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 The widely used generalized linear model is no longer applicable, since it implicitly assumes that different subjects are completely independent.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 non-overlapped 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.