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

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Abstract
Since coarse(ned) data naturally induce setvalued estimators, analysts often assume coarsening at random (CAR) to force them to be singlevalued. Focusing on a coarse categorical response variable and a precisely observed categorical covariate, we reillustrate 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 pointidentifying as CAR, but testable unlike CAR. A main goal of this paper is the construction of the likelihoodratio 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.