Semiparametric Bayesian Regression Analysis of Multi-Typed Matrix-Variate Responses

• Activity Number: 290 - Advanced Bayesian Topics (Part 3)
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Inkoo Lee* and Dipankar Bandyopadhyay
• Companies: Rice University and Virginia Commonwealth University
• Keywords: Exponential factor copula models; Markov chain Monte Carlo; Matrix-variate responses; Multiple response-types

Abstract

Complex data such as tensor and multiple types of responses can be found in dental medicine. Dental hygienists measured triple biomarkers at 28 teeth and 6 tooth-sites for each participant. These data have challenging characteristics: 1) binary and continuous responses, 2) matrix-variate responses for each biomarker have heavy tails, 3) pattern for missing teeth is not random. To circumvent these difficulties, we propose a joint model of multiple types of matrix-variate responses via a latent variable. This statistical framework incorporates exponential factor copula models to capture heavy-tail dependence and asymmetry. Since the number of existing teeth presents the magnitude of periodontal disease (PD) we model the missing mechanism. We also propose a tensor regularized horseshoe prior to identifying a sparse subset of regression coefficients. Our method guarantees posterior consistency under suitable priors. We illustrate the substantial advantages of our method over alternatives through simulation studies and the analysis of PD data.