Latent Variable Modelling with Non-Ignorable Item Nonresponse: A General Framework and Multigroup Models for Cross-National Analysis

When missing data are produced by a non-ignorable nonresponse mechanism, analysis of the observed data should include a model for the probabilities of responding. In this paper we propose such models for nonresponse in survey questions which are treated as multiple-item measures of latent constructs and analysed using latent variable models. The nonresponse 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 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 themselves, and an association between the latent variables measured by the items and the latent response propensities implies a model with non-ignorable nonresponse. We consider in particular the analysis of data from cross-national surveys, where the nonresponse model may also vary across the countries. The models are applied to analyse data on welfare attitudes in 29 countries in the European Social Survey.