Revealing Subgroups That Differ in Common and Distinctive Variation in Multi-Block Data: Clusterwise Sparse Simultaneous Component Analysis

Abstract

Social and behavioral studies more and more often yield multi-block data, which consist of novel blocks of data (e.g., data from wearable devices) and traditional blocks of data (e.g., survey data) collected from the same sample. Multi-block data offer researchers valuable insights into complex social mechanisms, where several influences act together. Yet such mechanisms are likely to differ among subgroups. Hence, fully revealing the composite mechanisms underlying multi-block data is challenging, since proper clustering analysis of such data requires methods that simultaneously detect the covariation of variables underlying all data blocks and the group differences therein. Additionally, the methods should be able to handle high-dimensional datasets, which might include many irrelevant variables. Here, we present Clusterwise Sparse Simultaneous Component Analysis (CSSCA), a method that groups the subjects that are driven by the same mechanisms and, at the same time, extracts cluster-specific components that model these mechanisms. By imposing structure constraints, CSSCA further distinguishes common mechanisms that underlie all data blocks from distinctive mechanisms that only underlie one or a few data blocks. In extensive simulations, CSSCA delivered convincing results in recovering the clusters and their associated component structures across various conditions. More importantly, CSSCA showed a clear advantage over existing methods when substantial cluster differences in the component structure were present. We demonstrated the usefulness of CSSCA in an application to data stemming from a study on personality.