IEEE SIGNAL PROCESSING MAGAZINE [77] MARCH 2012 H ow can we model influence between individuals in a social system, even when the network of interactions is unknown? In this article, we review the literature on the “influence model,” which utilizes independent time series to esti- mate how much the state of one actor affects the state of another actor in the system. We extend this model to incorpo- rate dynamical parameters that allow us to infer how influ- ence changes over time, and we provide three examples of how this model can be applied to simulated and real data. The results show that the model can recover known estimates of influence, it generates results that are consistent with other measures of social networks, and it allows us to uncover important shifts in the way states may be transmitted between actors at different points in time. INTRODUCTION The concept of influence is extraordinarily important in the natural sciences. The basic idea of influence is that an out- come in one entity can cause an outcome in another entity. Flip over the first domino, and the second domino will fall. If we understand exactly how two dominoes interact—how one domino influences another—and we know the initial state of the dominoes and how they are situated relative to one anoth- er, then we can predict the outcome of the whole system. For decades, social scientists have also been interested in analyzing and understanding who influences whom in social systems [1], [2]. But the analogue with the physical world is not exact. In the social world, influence can be more complicat- ed because internal states are often unobservable, intentional Digital Object Identifier 10.1109/MSP.2011.942737 Modeling Dynamical Influence in Human Interaction [ Wei Pan, Wen Dong, Manuel Cebrian, Taemie Kim, James H. Fowler, and Alex (Sandy) Pentland ] Date of publication: 17 February 2012 [ Using data to make better inferences about influence within social systems ] ©iSTOCKPHOTO.COM/ANDREY PROKHOROV Signal and Information Processing for Social Learning and Networking 1053-5888/12/$31.00©2012IEEE