Imputation in High-Dimensional Economic Data as Applied to the Agricultural Resource Management Survey

Abstract

In this article, we consider imputation in the USDA’s Agricultural Resource Management Survey (ARMS) data, which is a complex, high-dimensional economic dataset. We develop a robust joint model for ARMS data, which requires that variables are transformed using a suitable class of marginal densities (e.g., skew normal family). We assume that the transformed variables may be linked through a Gaussian copula, which enables construction of the joint model via a sequence of conditional linear models. We also discuss the criteria used to select the predictors for each conditional model. For the purpose of developing an imputation method that is conducive to these model assumptions, we propose a regression-based technique that allows for flexibility in the selection of conditional models while providing a valid joint distribution. In this procedure, labeled as iterative sequential regression (ISR), parameter estimates and imputations are obtained using a Markov chain Monte Carlo sampling method. Finally, we apply the proposed method to the full ARMS data, and we present a thorough data analysis that serves to gauge the appropriateness of the resulting imputations. Our results demonstrate the effectiveness of the proposed algorithm and illustrate the specific deficiencies of existing methods. Supplementary materials for this article are available online.

Keywords:

• ARMS
• Gaussian copula
• Imputation
• Markov chain Monte Carlo
• Missing data

Acknowledgments

This research was sponsored by the Cross-Sector Research in Residence Program between the National Institute of Statistical Sciences (NISS) and National Agricultural Statistics Service (NASS). Foremost, the authors thank Barry Goodwin, Darcy Miller, and Kirk White and acknowledge their contributions to the research project associated with the work presented here. Additionally, the authors thank Dale Atkinson, Wendy Barboza, Cynthia Clark, Mark Harris, Alan Karr, and Nell Sedransk for helpful comments and organizational support of the research project, as well as Phillip Kott for helpful comments. The authors also thank Beth Edwards, Bob Garino, and Matthew Henderson for data and computing support. Further, the authors thank the editor, an associate editor, and two anonymous reviewers for detailed comments and suggestions that greatly helped to improve this article. Much of this research was conducted while M. W. Robbins was a Postdoctoral Fellow with NISS. The views expressed are those of the authors and do not necessarily represent the views of NASS or the USDA.

Notes

^aExcludes the 24 global covariates.