A Fused Latent and Graphical Model for Multivariate Binary Data

• Activity Number: 81 - Graphical Models
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Yunxiao Chen* and Xiaoou Li and Jingcheng Liu and Zhiliang Ying
• Companies: Emory University and University of Minnesota Twin Cities and Columbia University and Columbia University
• Keywords: latent variable model ; graphical model ; IRT model ; psychometrics ; convex optimization ; personality assessment

Abstract

We consider modeling, inference, and computation for analyzing multivariate binary data. We propose a new model that consists of a low dimensional latent variable component and a sparse graphical component. Our study is motivated by analysis of item response data in cognition assessment and has applications to many disciplines where item response data are collected. Standard approaches to item response data in cognition assessment adopt multidimensional nonlinear factor models, also known as the multidimensional item response theory (IRT) models. However, human cognition is typically a complicated process and thus may not be adequately described by just a few factors. Consequently, a low-dimensional latent factor model is often insufficient to capture the structure of the data. The proposed model adds a sparse graphical component that captures the remaining ad hoc dependence. Model selection and parameter estimation are carried out simultaneously through construction of a pseudo-likelihood function and properly chosen penalty terms.