An Imputation model by Dirichlet Process Mixture of Elliptical Copulas for Data of Mixed Type

TL;DR

This paper introduces a Bayesian nonparametric imputation model using an infinite mixture of elliptical copulas via Dirichlet process, improving data imputation accuracy for mixed-type data, especially in capturing tail dependence.

Contribution

It develops a flexible copula-based imputation method with a novel infinite mixture approach, extending prior finite mixture models to better handle multimodal distributions and tail dependence.

Findings

Infinite mixture copula model outperforms single component models in fit.

Model captures tail dependence more effectively.

Achieves more accurate imputation for continuous variables.

Abstract

Copula-based methods provide a flexible approach to build missing data imputation models of multivariate data of mixed types. However, the choice of copula function is an open question. We consider a Bayesian nonparametric approach by using an infinite mixture of elliptical copulas induced by a Dirichlet process mixture to build a flexible copula function. A slice sampling algorithm is used to sample from the infinite dimensional parameter space. We extend the work on prior parallel tempering used in finite mixture models to the Dirichlet process mixture model to overcome the mixing issue in multimodal distributions. Using simulations, we demonstrate that the infinite mixture copula model provides a better overall fit compared to their single component counterparts, and performs better at capturing tail dependence features of the data. Simulations further show that our proposed model achieves more accurate imputation especially for continuous variables and better inferential results in some analytic models. The proposed model is applied to a medical data set of acute stroke patients in Australia.