Multivariate Regression with Block-Structured Predictors with an Application to Eye-Tracking Data Analysis

• Activity Number: 652
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Saier Ye*+ and Lisha Chen and Katarzyna Chawarska
• Companies: and Yale and Yale School of Medicine
• Keywords: reduced-rank regression ; rank selection ; data integration ; model identifiability ; supervised factor model

Abstract

We study the problem of predicting multiple responses from a common set of predictor variables. Applying Ordinary Least Squares separately on the responses overlooks possible correlations between them and is not desirable. Reduced Rank Regression (RRR) takes advantage of those interrelationships by imposing rank constraints on the coefficient matrix. We explore an extension of RRR to accommodate data with "multi-block" structure in the predicting variables. The block structure accounts for the fact that multiple types of data or multiple measures under different experiment conditions are available for a common set of objects. Our extensive simulation studies show that our model exceeds the classic RRR in terms of prediction accuracy and model interpretability. In a particular autism study, we are interested in predicting multiple diagnostic scores of a common group of toddlers, based on four blocks of eye-tracking data reflecting their attentional patterns responding to four distinct social scenes. Our model achieves two types of latent factors, with one constructed jointly by all the conditions and the other formed within each individual condition.