The heterogeneous thresholds ordered response model: Identification and inference

Although many surveys ask respondents to evaluate their own condition or to report their degree of satisfaction with various aspects of life, there is a persistent concern about interpersonal comparability of these self-assessments. Statistically, the problem is one of identification in ordered r… esponse models where the observed responses are derived from latent continuous random variables discretized through a set of heterogeneous thresholds or cutoff points. As a solution to the identification problem, King et al. (2004) propose the use of anchoring vignettes, namely brief descriptions of hypothetical people or situations that survey respondents are asked to evaluate on the same scale they used to rate their own situation. While vignettes have been introduced in several social surveys and are increasingly used in a variety of fields, reliability of this approach hinges crucially on the validity of the assumptions of response consistency and vignette equivalence. This paper proposes a joint test of these key assumptions based on the fact that the underlying statistical model is overidentified if the two assumptions hold. We apply our test to self-assessment on various components or domains of health using data from Release 2 of the first wave of the Survey of Health, Ageing and Retirement in Europe (SHARE). We find that, in most cases, the test rejects the overidentifying restrictions imposed by the assumptions of response consistency and vignette equivalence. Thus, our results cast doubts on the usefulness of anchoring vignettes for identifying and correcting interpersonal incomparability of answers to subjective survey questions