Nonparametric Copula Models for Multivariate, Mixed, and Missing Data

TL;DR

This paper introduces a Bayesian mixture copula model for flexible, nonparametric joint modeling of multivariate mixed data with missing values, improving inference, prediction, and imputation in complex datasets.

Contribution

The paper develops a novel Bayesian mixture copula that handles mixed data types and missingness without specifying marginal models, ensuring posterior consistency and computational efficiency.

Findings

Demonstrates superior imputation accuracy over existing methods.

Effectively models complex dependencies in mixed data.

Addresses biases caused by improper missing data treatment.

Abstract

Modern datasets commonly feature both substantial missingness and many variables of mixed data types, which present significant challenges for estimation and inference. Complete case analysis, which proceeds using only the observations with fully-observed variables, is often severely biased, while model-based imputation of missing values is limited by the ability of the model to capture complex dependencies among (possibly many) variables of mixed data types. To address these challenges, we develop a novel Bayesian mixture copula for joint and nonparametric modeling of multivariate count, continuous, ordinal, and unordered categorical variables, and deploy this model for inference, prediction, and imputation of missing data. Most uniquely, we introduce a new and computationally efficient strategy for marginal distribution estimation that eliminates the need to specify any marginal models yet delivers posterior consistency for each marginal distribution and the copula parameters under missingness-at-random. Extensive simulation studies demonstrate exceptional modeling and imputation capabilities relative to competing methods, especially with mixed data types, complex missingness mechanisms, and nonlinear dependencies. We conclude with a data analysis that highlights how improper treatment of missing data can distort a statistical analysis, and how the proposed approach offers a resolution.