Analysis of Connection Times in Bipartite Network Data: Development of the Bayesian Latent Space Accumulator Model with Applications to Assessment Data

Conventional social network analysis typically focuses on analyzing the structure of the connections between pairs of nodes in a sample dataset. However, the process and the consequences of how long it takes pairs of nodes to be connected, i.e., node connection times, on the network structure have been understudied in the literature. In this article, we propose a novel statistical approach, so-called the Bayesian latent space accumulator model, for modeling connection times and their influence on the structure of connections. We focus on a special type of bipartite network composed of respondents and test items, where connection outcomes are binary and mutually exclusive. To model connection times for each connection outcome, we leverage ideas from the competing risk modeling approach and embed latent spaces into the competing risk models to capture heterogeneous dependence structures of connection times across connection outcome types. The proposed approach is applied and illustrated with two real data examples.