Bayesian model assisted strategies for the 2011 Italian Census

The Italian National Institute of Statistics (Istat) intends to collect some required information for the 2011 Population Census using a sample survey. Specifically, de-tailed information from large municipalities (with a population over 20,000 inhabit-ants) will be collected from a sample of the population using a long-form question-naire. For the rest of the population, partial data, consisting mainly of demographic variables, will be collected using a short-form questionnaire. Thus, data will be ob-tained from a combination of long and short-form questionnaires. In municipalities with a population under 20,000 inhabitants, a traditional census (based on the long-form) will be carried out. Moreover, in each larger municipality, only census areas with a population over 10,000 inhabitants will be sampled. In terms of the sampling design, simple random sampling (SRS) of households with a sampling fraction of 0.33 from population registers will be adopted (Carbonetti and Fortini, 2008). The innovations produce methodological challenges. For example, estimating a contingency table involving variables from both short and long-form ques-tionnaires is difficult because estimates of the joint distribution must be coherent with the marginal distribution collected by a census. Moreover, several constraints at different levels of geographical aggregation are imposed by the Istat dissemination plan. In a design-based approach, calibration estimation (Deville and Särndal, 1992) is a natural choice for contingency table estimation that comply to such constraints. In this paper, we propose a small area model-based approach that takes into account the coherence constraints and allows borrowing strength between areas to reduce the variance of the estimates.