Abstract
After showing that plain covariance or correlation-based criteria are generally not suitable to deal with multiple-block component models in an exploratory framework, we propose an extended criterion: multiple co-structure (MCS). MCS combines the goodness-of-fit indicator of the component model to a flexible measure of structural relevance of the components. Thus, it allows to track various kinds of interpretable structures within the data, on top of variance–maximizing components: variable-bundles, components close to satisfying relevant structural constraints, and so on. MCS is to be maximised under unit-norm constraints on coefficient-vectors. We provide a dedicated ascent algorithm for it. This algorithm is nested into a more general one, named THEME (thematic equation model explorator), which calculates several components per data-array and extracts nested structural component models. The method is tested on simulated data and applied to physicochemical data.