Tucker3-PCovR: The Tucker3 principal covariates regression model

In behavioral research, it is very common to have manage multiple datasets containing information about the same set of individuals, in such a way that one dataset attempts to explain the others. To address this need, in this paper the Tucker3-PCovR model is proposed. This model is a particular case of PCovR models which focuses on the analysis of a three-way data array and a two-way data matrix where the latter plays the explanatory role. The Tucker3-PCovR model reduces the predictors to a few components and predicts the criterion by using these components and, at the same time, the three-way data is fitted by the Tucker3 model. Both the reduction of the predictors and the prediction of the criterion are done simultaneously. An alternating least squares algorithm is proposed to estimate the Tucker3-PCovR model. A biplot representation is presented to facilitate the interpretation of the results. Some applications are made to empirical datasets from the field of psychology.