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

Plass, Julia; Cattaneo, Marco E. G. V.; Schollmeyer, Georg; Augustin, Thomas (22. March 2017): On the testability of coarsening assumptions: A hypothesis test for subgroup independence. Department of Statistics: Technical Reports, No.201

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.

• Item Type: Paper (Technical Report)
• Keywords: coarse data, missing data, coarsening at random (CAR), likelihood-ratio test, partial identification, sensitivity analysis
• Faculties: Mathematics, Computer Science and Statistics > Statistics > Technical Reports
• Subjects: 500 Science > 510 Mathematics
• JEL Classification: C
• Language: English