Statistical inference on group Rasch mixture network models

• Published in: Stat (International Statistical Institute) Vol. 11; no. 1
• Main Authors: Long, Yuhang, Huang, Tao
• Format: Journal Article
• Language: English
• Published: The Hague Wiley Subscription Services, Inc 01.12.2022
• Subjects: Algorithms; Asymptotic methods; expectation–maximization algorithm; likelihood‐ratio test; mixture model; Mixtures; Nodes; Rasch model; Statistical analysis; Statistical inference
• ISSN: 2049-1573; 2049-1573
• DOI: 10.1002/sta4.436

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.