Exploring a Diagnostic Test for Missingness at Random

Dominick Sutton (), Anahid Basiri and Ziqi Li
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Dominick Sutton: School of Geographical & Earth Sciences, University of Glasgow, Glasgow G12 8QQ, UK
Anahid Basiri: School of Geographical & Earth Sciences, University of Glasgow, Glasgow G12 8QQ, UK
Ziqi Li: Department of Geography, Florida State University, Tallahassee, FL 32306, USA

Mathematics, 2025, vol. 13, issue 11, 1-28

Abstract: Missing data remain a challenge for researchers and decision-makers due to their impact on analytical accuracy and uncertainty estimation. Many studies on missing data are based on randomness, but randomness itself is problematic. This makes it difficult to identify missing data mechanisms and affects how effectively the missing data impacts can be minimized. The purpose of this paper is to examine a potentially simple test to diagnose whether the missing data are missing at random. Such a test is developed using an extended taxonomy of missing data mechanisms. A key aspect of the approach is the use of single mean imputation for handling missing data in the test development dataset. Changing this to random imputation from the same underlying distribution, however, has a negative impact on the diagnosis. This is aggravated by the possibility of high inter-variable correlation, confounding, and mixed missing data mechanisms. The verification step uses data from a high-quality real-world dataset and finds some evidence—in one case—that the data may be missing at random, but this is less persuasive in the second case. Confidence in these results, however, is limited by the potential influence of correlation, confounding, and mixed missingness. This paper concludes with a discussion of the test’s merits and finds that sufficient uncertainties remain to render it unreliable, even if the initial results appear promising.

Keywords: missing data; survey nonresponse; generalized linear model; verification data; missing at random test; extended missing data taxonomy; confounding (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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