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

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


J. Plass

M. Cattaneo

G. Schollmeyer

T. Augustin


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.


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.

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
Electronic ISSN 0888-613X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 90
Pages 292-306
Keywords Coarse data; Missing data; Coarsening at random (CAR); Likelihood-ratio test; Partial identification; Sensitivity analysis
Public URL
Publisher URL
Additional Information This is a description of an article accepted for future publication in: International journal of approximate reasoning, 2017, v.90.


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