Partial Least Squares Regression for Binary Data

Laura Vicente-Gonzalez, Elisa Frutos-Bernal and Jose Luis Vicente-Villardon ()
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Laura Vicente-Gonzalez: Departamento de Estadística, Facultad de Medicina, Universidad de Salamanca, 37007 Salamanca, Spain
Elisa Frutos-Bernal: Departamento de Estadística, Facultad de Medicina, Universidad de Salamanca, 37007 Salamanca, Spain
Jose Luis Vicente-Villardon: Departamento de Estadística, Facultad de Medicina, Universidad de Salamanca, 37007 Salamanca, Spain

Mathematics, 2025, vol. 13, issue 3, 1-29

Abstract: Classical Partial Least Squares Regression (PLSR) models were developed primarily for continuous data, allowing dimensionality reduction while preserving relationships between predictors and responses. However, their application to binary data is limited. This study introduces Binary Partial Least Squares Regression (BPLSR), a novel extension of the PLSR methodology designed specifically for scenarios involving binary predictors and responses. BPLSR adapts the classical PLSR framework to handle the unique properties of binary datasets. A key feature of this approach is the introduction of a triplot representation that integrates logistic biplots. This visualization tool provides an intuitive interpretation of relationships between individuals and variables from both predictor and response matrices, enhancing the interpretability of binary data analysis. To illustrate the applicability and effectiveness of BPLSR, the method was applied to a real-world dataset of strains of Colletotrichum graminicola , a pathogenic fungus. The results demonstrated the ability of the method to represent binary relationships between predictors and responses, underscoring its potential as a robust analytical tool. This work extends the capabilities of traditional PLSR methods and provides a practical and versatile solution for binary data analysis with broad applications in diverse research areas.

Keywords: partial least squares; binary data; biplot; NIPALS (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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