Nonparametric Copula Models for Mixed Data with Informative Missingness
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Modern datasets commonly feature both substantial missingness and 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 and accommodate mixed data types. To address these challenges, we develop a novel Bayesian mixture copula for joint and nonparametric modelling of 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 efficient strategy for marginal distribution estimation, which eliminates the need to specify any marginal models yet delivers strong posterior consistency for both the marginal distributions and the copula parameters even in the presence of informative missingness (i.e., 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.
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