Network Hawkes process models for exploring latent hierarchy in social animal interactions

Group-based social dominance hierarchies are of essential interest in understanding social structure (DeDeo & Hobson in, Proceedings of the National Academy of Sciences 118(21), 2021). Recent animal behaviour research studies can record aggressive interactions observed over time. Models that can explore the underlying hierarchy from the observed temporal dynamics in behaviours are therefore crucial. Traditional ranking methods aggregate interactions across time into win/loss counts, equalizing dynamic interactions with the underlying hierarchy. Although these models have gleaned important behavioural insights from such data, they are limited in addressing many important questions that remain unresolved. In this paper, we take advantage of the observed interactions' timestamps, proposing a series of network point process models with latent ranks. We carefully design these models to incorporate important theories on animal behaviour that account for dynamic patterns observed in the interaction data, including the winner effect, bursting and pair-flip phenomena. Through iteratively constructing and evaluating these models we arrive at the final cohort Markov-modulated Hawkes process (C-MMHP), which best characterizes all aforementioned patterns observed in interaction data. As such, inference on our model components can be readily interpreted in terms of theories on animal behaviours. The probabilistic nature of our model allows us to estimate the uncertainty in our ranking. In particular, our model is able to provide insights into the distribution of power within the hierarchy which forms and the strength of the established hierarchy. We compare all models using simulated and real data. Using statistically developed diagnostic perspectives, we demonstrate that the C-MMHP model outperforms other methods, capturing relevant latent ranking structures that lead to meaningful predictions for real data.