Generalized orthogonal multiple co-inertia analysis(-PLS): new multiblock component and regression methods

The purpose of this paper is to develop new component-wise component and regression multiblock methods that overcome some of the difficulties traditionally associated with multiblocks, such as the step-by-step optimization and component orthogonalities. Generalized orthogonal multiple co-inertia analysis (GOMCIA) and generalized orthogonal multiple co-inertia analysis-partial least squares (GOMCIA-PLS) are proposed for modelling two sets of blocks measured on the same observations. We especially emphasize GOMCIA-PLS methods in which we consider one of the sets as predictive. All these methods are based on the step-by-step maximization of the same criterion under normalization constraints and produce orthogonal components or super-components. The solutions of the problem have to be computed with an iterative algorithm (which we prove to be convergent). We also give some interesting special cases and discuss the differences compared with a few other multiblock and/or multiway methods. Finally, short examples of real data are processed to show how GOMCIA-PLS can be used and its properties. Copyright (C) 2003 John Wiley Sons, Ltd.