on October 11, 2016 at 3:00 pm
Choices of different individuals over time exhibit pairwise associations in a wide range of economic contexts. Network models for the processes by which ideas and decisions propagate through social interaction have been studied in different streams of literature. However, when the network structure is unknown, only few contributions have focus on detecting the underlying pattern of pairwise interaction from sequences of multidimensional decisions. In fact, while it is typically possible to directly observe individual choices, inferring individual influences (who influences who) might be difficult in the general case, as it requires strong modeling assumptions on the cross-section dependencies of the associated multidimensional panels. We provide an overview of the existing approaches and investigate a class of exponential random models to jointly deal with dynamic choices of individuals over items together with the structure of pairwise influences between them. We argue that computational problems, related to the intractability of the normalizing constant, emerge when estimating the unknown parameters of this class of models. This drawback can be overcome by embedding the defined model into a Bayesian estimation framework and applying a specialized MCMC procedure, based on the joint simulation both from the parameter and the sample spaces. After a detailed analysis of the proposed statistical methodology, we present a practical application to a data set of songs, that are diffused over radio and TV stations; we infer station-to-station influences. This allows solving the classical influence propagation problem and take decision over the best stations in which one should first launch a song to guarantee maximum propagation.
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