Likelihood-Based Methods Improve Parameter Estimation in Opinion Dynamics Models

Abstract: We show that a maximum likelihood approach for parameter estimation in agent-based models (ABMs) of opinion dynamics outperforms the typical simulation-based approach. Simulation-based approaches simulate the model repeatedly in search of a set of parameters that generates data similar enough to the observed one. In contrast, likelihood-based approaches derive a likelihood function that connects the unknown parameters to the observed data in a statistically principled way. We compare these two approaches on the well-known bounded-confidence model of opinion dynamics. We do so on three realistic scenarios of increasing complexity depending on data availability: (i) fully observed opinions and interactions, (ii) partially observed interactions, (iii) observed interactions with noisy proxies of the opinions. We highlight how identifying observed and latent variables is fundamental for connecting the model to the data. To realize the likelihood-based approach, we first cast the model into a probabilistic generative guise that supports a proper data likelihood. Then, we describe the three scenarios via probabilistic graphical models and show the nuances that go into translating the model. Finally, we implement the resulting probabilistic models in an automatic differentiation framework (PyTorch). This step enables easy and efficient maximum likelihood estimation via gradient descent. Our experimental results show that the maximum likelihood estimates are up to 4x more accurate and require up to 200x less computational time.