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Activity Number: 143 - SPEED: Bayesian Methods and Social Statistics Part 1
Type: Contributed
Date/Time: Monday, August 8, 2022 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #323495
Title: Parameter-Expanded Data Augmentations for Analyzing Mixed Ordinal and Continuous Data with Missing Values
Author(s): Xiao Zhang*
Companies: Michigan Technological University
Keywords: MCMC; multivariate probit model; non-identifiable multivariate probit model; mixed ordinal and continuous data; parameter-expanded data augmentation; missing data

It is a rigorous task to jointly analyze mixed ordinal and continuous data, especially with substantial missing values, due to the complicated correlated structure of those mixed data and nonidentifiability induced by variance parameters (such as in joint mixed effect models). Also, the identifiable multivariate probit model requires the variances of the latent normal variables fixed at 1, thus the joint covariance matrix of the latent variables and the continuous multivariate normal variables is restricted at some of the diagonal elements which are fixed at 1. This hinders to develop efficient Markov chain Monte Carlo (MCMC) sampling methods. In this investigation, we propose a parameter-expanded data augmentation to analyze mixed ordinal and continuous data with missing values by assuming multivariate probit model for ordinal data and continuous variables following multivariate normal distributions. By introducing redundant variance parameters our algorithm shows that the convergence and mixing of the MCMC sampling components exceed those based on the identifiable model. We illustrate our method through simulation studies and a real data application.

Authors who are presenting talks have a * after their name.

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