A New Two-Mode Component Model with Applications to Marketing Analytics

In many studies, it is important to reduce not only the variable mode of a data matrix but also the individual mode, because characterizing entities in the first mode can be equally desirable. In this manuscript, we propose a new two-mode component model, introduced as Disjoint-TMC, together with an algorithm for computing disjoint orthogonal components in both modes. The method combines an Alternating Least Squares (ALS) technique with a heuristic procedure to enforce disjointness in the loading matrices. As a result, two disjoint orthogonal loading matrices are obtained, along with a core structure that captures the most relevant interactions between reduced modes. A distinctive feature of the Disjoint-TMC model is that it enables grouping of entities in the first mode-such as firms, consumers, suppliers, products, brands, time periods or regions in marketing applications-and allows a formal characterization of these groups. While this approach produces a loss of fit compared to unconstrained decompositions, our computational experiments demonstrate clear benefits in interpretability. Applications in marketing analytics are included to demonstrate the benefits of the proposed model, and a Python library is provided to facilitate its use and extension by other researchers. This work provides both methodological innovation and practical tools for interpretable two-mode analysis.