Multiple Imputation Using Gaussian Copulas

TL;DR

This paper introduces a Gaussian copula-based method for multiple imputation of missing data, demonstrating improved bias, coverage, and efficiency over existing methods in social science research.

Contribution

The paper presents a novel, easy-to-use Gaussian copula approach for multiple imputation that performs better than traditional methods, especially with non-normal data.

Findings

Gaussian copula method has smaller bias

Higher coverage rates with the copula approach

Narrower confidence intervals, especially with non-normal variables

Abstract

Missing observations are pervasive throughout empirical research, especially in the social sciences. Despite multiple approaches to dealing adequately with missing data, many scholars still fail to address this vital issue. In this paper, we present a simple-to-use method for generating multiple imputations using a Gaussian copula. The Gaussian copula for multiple imputation (Hoff, 2007) allows scholars to attain estimation results that have good coverage and small bias. The use of copulas to model the dependence among variables will enable researchers to construct valid joint distributions of the data, even without knowledge of the actual underlying marginal distributions. Multiple imputations are then generated by drawing observations from the resulting posterior joint distribution and replacing the missing values. Using simulated and observational data from published social science research, we compare imputation via Gaussian copulas with two other widely used imputation methods: MICE and Amelia II. Our results suggest that the Gaussian copula approach has a slightly smaller bias, higher coverage rates, and narrower confidence intervals compared to the other methods. This is especially true when the variables with missing data are not normally distributed. These results, combined with theoretical guarantees and ease-of-use suggest that the approach examined provides an attractive alternative for applied researchers undertaking multiple imputations.