Spatial autoregression with repeated measurements for social networks

ABSTRACT

Spatial autoregressive model (SAR) is found useful to estimate the social autocorrelation in social networks recently. However, the rapid development of information technology enables researchers to collect repeated measurements for a given social network. The SAR model for social networks is designed for cross-sectional data and is thus not feasible. In this article, we propose a new model which is referred to as SAR with random effects (SARRE) for social networks. It could be considered as a natural combination of two types of models, the SAR model for social networks and a particular type of mixed model. To solve the problem of high computational complexity in large social networks, a pseudo-maximum likelihood estimate (PMLE) is proposed. The asymptotic properties of the estimate are established. We demonstrate the performance of the proposed method by extensive numerical studies and a real data example.

KEYWORDS:

• Pseudo-maximum likelihood estimate
• Repeated measurements
• Social autocorrelation
• Social network.

MATHEMATICS SUBJECT CLASSIFICATION:

• 05C82
• 94C15

Additional information

Funding

Wang's research was supported in part by National Natural Science Foundation of China (NSFC, 11131002, 11271032, 71532001, 11525101) and Center for Statistical Science at Peking University. Huang's research was supported by National Natural Science Foundation of China (NSFC,11701560), Beijing Municipal Social Science Foundation (Grant No. 17GLC051), the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (Grant No. 16XNLF01). Chang's research was supported by the National Natural Science Foundation of China (NSFC, 11401462, 11771012). We deeply appreciate Beijing Baifendian Information Technology Inc. for the computing resources.