determination of the solution, the first criterion cuts out the inertia in the spaces of the individuals, on the other hand, the second criterion cuts out inertia in the spaces of variables. These methods allow to characterize the stability of the relationship between these two groups of variables. To show the interest of the conceived methods in this article with respect to the other methods, an example of application is treated by the sCIA2 and sOCIA2 methods, it refers to the ecological data on the Méaudret river of France.

common analysis, components, unit weights, M-tables, STATIS, co-inertia, coupling of the tables, STATICO.