  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.
