Abstract: Social network data include social ties, node characteristics, and behaviors over time. Furthermore, studies have known that people who are close on a social network are more likely to behave in a similar way, owing, in part, to the influence of peers and the social contagion that acts along network ties. A primary interest of social network data analyses is to identify contagion-based social correlations. Therefore, in this work, we model and estimate contagion-based social network dependence based on time-to-event data. A generalized linear transformation model is proposed for the conditional survival probability at each observed event time. This model uses a time-varying covariate to incorporate the network structure and to quantify contagion-based social correlations. We develop a nonparametric maximum likelihood estimation for the proposed model. The consistency and asymptotic normality of the resulting estimators for the regression parameters are established. Simulations are conducted to evaluate the empirical performance of the proposed estimators. Then, we apply the proposed method to analyze time-to-event data from a popular mobile game provided by one of the largest online social network platforms. The results show significant contagion-based social correlations between when people choose to play the game.

Key words and phrases: Contagion-based social correlation, generalized linear transformation model, nonparametric maximum likelihood estimation, social network, time-to-event data.