Multivariate Bayesian Lasso Regression for Latent Achievement Scores

• Activity Number: 535
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Trevor Park* and Steven A. Culpepper
• Companies: University of Illinois at Urbana-Champaign and University of Illinois at Urbana-Champaign
• Keywords: generalized Laplace distribution ; item response theory ; NAEP ; group Lasso

Abstract

We introduce multivariate regression with the Bayesian Lasso (Park & Casella 2008). The prior on the regression coefficients is a generalized version of the Laplace distribution. An efficient Gibbs sampler can be constructed based on a connection with the inverse Gaussian distribution. The multivariate Bayesian Lasso is easily included in larger models for latent response variables. We demonstrate its ability to relate latent multivariate achievement scores to student characteristics using mathematics achievement data from 175,200 8th graders in the 2011 National Assessment of Educational Progress.