Inferring a population composition from survey data with nonignorable nonresponse: Borrowing information from external sources

We introduce a method to make inference on the composition of a heterogeneous population using survey data, accounting for the possibility that capture heterogeneity is related to key survey variables. To deal with nonignorable nonresponse, we combine different data sources and propose the use of Fisher's noncentral hypergeometric model in a Bayesian framework. To illustrate the potentialities of our methodology, we focus on a case study aimed at estimating the composition of the population of Italian graduates by their occupational status one year after graduating, stratifying by gender and degree program. We account for the possibility that surveys inquiring about the occupational status of new graduates may have response rates that depend on individuals' employment status, implying the nonignorability of the nonresponse. Our findings show that employed people are generally more inclined to answer the questionnaire. Neglecting the nonresponse bias in such contexts might lead to overestimating the employment rate.