The emergence and wide-spread use of online social networks has led to a
dramatic increase on the availability of social activity data. Importantly,
this data can be exploited to investigate, at a microscopic level, some of the
problems that have captured the attention of economists, marketers and
sociologists for decades, such as, e.g., product adoption, usage and
competition.
In this paper, we propose a continuous-time probabilistic model, based on
temporal point processes, for the adoption and frequency of use of competing
products, where the frequency of use of one product can be modulated by those
of others. This model allows us to efficiently simulate the adoption and
recurrent usages of competing products, and generate traces in which we can
easily recognize the effect of social influence, recency and competition. We
then develop an inference method to efficiently fit the model parameters by
solving a convex program. The problem decouples into a collection of smaller
subproblems, thus scaling easily to networks with hundred of thousands of
nodes. We validate our model over synthetic and real diffusion data gathered
from Twitter, and show that the proposed model does not only provides a good
fit to the data and more accurate predictions than alternatives but also
provides interpretable model parameters, which allow us to gain insights into
some of the factors driving product adoption and frequency of use