Statistical inference on group Rasch mixture network models

In a two‐mode network, the nodes are divided into two types (primary nodes and secondary nodes), and connections exist only between nodes of different types. In reality, in such a two‐mode network, one‐mode network connections may also exist among primary nodes, and these two kinds of networks are usually not independent and coexistent. In this paper, we first propose a group Rasch mixture network model that focuses on the connections between primary nodes and secondary nodes, while incorporating the group structure and linkage information of primary nodes. We then develop a modified expectation–maximization algorithm to estimate the proposed model with a λ ‐BIC method for selecting the tuning parameter. Additionally, we provide a likelihood‐ratio test statistic to examine whether the two kinds of networks are independent and implement the leave‐one‐out method to construct a network prediction rule. Finally, we establish asymptotic results and demonstrate the numerical performance of the proposed methods using both simulations and the Last.fm dataset.