Anchoring vignettes with sample selection due to non-response

Anchoring vignettes are a powerful tool for enhancing self-reported data comparability across countries or socio-economic groups, since they may correct for differential item functioning, i.e. the individual heterogeneity in the interpretation of the survey questions. The parametric solution of this approach is called the compound hierarchical ordinal probit (CHOPIT) model. Since vignettes are particular versions of questionnaires, their collection can suffer from sample selection bias due to non-response.We extend the CHOPIT model to account forthis problem. This extension is, however, complicated by the fact that the variable of interest is ordinal, so the procedures that are adopted in the case of a strictly continuous outcome are no longer applicable and the maximum likelihood approach is therefore the suggested solution. The extended model is then applied to investigate and compare across countries the effects of differential item functioning and sample selection on the response scale differences in the self-reported work disability vignettes that were collected in the Survey of Health, Ageing and Retirement in Europe. When the collected vignette rate is high, the bias that is induced by the selection mechanism on the CHOPIT estimates is negligible. When the collected vignette rate is low, sample selection affects the model estimates, leading to a reversing of the directions of some differential item functioning corrections provided by the standard CHOPIT model.