Specification and testing of hierarchical ordered response models with anchoring vignettes

Anchoring vignettes have been proposed as a way to correct for differential item functioning when individuals self-assess their health, or other aspects of their circumstances on an ordered categorical scale. The model relies on two key underlying assumptions of response consistency and vignette equivalence. Adopting a modified specification of the boundary equations in the compound hierarchical ordered probit model this paper develops joint and separate tests of these assumptions based on a score approach. Monte Carlo simulations show that the tests have good size and power properties in finite samples. We provide an application of the test to data from the Survey of Health, Aging and Retirement in Europe (SHARE, using self-reported data on pain. The tests are easy to implement, only requiring estimation of the restricted model under the null hypothesis.