One-step Gibbs sampling for the generation of synthetic households

The generation of synthetic households is challenging due to the necessity of maintaining consistency between the two layers of interest: the household itself, and the individuals composing it. Hence, the problem is typically tackled in two steps, first focusing on the individual layer and then on the household layer. The existing two-step simulation method proposes generating the households based on their roles which diminishes the generality of the approach and makes it difficult to reproduce despite its beneficial properties. In this paper, we propose an alternative extension of Gibbs sampling for generating hierarchical datasets such as synthetic households, in order to make simulation more general and reusable. We demonstrate the performance of our method in a case study based on the 2015 Swiss micro-census data and compare it against state-of-the-art approaches. We show the influence of modeling decisions on different performance metrics and how the analyst can easily enforce consistency while avoiding generating illogical households. We show that the algorithm maintains the conditional distributions while satisfying the marginals of all variables simultaneously, all while generating consistent synthetic households.