Integrative Interaction Analysis using Threshold Gradient Directed Regularization

For many complex business and industry problems, high-dimensional data collection and modeling have been conducted. It has been shown that interactions may have important implications beyond main effects. The number of unknown parameters in an interaction analysis can be larger or much larger than the sample size. As such, results generated from analyzing a single dataset are often unsatisfactory. Integrative analysis, which jointly analyzes the raw data from multiple independent studies, has been conducted in a series of recent studies and shown to outperform single-dataset analysis, meta-analysis, and other multi-datasets analyses. In this study, our goal is to conduct integrative analysis in interaction analysis. For regularized estimation and selection of important interactions (and main effects), we apply a Threshold Gradient Directed Regularization (TGDR) approach. Advancing from the exiting studies, the TGDR approach is modified to respect the "main effects, interactions" hierarchy. The proposed approach has an intuitive formulation and is computationally simple and broadly applicable. Simulations and the analyses of financial early warning system data and news-APP recommendation behavior data demonstrate its satisfactory practical performance.