A latent moving average model for network regression

Different from traditional statistical analysis that concerns about individuals, network analysis focuses more on the dichotomous relationships between those individuals. It is then of interest to investigate the relationship against a set of predictive variables. The widely used generalized linear model is no longer applicable, since it implicitly assumes that different subjects are completely independent. To solve this problem, we propose a latent moving average model (LMAM), which allows for nontrivial dependence for overlapped relationships. It is only assumed that the nonoverlapped relationships are independent. Under such an assumption, the asymptotic theory, including the rate of convergence and asymptotic normality, can be established. A number of numerical studies are conducted to demonstrate the finite sample performance of our proposed method. At last, a real dataset is analyzed for illustration purpose.

Keywords

generalized linear model, latent moving average model, network regression, social networks

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The research of Rui Pan is supported in part by National Natural Science Foundation of China (NSFC, 11601539, 11631003).

The research of Rong Guan is supported in part by National Natural Science Foundation of China (NSFC, 71401192, 71771204), and Program for Innovation Research in Central University of Finance and Economics (011650317002).

The research of Hansheng Wang is supported in part by National Natural Science Foundation of China (NSFC, 71532001, 11525101), China’s National Key Research Special Program grant 2016YFC0207700, and the Business Intelligence Research Center at Peking University.

Received 4 November 2016

Published 19 September 2018