Component- and Factor-Based Models for Data Fusion in the Behavioral Sciences

We start from a few examples of coupled behavioral sciences data, along with associated research questions and data-analytic methods. Linking up with these, we introduce a few concepts and distinctions, by means of which we specify the focus of this paper: 1) data that take the form of a collection of coupled matrices that are linked in either the experimental unit or the variable data mode; 2) associated with questions about the mechanisms underlying these data matrices; 3) which are to be addressed by data-analytic methods that rely on a submodel per data matrix, with a common parameterization of the shared data mode. Next, we outline the principles of two closely related families within this focus: the families of multiblock component- and factor-based models for data fusion (while considering both deterministic and stochastic model variants). Then, we review developments within these families to capture both similarities and differences between the different data matrices under study. We follow with a discussion on recent attempts to address quite a few challenges in data fusion based on multiblock component and factor models, including whether and how to differentially weigh the different data matrices under study, and problems such as dealing with large numbers of variables, outliers, and missing values. While the focus of this paper is on data and modeling contributions from the behavioral sciences, we point in a concluding section at their relevance for other domains and at the importance of related methods developed in those domains.