Survival Mixed Membership Blockmodel

Whenever we send a message via a channel such as E-mail, Facebook, WhatsApp, WeChat, or LinkedIn, we care about the response rate—the probability that our message will receive a response—and the response time—how long it will take to receive a reply. Recent studies have made considerable efforts to model the sending behaviors of messages in social networks with point processes. However, statistical research on modeling response rates and response times on social networks is still lacking. Compared with sending behaviors, which are often determined by the sender’s characteristics, response rates and response times further depend on the relationship between the sender and the receiver. Here, we develop a survival mixed membership blockmodel (SMMB) that integrates semiparametric cure rate models with a mixed membership stochastic blockmodel to analyze time-to-event data observed for node pairs in a social network, and we are able to prove its model identifiability without the pure node assumption. We develop a Markov chain Monte Carlo algorithm to conduct posterior inference and select the number of social clusters in the network according to the conditional deviance information criterion. The application of the SMMB to the Enron E-mail corpus offers novel insights into the company’s organization and power relations. Supplementary materials for this article are available online.