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  • March 2020
  • Article
  • Biometrika

Diagnosing Missing Always at Random in Multivariate Data

By: Iavor I. Bojinov, Natesh S. Pillai and Donald B. Rubin
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Abstract

Models for analyzing multivariate data sets with missing values require strong, often assessable, assumptions. The most common of these is that the mechanism that created the missing data is ignorable—a twofold assumption dependent on the mode of inference. The first part, which is the focus here, under the Bayesian and direct-likelihood paradigms, requires that the missing data are missing at random; in contrast, the frequentist-likelihood paradigm demands that the missing data mechanism always produces missing at random data, a condition known as missing always at random. Under certain regularity conditions, assuming missing always at random leads to an assumption that can be tested using the observed data alone, namely, the missing data indicators only depend on fully observed variables. Here, we propose three different diagnostic tests that not only indicate when this assumption is incorrect but also suggest which variables are the most likely culprits. Although missing always at random is not a necessary condition to ensure validity under the Bayesian and direct-likelihood paradigms, it is sufficient, and evidence for its violation should encourage the careful statistician to conduct targeted sensitivity analyses.

Keywords

Missing Data; Diagnostic Tools; Sensitivity Analysis; Hypothesis Testing; Missing At Random; Row Exchangeability; Analytics and Data Science; Mathematical Methods

Citation

Bojinov, Iavor I., Natesh S. Pillai, and Donald B. Rubin. "Diagnosing Missing Always at Random in Multivariate Data." Biometrika 107, no. 1 (March 2020): 246–253.
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About The Author

Iavor I. Bojinov

Technology and Operations Management
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More from the Authors
  • Nailing Prediction: Experimental Evidence on the Value of Tools in Predictive Model Development By: Daniel Yue, Paul Hamilton and Iavor Bojinov
  • On Ramp to Crypto By: Iavor Bojinov, Michael Parzen and Paul Hamilton
  • A Causal Test of the Strength of Weak Ties By: Karthik Rajkumar, Guillaume Saint-Jacques, Iavor I. Bojinov, Erik Brynjolfsson and Sinan Aral
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