Latent variable modelling with non‐ignorable item non‐response: multigroup response propensity models for cross‐national analysis

When missing data are produced by a non‐ignorable non‐response mechanism, analysis of the observed data should include a model for the probabilities of responding. We propose such models for non‐response in survey questions which are treated as measures of latent constructs and analysed by using latent variable models. The non‐response models that we describe include additional latent variables (latent response propensities) which determine the response probabilities. We argue that this model should be specified as flexibly as possible, and we propose models where the response propensity is a categorical variable (a latent response class). This can be combined with any latent variable model for the survey items, and an association between the latent variables measured by the items and the latent response propensities then implies a model with non‐ignorable non‐response. We consider in particular such models for the analysis of data from cross‐national surveys, where the non‐response model may also vary across the countries. The models are applied to data on welfare attitudes in 29 countries in the European Social Survey.