On the testability of coarsening assumptions: a hypothesis test for subgroup independence

Plass, J.; Cattaneo, M.; Schollmeyer, G.; Augustin, T.

Abstract

Since coarse(ned) data naturally induce set-valued estimators, analysts often assume coarsening at random (CAR) to force them to be single-valued. Focusing on a coarse categorical response variable and a precisely observed categorical covariate, we re-illustrate the impossibility to test CAR and contrast it to another type of coarsening called subgroup independence (SI), using the data of the German Panel Study ``Labour Market and Social Security'' as an example. It turns out that -- depending on the number of subgroups and categories of the response variable -- SI can be point-identifying as CAR, but testable unlike CAR. A main goal of this paper is the construction of the likelihood-ratio test for SI. All issues are similarly investigated for the here proposed generalized versions, gCAR and gSI, thus allowing a more flexible application of this hypothesis test.

Citation

Plass, J., Cattaneo, M., Schollmeyer, G., & Augustin, T. (2017). On the testability of coarsening assumptions: a hypothesis test for subgroup independence. International Journal of Approximate Reasoning, 90, 292-306. https://doi.org/10.1016/j.ijar.2017.07.014

• Journal Article Type: Article
• Acceptance Date: Jul 25, 2017
• Online Publication Date: Sep 19, 2017
• Publication Date: 2017-11
• Deposit Date: Jul 26, 2017
• Publicly Available Date: Sep 19, 2018
• Journal: International journal of approximate reasoning
• Print ISSN: 0888-613X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 90
• Pages: 292-306
• DOI: https://doi.org/10.1016/j.ijar.2017.07.014
• Keywords: Coarse data; Missing data; Coarsening at random (CAR); Likelihood-ratio test; Partial identification; Sensitivity analysis
• Public URL: https://hull-repository.worktribe.com/output/453792
• Publisher URL: http://www.sciencedirect.com/science/article/pii/S0888613X17304905
• Additional Information: This is a description of an article accepted for future publication in: International journal of approximate reasoning, 2017, v.90.
• Contract Date: Jul 26, 2017