A new adaptive two-layer model for opinion spread in hypergraphs: parameter sensitivity and estimation

In studies of opinion spread, peer pressure is often modeled through interactions of more than two individuals (higher-order interactions). We introduce a two-layer random hypergraph model, in which households and workplaces form the layers and hyperedges represent individual households and workplaces. Within this overlapping adaptive structure, individuals may react when their opinion is in the minority within their groups. The process evolves through stochastic steps: individuals can either change their opinion, or quit their workplace and join another one in which their opinion belongs to the majority. Our first goal is to describe, via computer simulations, the effects of the parameters governing opinion change and workplace switching on homophily, speed of polarization, and number of components. We also analyze the model as a Markov chain, and study the absorbing states. We then quantitatively compare how different statistical and machine learning methods—namely linear regression, XGBoost, convolutional neural network (CNN) and long short-term memory network (LSTM)—perform in estimating these parameters from partial observations of the process, such as the distribution of opinion configurations within households and workplaces. Among other observations, we conclude that in most of the cases, especially for shorter observation periods LSTM is the best, while in many cases XGBoost is also a strong contender. For longer time horizons, CNN is also competitive. It is also an important observation that the information required for accurate estimation depends on the strength of the peer pressure effect.