A New Algorithm for Computing Disjoint Orthogonal Components in the Parallel Factor Analysis Model with Simulations and Applications to Real-World Data

Abstract

In this paper, we extend the use of disjoint orthogonal components to three-way table analysis with the parallel factor analysis model. Traditional methods, such as scaling, orthogonality constraints, non-negativity constraints, and sparse techniques, do not guarantee that interpretable loading matrices are obtained in this model. We propose a novel heuristic algorithm that allows simple structure loading matrices to be obtained by calculating disjoint orthogonal components. This algorithm is also an alternative approach for solving the well-known degeneracy problem. We carry out computational experiments by utilizing simulated and real-world data to illustrate the benefits of the proposed algorithm.

Keywords

• degeneracy
• disjoint components
• heuristic algorithms
• Parafac model
• PCA
• R software