A Zero-Inflated Poisson Latent Position Cluster Model

Chaoyi Lu, University College Dublin

Co-authors: Riccardo Rastelli, University College Dublin; Nial Friel, University College Dublin

Abstract: The Latent Position Model (LPM) is a popular approach for statistical analysis of network data. A key aspect of this model is that it assigns nodes to random positions in a latent space, and the probability of an interaction/edge between each pair of individuals/nodes is determined by their distance, allowing one to visualize nuanced structures via the latent space representation. Missing data is a common issue in statistical data analysis which generally leads to excess zero interactions that are often observed in real network data. In this paper, we focus on non-negative discrete weighted social networks. By treating missing data as “unusual” zero interactions, we propose a combination of the Zero-Inflated Poisson (ZIP) distribution with the Latent Position Cluster Model (LPCM), which extends the LPM to accommodate the clustering of individuals, to simultaneously characterize weighted interactions, missing data, clustering and visualizations of real networks. Statistical inference is based on a novel partially collapsed Markov chain Monte Carlo approach, where a Mixture of Finite Mixtures (MFM) model and a novel truncated absorb-eject move is adopted. We illustrate our results on 3-dimensional latent spaces, maintaining clear visualizations while achieving more flexibility than 2-dimensional models.