Separable models for dynamic signed networks

Signed networks capture the polarity of relationships between nodes, providing valuable insights into complex systems where both supportive and antagonistic interactions play a critical role in shaping the network's dynamics. We propose a separable temporal generative framework based on multi-layer exponential random graph models, characterised by the assumption of conditional independence between the sign and interaction effects. This structure preserves the flexibly and explanatory power inherent in the binary network specification while adhering to consistent balance theory assumptions. Using a fully probabilistic Bayesian paradigm, we infer the doubly intractable posterior distribution of model parameters via an adaptive Metropolis-Hastings approximate exchange algorithm. We illustrate the interpretability of our model by analysing signed relations among U.S. Senators during Ronald Reagan's second term (1985-1989). Specifically, we aim to understand whether these relations are consistent and balanced or reflect patterns of supportive or antagonistic alliances.