Bin-3-Way-PARAFAC-PLS: A 3-Way Partial Least Squares for Binary Response

In various research domains, researchers frequently encounter multiple datasets pertaining to the same subjects, with one dataset providing explanatory variables for the others. To address this structure, we introduce the Binary 3-way PARAFAC Partial Least Squares (Bin-3-Way-PARAFAC-PLS), a novel multiway regression method. This method is specifically engineered for scenarios involving a three-way real-valued explanatory data array and a matrix of binary response data. We detail the algorithm’s implementation and illustrate its practical application. Furthermore, we describe biplot representations to aid in result interpretation. The accompanying software necessary for implementing the method is also provided. Finally, the proposed method’s utility in real-world problem-solving is demonstrated through its application to a psychological dataset.