Flexible Multivariate Imputation Modeling Based on Copulas and Dirichlet Processes

• Activity Number: 374
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Patrick Joyce*+ and Joseph Schafer and Joshua Tokle
• Companies: U.S. Census Bureau and U.S. Census Bureau and U.S. Census Bureau
• Keywords: Missing Data ; Multivariate Models

Abstract

Traditional model-based imputation methods describe the complete data by common parametric forms. In some applications, however, it is desirable to relax parametric assumptions, especially with respect to the marginal distributions of the variables to be imputed. We propose flexible imputation procedures that preserve distributional features and inter-variable relationships. We separate the modeling of marginal distributions from the modeling of relationships through the use of copulas. A copula describes the relationships among the the random variables by translating their quantiles to standard uniform variates and applying a joint distribution (e.g., multivariate normal) with a similar translation. For the marginal distributions, we apply nonparametric Bayesian techniques based on Dirichlet processes. We describe a Markov chain Monte Carlo procedure for simulating multiple imputations of missing values assuming that nonresponse is ignorable, and we apply the method to a realistic data example.