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

Carlos Martin-Barreiro, John A. Ramirez-Figueroa, Xavier Cabezas, Victor Leiva, Ana Martin-Casado and M. Purificación Galindo-Villardón
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Carlos Martin-Barreiro: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
John A. Ramirez-Figueroa: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
Xavier Cabezas: Faculty of Natural Sciences and Mathematics, Universidad Politécnica ESPOL, Guayaquil 090902, Ecuador
Victor Leiva: School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
Ana Martin-Casado: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain
M. Purificación Galindo-Villardón: Department of Statistics, Universidad de Salamanca, 37008 Salamanca, Spain

Mathematics, 2021, vol. 9, issue 17, 1-22

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; three-way tables (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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