Beyond Kaiser's Rule. A Hierarchical Disjoint PCA Approach to Digitalization and Growth.

High-dimensional data analysis often relies on latent variables for simplification, yet standard techniques like Principal Component Analysis (PCA) frequently suffer from poor interpretability. This paper proposes the use of Disjoint PCA to unveil naturally emergent, data-driven hierarchical structures. By iteratively solving the model for different levels of complexity, we visualize the “price of simplicity” through a variance-based dendrogram. This methodology also offers a selection tool for the number of components (Q) where traditional heuristics fail. An application on economic data demonstrates a stable, nested architecture across different levels of abstraction.