An extended hierarchical ordered probit model robust to heteroskedastic vignette perceptions with an application to functional limitation assessment

Abstract

To improve interpersonal comparability of self-reported measures, anchoring vignettes are increasingly collected in surveys and modeled as the hierarchical ordered probit (HOPIT) model. This paper—based on the idea of psychological distance—relaxes the assumption of vignette equivalence in the HOPIT by allowing for heteroscedasticity in respondents’ perceptions of vignettes. Particularly, we assume that respondents who are more similar to a vignette are more familiar with the condition described and therefore are capable of forming a more precise perception of the vignette. We show evidence in favor of this extended HOPIT through Monte Carlo simulations and an application concerning self-reported vision difficulty from the WHO Study on Global Aging and Adult Health (SAGE).