  We provide a general framework to model the growth of networks consisting of
different coupled layers. Our aim is to estimate the impact of one such layer
on the dynamics of the others. As an application, we study a scientometric
network, where one layer consists of publications as nodes and citations as
links, whereas the second layer represents the authors. This allows to address
the question how characteristics of authors, such as their number of
publications or number of previous co-authors, impacts the citation dynamics of
a new publication. To test different hypotheses about this impact, our model
combines citation constituents and social constituents in different ways. We
then evaluate their performance in reproducing the citation dynamics in nine
different physics journals. For this, we develop a general method for
statistical parameter estimation and model selection that is applicable to
growing multi-layer networks. It takes both the parameter errors and the model
complexity into account and is computationally efficient and scalable to large
networks.
