A0189
Title: A two-way heterogeneity model for dynamic networks
Authors: Binyan Jiang - The Hong Kong Polytechnic University (Hong Kong) [presenting]
Abstract: Analysis of networks that evolve dynamically requires the joint modelling of individual snapshots and time dynamics. A new flexible two-way heterogeneity model towards this goal is proposed. The new model equips each node of the network with two heterogeneity parameters, one to characterize the propensity to form ties with other nodes statically and the other to differentiate the tendency to retain existing ties over time. With $n$ observed networks each having $p$ nodes, we develop a new asymptotic theory for the maximum likelihood estimation of $2p$ parameters when $np\rightarrow\infty$ in which $n\ge 2$ can be finite. We overcome the global non-convexity of the negative log-likelihood function by virtue of its local convexity, and propose a novel method of moment estimator as the initial value for a simple algorithm that leads to the global maximum likelihood estimator (MLE). To establish the upper bounds for the estimation error of the MLE, we derive a new uniform deviation bound, which is of independent interest. The theory of the model and its usefulness are further supported by extensive simulation and a data analysis examining the social interactions of ants.
