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A0530
Title: Bayesian inference for multivariate probit model with latent envelope Authors:  Kwangmin Lee - University of Wisconsin-Madison (United States) [presenting]
Abstract: The response envelope model is known to be an efficient method to estimate the regression coefficient under the context of the multivariate linear regression model. It identifies material and immaterial parts of responses to improve estimation efficiency. The response envelope model has been investigated only for continuous response variables. We suggest the multivariate probit model with latent envelope, in short, the probit envelope model, to apply the idea of the response envelope models to multivariate binary response data. In the probit envelope model, we employ the Gaussian latent vector formulation of the multivariate probit model. We assume that the latent vector follows the assumption by the response envelope models, i.e., the latent vector is assumed to have a covariate-invariant part called the immaterial part. Then, the response vector of the probit envelope model is derived by thresholding the latent vector. We address the identifiability of the probit envelope model by reparametrizing the model, and we suggest an MCMC algorithm for the Bayesian inference. We illustrate the probit envelope model via simulation studies and real data analysis, in which we also apply the probit envelope model to the multilabel classification problem.