A Bayesian Singular Value Decomposition Procedure for Missing Data Imputation

Abstract

Missing data are common in empirical studies. Multiple imputation is a method to handle missing values by replacing them with plausible values. A common imputation method is multiple imputation with chain equations (MICE). MICE defines a series of conditional distributions to impute missing values. Although MICE is relatively easy to implement, it may not converge to a proper joint distribution. An alternative strategy is to model the variables jointly using the general location model, but this model can become complex when the number of variables increases. Both approaches require integration of prior information when there are more variables than cases. We propose a Bayesian model that is based on the singular value decomposition components of a continuous data matrix to impute missing values. The model assumes that the matrix is of low rank by applying double exponential prior distributions on the singular values. We describe an efficient sampling algorithm to estimate the model’s parameters and impute the missing data. The performance of the model is compared to current imputation methods in simulated and real datasets. Of all the methods considered and in most of the simulated and real datasets, the proposed procedure appears to be the most accurate and precise. Supplementary materials for this article are available online.

Keywords:

• Double exponential prior distribution
• Matrix decomposition
• Matrix recovery algorithm
• Multiple imputation

Disclaimer

Roee Gutman served as an expert witness for Janssen/Johnson & Johnson on an unrelated matter. Roee Gutman served as a consultant to Lion Point Capital on an unrelated matter.

Acknowledgments

We thank to the associate editor and referees for their constructive advice.

Additional information

Funding

Division of Mathematical Sciences; This research was supported by National Science Foundation grant DMS-1557466.